Knott, Gary D
2000-01-01
A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline func...
Xiaolong Wang; Yi Wang; Zhizhu Cao; Weizhong Zou; Liping Wang; Guojun Yu; Bo Yu; Jinjun Zhang
2013-01-01
In general, proper orthogonal decomposition (POD) method is used to deal with single-parameter problems in engineering practice, and the linear interpolation is employed to establish the reduced model. Recently, this method is extended to solve the double-parameter problems with the amplitudes being achieved by cubic B-spline interpolation. In this paper, the accuracy of reduced models, which are established with linear interpolation and cubic B-spline interpolation, respectively, is verified...
Directory of Open Access Journals (Sweden)
Xiaolong Wang
2013-01-01
Full Text Available In general, proper orthogonal decomposition (POD method is used to deal with single-parameter problems in engineering practice, and the linear interpolation is employed to establish the reduced model. Recently, this method is extended to solve the double-parameter problems with the amplitudes being achieved by cubic B-spline interpolation. In this paper, the accuracy of reduced models, which are established with linear interpolation and cubic B-spline interpolation, respectively, is verified via two typical examples. Both results of the two methods are satisfying, and the results of cubic B-spline interpolation are more accurate than those of linear interpolation. The results are meaningful for guiding the application of the POD interpolation to complex multiparameter problems.
Perbaikan Metode Penghitungan Debit Sungai Menggunakan Cubic Spline Interpolation
Directory of Open Access Journals (Sweden)
Budi I. Setiawan
2007-09-01
Full Text Available Makalah ini menyajikan perbaikan metode pengukuran debit sungai menggunakan fungsi cubic spline interpolation. Fungi ini digunakan untuk menggambarkan profil sungai secara kontinyu yang terbentuk atas hasil pengukuran jarak dan kedalaman sungai. Dengan metoda baru ini, luas dan perimeter sungai lebih mudah, cepat dan tepat dihitung. Demikian pula, fungsi kebalikannnya (inverse function tersedia menggunakan metode. Newton-Raphson sehingga memudahkan dalam perhitungan luas dan perimeter bila tinggi air sungai diketahui. Metode baru ini dapat langsung menghitung debit sungaimenggunakan formula Manning, dan menghasilkan kurva debit (rating curve. Dalam makalah ini dikemukaan satu canton pengukuran debit sungai Rudeng Aceh. Sungai ini mempunyai lebar sekitar 120 m dan kedalaman 7 m, dan pada saat pengukuran mempunyai debit 41 .3 m3/s, serta kurva debitnya mengikuti formula: Q= 0.1649 x H 2.884 , dimana Q debit (m3/s dan H tinggi air dari dasar sungai (m.
Cubic Spline Interpolation Reveals Different Evolutionary Trends of Various Species
Directory of Open Access Journals (Sweden)
Li Zhiqiang
2016-01-01
Full Text Available Instead of being uniform in each branch of the biological evolutionary tree, the speed of evolution, measured in the number of mutations over a fixed number of years, seems to be much faster or much slower than average in some branches of the evolutionary tree. This paper describes an evolutionary trend discovery algorithm that uses cubic spline interpolation for various branches of the evolutionary tree. As shown in an example, within the vertebrate evolutionary tree, human evolution seems to be currently speeding up while the evolution of chickens is slowing down. The new algorithm can automatically identify those branches and times when something unusual has taken place, aiding data analytics of evolutionary data.
GA Based Rational cubic B-Spline Representation for Still Image Interpolation
Samreen Abbas; Malik Zawwar Hussain; Misbah Irshad
2016-01-01
In this paper, an image interpolation scheme is designed for 2D natural images. A local support rational cubic spline with control parameters, as interpolatory function, is being optimized using Genetic Algorithm (GA). GA is applied to determine the appropriate values of control parameter used in the description of rational cubic spline. Three state-of-the-art Image Quality Assessment (IQA) models with traditional one are hired for comparison with existing image interpolation schemes and perc...
GA Based Rational cubic B-Spline Representation for Still Image Interpolation
Directory of Open Access Journals (Sweden)
Samreen Abbas
2016-12-01
Full Text Available In this paper, an image interpolation scheme is designed for 2D natural images. A local support rational cubic spline with control parameters, as interpolatory function, is being optimized using Genetic Algorithm (GA. GA is applied to determine the appropriate values of control parameter used in the description of rational cubic spline. Three state-of-the-art Image Quality Assessment (IQA models with traditional one are hired for comparison with existing image interpolation schemes and perceptual quality check of resulting images. The results show that the proposed scheme is better than the existing ones in comparison.
Convex preserving scattered data interpolation using bivariate C1 cubic splines
Lai, Ming-Jun
2000-07-01
We use bivariate C1 cubic splines to deal with convexity preserving scattered data interpolation problem. Using a necessary and sufficient condition on Bernstein-Bézier polynomials, we set the convexity-preserving interpolation problem into a quadratically constraint quadratic programming problem. We show the existence of convexity preserving interpolatory surfaces under certain conditions on the data. That is, under certain conditions on the data, there always exists a convexity preservation C1 cubic spline interpolation if the triangulation is refined sufficiently many times. We then replace the quadratical constrains by three linear constrains and formulate the problem into linearly constraint quadratic programming problems in order to be able to solve it easily. Certainly, the existence of convexity preserving interpolatory surfaces is equivalent to the feasibility of the linear constrains. We present a numerical experiment to test which of these three linear constraints performs the best.
Csébfalvi, Balázs
2010-01-01
In this paper, we demonstrate that quasi-interpolation of orders two and four can be efficiently implemented on the Body-Centered Cubic (BCC) lattice by using tensor-product B-splines combined with appropriate discrete prefilters. Unlike the nonseparable box-spline reconstruction previously proposed for the BCC lattice, the prefiltered B-spline reconstruction can utilize the fast trilinear texture-fetching capability of the recent graphics cards. Therefore, it can be applied for rendering BCC-sampled volumetric data interactively. Furthermore, we show that a separable B-spline filter can suppress the postaliasing effect much more isotropically than a nonseparable box-spline filter of the same approximation power. Although prefilters that make the B-splines interpolating on the BCC lattice do not exist, we demonstrate that quasi-interpolating prefiltered linear and cubic B-spline reconstructions can still provide similar or higher image quality than the interpolating linear box-spline and prefiltered quintic box-spline reconstructions, respectively.
Bejancu, Aurelian
2006-12-01
This paper considers the problem of interpolation on a semi-plane grid from a space of box-splines on the three-direction mesh. Building on a new treatment of univariate semi-cardinal interpolation for natural cubic splines, the solution is obtained as a Lagrange series with suitable localization and polynomial reproduction properties. It is proved that the extension of the natural boundary conditions to box-spline semi-cardinal interpolation attains half of the approximation order of the cardinal case.
Cubic generalized B-splines for interpolation and nonlinear filtering of images
Tshughuryan, Heghine
1997-04-01
This paper presents the introduction and using of the generalized or parametric B-splines, namely the cubic generalized B-splines, in various signal processing applications. The theory of generalized B-splines is briefly reviewed and also some important properties of generalized B-splines are investigated. In this paper it is shown the use of generalized B-splines as a tool to solve the quasioptimal algorithm problem for nonlinear filtering. Finally, the experimental results are presented for oscillatory and other signals and images.
Directory of Open Access Journals (Sweden)
Zhiwei Pan
2016-05-01
Full Text Available Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss–Newton (IC-GN algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
Martinez, Leslie A.; Narea, Freddy J.; Cedeño, Fernando; Muñoz, Aaron A.; Reigosa, Aldo; Bravo, Kelly
2013-11-01
The noninvasive optical techniques have attracted considerable interest in recent years, because these techniques provide lot of information on the structure and composition of biological tissues more quickly and painlessly, in this study classifies the degrees of histological differentiation of neoplastic tissue of the breast in white adipose tissue samples through numerical pametrización of the diffuse reflection spectra using the Fourier series approximation. The white adipose tissue is irradiated with the spectrophotometer MiniScan XEplus and it from a mastectomy of patients with aged 38 and 50 who have a cancer lesion in the breast. The samples were provided by the pathologist with theirs medical report, it which we indicate the histological grade of tumor. We performed a parameterization algorithm where the classification criterion is the modulus of the minimum difference between the numerical approximation coefficients ai and average numerical approximation coefficients obtained for each histological grade ¯ al. Is confirmed that the cubic spline interpolation this low-power computing lets classified into histological grades with 91% certainty the tissues under study from |ai - ¯ al|
2-rational Cubic Spline Involving Tension Parameters
Indian Academy of Sciences (India)
M Shrivastava; J Joseph
2000-08-01
In the present paper, 1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonic interpolant to a given monotonic data set. It is observed that under certain conditions the interpolant preserves the convexity property of the data set. The existence and uniqueness of a 2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given.
Xu, Xu; Chang, Chien-Chi; Faber, Gert S; Kingma, Idsart; Dennerlein, Jack T
2010-02-10
Simple video-based methods previously proposed for field research to estimate L5/S1 net moments during real-world manual materials handling rely on polynomial interpolation on the joint angles from key frames extracted from video recordings; however, polynomial interpolations may not converge as the number of interpolation points increases. Therefore, we compared L5/S1 net moments calculated from continuous kinematic measurements to those calculated from both polynomial and cubic spline interpolation on body segments angles during lifting tasks. For small number of interpolation points (polynomial fits decreased with the increase in the number of interpolation points; however, above 6 interpolation points error for the polynomial fits started to increase while the error from the spline fit continued to decrease. These results suggest that cubic spline interpolation on body segments angles provides a more robust basis for calculating L5/S1 net moment from a few key video frames.
Zhiwei Pan; Wei Chen; Zhenyu Jiang; Liqun Tang; Yiping Liu; Zejia Liu
2016-01-01
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss–Newton (IC-GN) algorithm. The performance of this strategy, including accuracy, precision, and computation effi...
Chang, Nai-Fu; Chiang, Cheng-Yi; Chen, Tung-Chien; Chen, Liang-Gee
2011-01-01
On-chip implementation of Hilbert-Huang transform (HHT) has great impact to analyze the non-linear and non-stationary biomedical signals on wearable or implantable sensors for the real-time applications. Cubic spline interpolation (CSI) consumes the most computation in HHT, and is the key component for the HHT processor. In tradition, CSI in HHT is usually performed after the collection of a large window of signals, and the long latency violates the realtime requirement of the applications. In this work, we propose to keep processing the incoming signals on-line with small and overlapped data windows without sacrificing the interpolation accuracy. 58% multiplication and 73% division of CSI are saved after the data reuse between the data windows.
Kananenka, Alexei A; Lan, Tran Nguyen; Gull, Emanuel; Zgid, Dominika
2016-01-01
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about two orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be double...
Weighted cubic and biharmonic splines
Kvasov, Boris; Kim, Tae-Wan
2017-01-01
In this paper we discuss the design of algorithms for interpolating discrete data by using weighted cubic and biharmonic splines in such a way that the monotonicity and convexity of the data are preserved. We formulate the problem as a differential multipoint boundary value problem and consider its finite-difference approximation. Two algorithms for automatic selection of shape control parameters (weights) are presented. For weighted biharmonic splines the resulting system of linear equations can be efficiently solved by combining Gaussian elimination with successive over-relaxation method or finite-difference schemes in fractional steps. We consider basic computational aspects and illustrate main features of this original approach.
Cubic Spline Interpolation on a Class of Triangulations%一类三角域上的三次样条插值
Institute of Scientific and Technical Information of China (English)
陈丽娟; 罗钟铉
2008-01-01
In this paper, we consider spaces of cubic C1-spline on a class of trian-gulations. By using the inductive algorithm, the posed Lagrange interpolation sets are constructed for cubic spline space. It is shown that the class of triangulations considered in this paper are nonsingular for S13 spaces. Moreover, the dimensions of those spaces exactly equal to L. L. Schumaker's low bounds of the dimensions. At the end of this paper, we present an approach to construct triangulations from any scattered planar points, which ensures that the obtained triangulations for S13 space are nonsingular.
C2 quartic spline surface interpolation
Institute of Scientific and Technical Information of China (English)
张彩明; 汪嘉业
2002-01-01
This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.
Csébfalvi, Balázs
2013-09-01
In this paper, Cosine-Weighted B-spline (CWB) filters are proposed for interpolation on the optimal Body-Centered Cubic (BCC) lattice. We demonstrate that our CWB filters can well exploit the fast trilinear texture-fetching capability of modern GPUs, and outperform the state-of-the-art box-spline filters not just in terms of efficiency, but in terms of visual quality and numerical accuracy as well. Furthermore, we rigorously show that the CWB filters are better tailored to the BCC lattice than the previously proposed quasi-interpolating BCC B-spline filters, because they form a Riesz basis; exactly reproduce the original signal at the lattice points; but still provide the same approximation order.
Positivity Preserving Interpolation Using Rational Bicubic Spline
Directory of Open Access Journals (Sweden)
Samsul Ariffin Abdul Karim
2015-01-01
Full Text Available This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE, our partially blended rational bicubic spline is on a par with the established methods.
DEFICIENT CUBIC SPLINES WITH AVERAGE SLOPE MATCHING
Institute of Scientific and Technical Information of China (English)
V. B. Das; A. Kumar
2005-01-01
We obtain a deficient cubic spline function which matches the functions with certain area matching over a greater mesh intervals, and also provides a greater flexibility in replacing area matching as interpolation. We also study their convergence properties to the interpolating functions.
Transfinite thin plate spline interpolation
Bejancu, Aurelian
2009-01-01
Duchon's method of thin plate splines defines a polyharmonic interpolant to scattered data values as the minimizer of a certain integral functional. For transfinite interpolation, i.e. interpolation of continuous data prescribed on curves or hypersurfaces, Kounchev has developed the method of polysplines, which are piecewise polyharmonic functions of fixed smoothness across the given hypersurfaces and satisfy some boundary conditions. Recently, Bejancu has introduced boundary conditions of Beppo Levi type to construct a semi-cardinal model for polyspline interpolation to data on an infinite set of parallel hyperplanes. The present paper proves that, for periodic data on a finite set of parallel hyperplanes, the polyspline interpolant satisfying Beppo Levi boundary conditions is in fact a thin plate spline, i.e. it minimizes a Duchon type functional.
Kiani, M A; Sim, K S; Nia, M E; Tso, C P
2015-05-01
A new technique based on cubic spline interpolation with Savitzky-Golay smoothing using weighted least squares error filter is enhanced for scanning electron microscope (SEM) images. A diversity of sample images is captured and the performance is found to be better when compared with the moving average and the standard median filters, with respect to eliminating noise. This technique can be implemented efficiently on real-time SEM images, with all mandatory data for processing obtained from a single image. Noise in images, and particularly in SEM images, are undesirable. A new noise reduction technique, based on cubic spline interpolation with Savitzky-Golay and weighted least squares error method, is developed. We apply the combined technique to single image signal-to-noise ratio estimation and noise reduction for SEM imaging system. This autocorrelation-based technique requires image details to be correlated over a few pixels, whereas the noise is assumed to be uncorrelated from pixel to pixel. The noise component is derived from the difference between the image autocorrelation at zero offset, and the estimation of the corresponding original autocorrelation. In the few test cases involving different images, the efficiency of the developed noise reduction filter is proved to be significantly better than those obtained from the other methods. Noise can be reduced efficiently with appropriate choice of scan rate from real-time SEM images, without generating corruption or increasing scanning time.
Jiwari, Ram
2015-08-01
In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.
Energy Technology Data Exchange (ETDEWEB)
Hernandez, Andrew M. [Biomedical Engineering Graduate Group, University of California Davis, Sacramento, California 95817 (United States); Boone, John M., E-mail: john.boone@ucdmc.ucdavis.edu [Departments of Radiology and Biomedical Engineering, Biomedical Engineering Graduate Group, University of California Davis, Sacramento, California 95817 (United States)
2014-04-15
Purpose: Monte Carlo methods were used to generate lightly filtered high resolution x-ray spectra spanning from 20 kV to 640 kV. Methods: X-ray spectra were simulated for a conventional tungsten anode. The Monte Carlo N-Particle eXtended radiation transport code (MCNPX 2.6.0) was used to produce 35 spectra over the tube potential range from 20 kV to 640 kV, and cubic spline interpolation procedures were used to create piecewise polynomials characterizing the photon fluence per energy bin as a function of x-ray tube potential. Using these basis spectra and the cubic spline interpolation, 621 spectra were generated at 1 kV intervals from 20 to 640 kV. The tungsten anode spectral model using interpolating cubic splines (TASMICS) produces minimally filtered (0.8 mm Be) x-ray spectra with 1 keV energy resolution. The TASMICS spectra were compared mathematically with other, previously reported spectra. Results: Using pairedt-test analyses, no statistically significant difference (i.e., p > 0.05) was observed between compared spectra over energy bins above 1% of peak bremsstrahlung fluence. For all energy bins, the correlation of determination (R{sup 2}) demonstrated good correlation for all spectral comparisons. The mean overall difference (MOD) and mean absolute difference (MAD) were computed over energy bins (above 1% of peak bremsstrahlung fluence) and over all the kV permutations compared. MOD and MAD comparisons with previously reported spectra were 2.7% and 9.7%, respectively (TASMIP), 0.1% and 12.0%, respectively [R. Birch and M. Marshall, “Computation of bremsstrahlung x-ray spectra and comparison with spectra measured with a Ge(Li) detector,” Phys. Med. Biol. 24, 505–517 (1979)], 0.4% and 8.1%, respectively (Poludniowski), and 0.4% and 8.1%, respectively (AAPM TG 195). The effective energy of TASMICS spectra with 2.5 mm of added Al filtration ranged from 17 keV (at 20 kV) to 138 keV (at 640 kV); with 0.2 mm of added Cu filtration the effective energy was 9
Cubic B-spline curve approximation by curve unclamping
Chen, Xiao-Diao; Ma, Weiyin; Paul, Jean-Claude
2010-01-01
International audience; A new approach for cubic B-spline curve approximation is presented. The method produces an approximation cubic B-spline curve tangent to a given curve at a set of selected positions, called tangent points, in a piecewise manner starting from a seed segment. A heuristic method is provided to select the tangent points. The first segment of the approximation cubic B-spline curve can be obtained using an inner point interpolation method, least-squares method or geometric H...
High Dynamic Range Imaging Based on Cubic Spline Interpolation%基于三次样条插值的高动态范围成像方法
Institute of Scientific and Technical Information of China (English)
赵蓝飞; 席志红
2015-01-01
针对由传统的相机响应函数标定法合成的高动态范围图像质量较差的问题，提出一种有效的高动态范围成像算法。首先根据多曝光图像灰度变化的特点，通过三次样条插值将相机响应函数标定问题转化为求解一个线性三对角线性方程组；然后根据拍摄场景动态范围的变化情况，通过手动调整曝光的方式使多曝光图像大部分像素的正序或倒序的灰度变化趋于恒定，再通过逐点递推的方式求出三次样条函数各离散端点的二阶导数，拟合出相机响应曲线；最后根据已选定的基准点并结合已标定的相机响应曲线恢复出单位曝光度下像素对应的曝光时间，即真实的亮度辐射值。实验结果表明，三次样条插值能够有效地提高图像的局部细节以及图像整体的清晰度，递推法简化了求解线性方程组烦琐的计算步骤，降低了算法的整体运算时间。%Due to the limited quality of high dynamic range image which is restored by traditional calibration methods, this paper proposes a novel high dynamic imaging method to improve the quality of image. By cu-bic spline interpolation method, our algorithm converts the calibration of camera response function into solving a system of linear equations primarily. According to the variation of dynamic range, our algorithm makes an adjustment to the ratio of exposure manually in order to guarantee that the variation of the gray value is tending towards stability mostly. Afterwards, a recursive method is proposed to calculate the sec-ond-order derivative of each end point of spline function which is the essential condition of calibration. At last, the radiance of each pixel is recovered according to the reference point which is chosen previously and the result of calibration. Experiment results show that cubic spline interpolation is able to improve the local detail and global clarity. The proposed recursive method reduces
Institute of Scientific and Technical Information of China (English)
冯健; 叶伯生; 周向东
2012-01-01
针对FPGA的特点对三次B样条曲线插补算法进行优化,使用VHDL语言实现了三次B样条插补算法,并在FPGA中进行实际验证.%The paper optimizes the cubic B -spline interpolation algorithm based on the characteristics of the FPGA,and verify the algorithm implemented by VHDL language on FPGA.
A family of quasi-cubic blended splines and applications
Institute of Scientific and Technical Information of China (English)
SU Ben-yue; TAN Jie-qing
2006-01-01
A class of quasi-cubic B-spline base functions by trigonometric polynomials are established which inherit properties similar to those of cubic B-spline bases. The corresponding curves with a shape parameter α, defined by the introduced base functions, include the B-spline curves and can approximate the B-spline curves from both sides. The curves can be adjusted easily by using the shape parameter α, where dpi(α,t) is linear with respect to dα for the fixed t. With the shape parameter chosen properly,the defined curves can be used to precisely represent straight line segments, parabola segments, circular arcs and some transcendental curves, and the corresponding tensor product surfaces can also represent spherical surfaces, cylindrical surfaces and some transcendental surfaces exactly. By abandoning positive property, this paper proposes a new C2 continuous blended interpolation spline based on piecewise trigonometric polynomials associated with a sequence of local parameters. Illustration showed that the curves and surfaces constructed by the blended spline can be adjusted easily and freely. The blended interpolation spline curves can be shape-preserving with proper local parameters since these local parameters can be considered to be the magnification ratio to the length of tangent vectors at the interpolating points. The idea is extended to produce blended spline surfaces.
CONSTRAINED RATIONAL CUBIC SPLINE AND ITS APPLICATION
Institute of Scientific and Technical Information of China (English)
Qi Duan; Huan-ling Zhang; Xiang Lai; Nan Xie; Fu-hua (Frank) Cheng
2001-01-01
In this paper, a kind of rational cubic interpolation functionwith linear denominator is constructed. The constrained interpolation with constraint on shape of the interpolating curves and on the second-order derivative of the interpolating function is studied by using this interpolation, and as the consequent result, the convex interpolation conditions have been derived.
基于误差控制的自适应3次B样条曲线插值%Adaptive curve interpolation of cubic B-spline based on error control
Institute of Scientific and Technical Information of China (English)
叶铁丽; 李学艺; 曾庆良
2013-01-01
Aiming at the problem of the existing curve interpolation algorithm on data compression, an adaptive curve interpolation algorithm of cubic B-spline is presented. An initial cubic B-spline curve is interpolated by selected minimum data points. Based on the presented algorithm for calculating the minimum distance from point to a curve, all the interpolation errors corresponding to remaining data points are calculated, and the maximum interpolation error is obtained. If the maximum error is greater than the threshold value, the point with the maximum error is added to the data points to interpolate a new curve. The process continues until the maximum interpolation error is less than the threshold value. Comparing to the current curve interpolation methods, the proposed algorithm can compress data points greatly with the same precision.%针对现有曲线插值算法不能有效压缩型值点的缺陷,研究了一种自适应三次B样条曲线插值算法.从型值点序列中选用最少的点插值一条初始曲线,基于提出的点到曲线的最小距离计算方法,分别计算各非插值点对应的插值误差,并从中提取最大插值误差.若最大误差大于给定的误差阈值,则将其对应的型值点加入插值型值点序列,重新插值曲线,直到最大插值误差满足误差要求.与现有曲线插值算法相比,该算法可以在保证插值精度的前提下有效压缩数据量.
CLOSED SMOOTH SURFACE DEFINED FROM CUBIC TRIANGULAR SPLINES
Institute of Scientific and Technical Information of China (English)
Ren-zhong Feng; Ren-hong Wang
2005-01-01
In order to construct closed surfaces with continuous unit normal, we introduce a new spline space on an arbitrary closed mesh of three-sided faces. Our approach generalizes an idea of Goodman and is based on the concept of 'Geometric continuity' for piecewise polynomial parametrizations. The functions in the spline space restricted to the faces are cubic triangular polynomials. A basis of the spline space is constructed of positive functions which sum to 1. It is also shown that the space is suitable for interpolating data at the midpoints of the faces.
非均匀三次B样条曲线插值的GS-PIA算法%Non-uniform Cubic B-spline Curve Interpolation Algorithm of GS-PIA
Institute of Scientific and Technical Information of China (English)
刘晓艳; 邓重阳
2015-01-01
提出了非均匀三次B样条曲线插值的GS-PIA算法。该算法与解线性方程组的高斯－赛德尔迭代法有同样的优点，即把已经更新的点参与到迭代过程来优化迭代过程；同时也具有渐进迭代逼近方法的优点，即有明确的几何意义，并能得到一系列逐次逼近插值点的非均匀三次 B样条曲线。%This paper presents a non-uniform cubic B-spline curve interpolation algorithm of GS-PIA.The algorithm and the Gauss-Seidel iterative method of solving linear equations have the same advantages , namely the points involved in the iterative process which has been updated to optimize the iterative process .At the same time, the algorithm also has the advantage of progressive iterative approximation method , namely, there is a clear geometric significance , and can make a series of non-uniform cubic B-spline curve approximation interpolation points .
Shape Designing of Engineering Images Using Rational Spline Interpolation
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Muhammad Sarfraz
2015-01-01
Full Text Available In modern days, engineers encounter a remarkable range of different engineering problems like study of structure, structure properties, and designing of different engineering images, for example, automotive images, aerospace industrial images, architectural designs, shipbuilding, and so forth. This paper purposes an interactive curve scheme for designing engineering images. The purposed scheme furnishes object designing not just in the area of engineering, but it is equally useful for other areas including image processing (IP, Computer Graphics (CG, Computer-Aided Engineering (CAE, Computer-Aided Manufacturing (CAM, and Computer-Aided Design (CAD. As a method, a piecewise rational cubic spline interpolant, with four shape parameters, has been purposed. The method provides effective results together with the effects of derivatives and shape parameters on the shape of the curves in a local and global manner. The spline method, due to its most generalized description, recovers various existing rational spline methods and serves as an alternative to various other methods including v-splines, gamma splines, weighted splines, and beta splines.
Institute of Scientific and Technical Information of China (English)
苏世栋; 刘鹏飞
2012-01-01
为了增强关节式工业机器人加工不规则工件的能力,将三次均匀B样条曲线应用于关节式机器人轨迹插补算法中,使机器人末端以三次B样条的曲线轨迹通过各加工点.在分析了三次均匀B样条曲线特性的基础上,给出了三次均匀B样条曲线的一般表达式.在增加曲线自由端点条件后,使用追赶算法快速反算出控制点.使用预估校正的方法推导出插补算法,该算法能使机器人末端遵循抛物线过渡型的加速-匀速-减速变化规律,给出了预测减速点的方法.对一个类花瓣型的加工对象进行仿真,证明文中方法的可行性.%To enhance capability of industry joint robot to machine irregular shape workpiece, the cubic uniform B - spline curve is introduced to manipulator trajectory interpolation. After reviewing characteristics of cubic uniform B-spline curve, the general expressions of such curve are proposed. A chasing method is used to calculate the control points,while conditions of two free endpoints are added to the solutions. A predict-correct method is used to derive the interpolation algorithm, which directs the velocity of end-effecter to follow a parabolic curve-accelerating, uniform and decelerating, and the prediction of deceleration point is presented. A simulation is tested in a flower-shaped workpiece and feasibility of manipulator trajectory interpolation algorithm is verified.
Conformal interpolating algorithm based on B-spline for aspheric ultra-precision machining
Li, Chenggui; Sun, Dan; Wang, Min
2006-02-01
Numeric control machining and on-line compensation for aspheric surface are key techniques for ultra-precision machining. In this paper, conformal cubic B-spline interpolating curve is first applied to fit the character curve of aspheric surface. Its algorithm and process are also proposed and imitated by Matlab7.0 software. To evaluate the performance of the conformal B-spline interpolation, comparison was made between linear and circular interpolations. The result verifies this method can ensure smoothness of interpolating spline curve and preserve original shape characters. The surface quality interpolated by B-spline is higher than by line and by circle arc. The algorithm is benefit to increasing the surface form precision of workpiece during ultra-precision machining.
Recovery of Graded Index Profile of Planar Waveguide by Cubic Spline Function
Institute of Scientific and Technical Information of China (English)
YANG Yong; CHEN Xian-Feng; LIAO Wei-Jun; XIA Yu-Xing
2007-01-01
A method is proposed to recover the refractive index profile of graded waveguide from the effective indices by a cubic spline interpolation function. Numerical analysis of several typical index distributions show that the refractive index profile can be reconstructed closely to its exact profile by the presented interpolation model.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh; Ahmad Abd. Majid; Ahmad Izani Md. Ismail
2012-01-01
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
三次均匀B样条与α-B样条的扩展%Extended Cubic Uniform B-spline and α-B-spline
Institute of Scientific and Technical Information of China (English)
徐岗; 汪国昭
2008-01-01
Spline curve and surface play an important role in CAD and computer graphics. In this paper, we propose several extensions of cubic uniform B-spline. Then, we present the ex- tensions of interpolating α-B-spline based on the new B-splines and the singular blending technique. The advantage of the ex- tensions is that they have global and local shape parameters. Furthermore, we also investigate their applications in data in- terpolation and polygonal shape deformation.
Institute of Scientific and Technical Information of China (English)
王东; 陶跃珍
2011-01-01
For increasing the optimal design accuracy of reappearing trajectory of link mechanism, the positions and the numbers on the locus of link mechanism must be suitable. Based on this, a new design method is proposed under the condition of discrete points and number is constant. Cubic spline interpolation in Matlab spline function is used on those points to get the mathematical interpolation curve model of the trajectory, then adds discrete points on the interpolation curve based the change rate, so the reappearing trajectory of optimum design of link mechanism is come to pass by fmincon function in optimistic toolbox of matlab. In comparing with the traditional optimization design method,this method can greatly improve the efficiency and accuracy because of adding interpolation points on the trajectory.The method is suitable to any optimal design of reappearing trajectory mechanism, so it has certain practical value.%为了提高连杆机构轨迹再现优化设计精度,连杆轨迹上已知点的位置和数目必须适当.基于此,在连杆预定轨迹上已知离散点位置和数目不变的情况下提出一种新的设计方法,利用MatlabSpline函数对离散点进行三次样条插值,得到预定运动轨迹插值曲线数学模型,在插值曲线上根据函数变化率增加离散点,调用Matlab优化工具箱中的fmincon函数,实现连杆机构轨迹再现优化设计.与传统优化设计方法相比,由于在预定运动轨迹上增加了插值节点,节点分布更为合理,所以能够明显提高连杆机构轨迹再现优化设计的效率和精度,该方法适用于任何机构轨迹再现优化设计,具有一定实用价值.
Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface
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Xinru Liu
2014-01-01
Full Text Available A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.
Generalized fairing algorithm of parametric cubic splines
Institute of Scientific and Technical Information of China (English)
WANG Yuan-jun; CAO Yuan
2006-01-01
Kjellander has reported an algorithm for fairing uniform parametric cubic splines. Poliakoff extended Kjellander's algorithm to non-uniform case. However, they merely changed the bad point's position, and neglected the smoothing of tangent at bad point. In this paper, we present a fairing algorithm that both changed point's position and its corresponding tangent vector. The new algorithm possesses the minimum property of energy. We also proved Poliakoff's fairing algorithm is a deduction of our fairing algorithm. Several fairing examples are given in this paper.
样条型矩阵有理插值%SPLINE-TYPE MATRIX VALUED RATIONAL INTERPOLATION
Institute of Scientific and Technical Information of China (English)
杨松林
2005-01-01
The matrix valued rational interpolation is very useful in the partial realization problem and model reduction for all the linear system theory. Lagrange basic functions have been used in matrix valued rational interpolation. In this paper, according to the property of cardinal spline interpolation, we constructed a kind of spline type matrix valued rational interpolation, which based on cardinal spline. This spline type interpolation can avoid instability of high order polynomial interpolation and we obtained a useful formula.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Directory of Open Access Journals (Sweden)
Joan Goh
2012-01-01
Full Text Available Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Interpolation by two-dimensional cubic convolution
Shi, Jiazheng; Reichenbach, Stephen E.
2003-08-01
This paper presents results of image interpolation with an improved method for two-dimensional cubic convolution. Convolution with a piecewise cubic is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a one-dimensional derivation. The traditional, separable method is sub-optimal for the usual case of non-separable images. The improved method in this paper implements the most general non-separable, two-dimensional, piecewise-cubic interpolator with constraints for symmetry, continuity, and smoothness. The improved method of two-dimensional cubic convolution has three parameters that can be tuned to yield maximal fidelity for specific scene ensembles characterized by autocorrelation or power-spectrum. This paper illustrates examples for several scene models (a circular disk of parametric size, a square pulse with parametric rotation, and a Markov random field with parametric spatial detail) and actual images -- presenting the optimal parameters and the resulting fidelity for each model. In these examples, improved two-dimensional cubic convolution is superior to several other popular small-kernel interpolation methods.
On the role of exponential splines in image interpolation.
Kirshner, Hagai; Porat, Moshe
2009-10-01
A Sobolev reproducing-kernel Hilbert space approach to image interpolation is introduced. The underlying kernels are exponential functions and are related to stochastic autoregressive image modeling. The corresponding image interpolants can be implemented effectively using compactly-supported exponential B-splines. A tight l(2) upper-bound on the interpolation error is then derived, suggesting that the proposed exponential functions are optimal in this regard. Experimental results indicate that the proposed interpolation approach with properly-tuned, signal-dependent weights outperforms currently available polynomial B-spline models of comparable order. Furthermore, a unified approach to image interpolation by ideal and nonideal sampling procedures is derived, suggesting that the proposed exponential kernels may have a significant role in image modeling as well. Our conclusion is that the proposed Sobolev-based approach could be instrumental and a preferred alternative in many interpolation tasks.
A Parameterization Method from Conic Spline Interpolation
Institute of Scientific and Technical Information of China (English)
MA Long; GUO Feng-hua
2014-01-01
Interpolating a set of planar points is a common problem in CAD. Most constructions of interpolation functions are based on the parameters at the sample points. Assigning parameters to all sample points is a vital step before constructing interpolation functions. The most widely used parameterization method is accumulative chord length parameterization. In this paper, we give out a better method based on the interpolation of conics. Based on this method, a sequence of fairer Hermite curves can be constructed.
Removal of Baseline Wander Noise from Electrocardiogram (ECG using Fifth-order Spline Interpolation
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John A. OJO
2016-10-01
Full Text Available Baseline wandering can mask some important features of the Electrocardiogram (ECG signal hence it is desirable to remove this noise for proper analysis and display of the ECG signal. This paper presents the implementation and evaluation of spline interpolation and linear phase FIR filtering methods to remove this noise. Spline interpolation method requires the QRS waves to be first detected and fifth-order (quintic interpolation technique applied to determine the smoothest curve joining several QRS points. Filtering of the ECG baseline wander was performed by using the difference between the estimated baseline wander and the noisy ECG signal. ECG signals from the MIT-BIT arrhythmia database was used to test the system, while the technique was implemented in MATLAB. The performance of the system was evaluated using Average Power (AP after filtering, Mean Square Error (MSE and the Signal to Noise Ratio (SNR. The quintic spline interpolation gave the best performance in terms of AP, MSE and SNR when compared with linear phase filtering and cubic (3rd-order spline interpolation methods.
Shape preserving rational cubic spline for positive and convex data
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Malik Zawwar Hussain
2011-11-01
Full Text Available In this paper, the problem of shape preserving C2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C2 rational cubic function with two families of free parameters has been introduced to attain the C2 positive curves from positive data and C2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.
Institute of Scientific and Technical Information of China (English)
周天祥
2009-01-01
本文讨论了一类凸四边形上的插值问题.指出这类插值问题是可解的,其解是分片二元三次多项式,且在凸四边形上是C~2-连续的.我们证明了这类插值问题的解的存在性和唯一性,给出了解样条的分片表达式及其逼近度的估计.最后还给出了一个应用实例和图形显示来说明本方法是可行的.%In this paper we consider interpolation problems by bivariate cubic splines on quadrilaterals with C~2-continuons. An interpolation scheme is presented. The existence and uniqueness of the interpolation are given, and we also give the piecewise polynomial expres-sion of the interpolating splines. The approximation order is discussed, and a numerical solution of PDE and graphical display are also provided.
Rational trigonometric cubic spline to conserve convexity of 2D data
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Farheen Ibraheem
2013-11-01
Full Text Available Researchers in different fields of study are always in dire need of spline interpolating function that conserve intrinsic trend of the data. In this paper, a rational trigonometric cubic spline with four free parameters has been used to retain convexity of 2D data. For this purpose, constraints on two of free parameters βi and γi in the description of the rational trigonometric function are derived while the remaining two αi and δi are set free. Numerical examples demonstrate that resulting curves using the technique of the underlying paper are C1.
A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements
A.A. Soliman
2012-01-01
Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.
A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements
Directory of Open Access Journals (Sweden)
A. A. Soliman
2012-01-01
Full Text Available Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.
Connecting the Dots Parametrically: An Alternative to Cubic Splines.
Hildebrand, Wilbur J.
1990-01-01
Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)
Cubic spline approximation techniques for parameter estimation in distributed systems
Banks, H. T.; Crowley, J. M.; Kunisch, K.
1983-01-01
Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
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Muhammad Abbas
Full Text Available In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
Abbas, Muhammad; Majid, Ahmad Abd; Md Ismail, Ahmad Izani; Rashid, Abdur
2014-01-01
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
On spline and polynomial interpolation of low earth orbiter data: GRACE example
Uz, Metehan; Ustun, Aydin
2016-04-01
GRACE satellites, which are equipped with specific science instruments such as K/Ka band ranging system, have still orbited around the earth since 17 March 2002. In this study the kinematic and reduced-dynamic orbits of GRACE-A/B were determined to 10 seconds interval by using Bernese 5.2 GNSS software during May, 2010 and also daily orbit solutions were validated with GRACE science orbit, GNV1B. The RMS values of kinematic and reduced-dynamic orbit validations were about 2.5 and 1.5 cm, respectively. Throughout the time period of interest, more or less data gaps were encountered in the kinematic orbits due to lack of GPS measurements and satellite manoeuvres. Thus, the least square polynomial and the cubic spline approaches (natural, not-a-knot and clamped) were tested to interpolate both small data gaps and 5 second interval on precise orbits. The latter is necessary for example in case of data densification in order to use the K / Ka band observations. The interpolated coordinates to 5 second intervals were also validated with GNV1B orbits. The validation results show that spline approaches have delivered approximately 1 cm RMS values and are better than those of least square polynomial interpolation. When data gaps occur on daily orbit, the spline validation results became worse depending on the size of the data gaps. Hence, the daily orbits were fragmented into small arcs including 30, 40 or 50 knots to evaluate effect of the least square polynomial interpolation on data gaps. From randomly selected daily arc sets, which are belonging to different times, 5, 10, 15 and 20 knots were removed, independently. While 30-knot arcs were evaluated with fifth-degree polynomial, sixth-degree polynomial was employed to interpolate artificial gaps over 40- and 50-knot arcs. The differences of interpolated and removed coordinates were tested with each other by considering GNV1B validation RMS result, 2.5 cm. With 95% confidence level, data gaps up to 5 and 10 knots can
Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors.
Okaniwa, Shoichi; Nasri, Ahmad; Lin, Hongwei; Abbas, Abdulwahed; Kineri, Yuki; Maekawa, Takashi
2012-09-01
This paper presents a geometric algorithm for the generation of uniform cubic B-spline curves interpolating a sequence of data points under tangent and curvature vectors constraints. To satisfy these constraints, knot insertion is used to generate additional control points which are progressively repositioned using corresponding geometric rules. Compared to existing schemes, our approach is capable of handling plane as well as space curves, has local control, and avoids the solution of the typical linear system. The effectiveness of the proposed algorithm is illustrated through several comparative examples. Applications of the method in NC machining and shape design are also outlined.
A new extension algorithm for cubic B-splines based on minimal strain energy
Institute of Scientific and Technical Information of China (English)
MO Guo-liang; ZHAO Ya-nan
2006-01-01
Extension ora B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve segment GC2-continuous with the original one, a family of cubic polynomial interpolation curves can be constructed. One curve is chosen as the solution from a sub-class of such a family by setting one GC2 parameter to be zero and determining the second GC2 parameter by minimizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C2-continuity with the given B-spline curve, and then knot removal from the curve is done. As a result, a sub-optimized solution subject to the given constraints and criteria is obtained. Additionally, new control points of the extension B-spline segment can be determined by solving lower triangular linear equations. Some computing examples for comparing our method and other methods are given.
Gravity Aided Navigation Precise Algorithm with Gauss Spline Interpolation
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WEN Chaobin
2015-01-01
Full Text Available The gravity compensation of error equation thoroughly should be solved before the study on gravity aided navigation with high precision. A gravity aided navigation model construction algorithm based on research the algorithm to approximate local grid gravity anomaly filed with the 2D Gauss spline interpolation is proposed. Gravity disturbance vector, standard gravity value error and Eotvos effect are all compensated in this precision model. The experiment result shows that positioning accuracy is raised by 1 times, the attitude and velocity accuracy is raised by 1～2 times and the positional error is maintained from 100~200 m.
Souto, Nelson; Thuillier, Sandrine; Andrade-Campos, A.
2016-10-01
Nowadays, full-field measurement methods are largely used to acquire the strain field developed by heterogeneous mechanical tests. Recent material parameters identification strategies based on a single heterogeneous test have been proposed considering that an inhomogeneous strain field can lead to a more complete mechanical characterization of the sheet metals. The purpose of this work is the design of a heterogeneous test promoting an enhanced mechanical behavior characterization of thin metallic sheets, under several strain paths and strain amplitudes. To achieve this goal, a design optimization strategy finding the appropriate specimen shape of the heterogeneous test by using either B-Splines or cubic splines was developed. The influence of using approximation or interpolation curves, respectively, was investigated in order to determine the most effective approach for achieving a better shape design. The optimization process is guided by an indicator criterion which evaluates, quantitatively, the strain field information provided by the mechanical test. Moreover, the design of the heterogeneous test is based on the resemblance with the experimental reality, since a rigid tool leading to uniaxial loading path is used for applying the displacement in a similar way as universal standard testing machines. The results obtained reveal that the optimization strategy using B-Splines curve approximation led to a heterogeneous test providing larger strain field information for characterizing the mechanical behavior of sheet metals.
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael
2015-10-24
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
Trivariate Polynomial Natural Spline for 3D Scattered Data Hermit Interpolation
Institute of Scientific and Technical Information of China (English)
XU YING-XIANG; GUAN L(U)-TAI; XU WEI-ZHI
2012-01-01
Consider a kind of Hermit interpolation for scattered data of 3D by trivariate polynomial natural spline,such that the objective energy functional (with natural boundary conditions) is minimal.By the spline function methods in Hilbert space and variational theory of splines,the characters of the interpolation solution and how to construct it are studied.One can easily find that the interpolation solution is a trivariate polynomial natural spline.Its expression is simple and the coefficients can be decided by a linear system.Some numerical examples are presented to demonstrate our methods.
Algorithms for spline and other approximations to functions and data
Phillips, G. M.; Taylor, P. J.
1992-12-01
A succinct introduction to splines, explaining how and why B-splines are used as a basis and how cubic and quadratic splines may be constructed, is followed by brief account of Hermite interpolation and Padé approximations.
Removal of Baseline Wander Noise from Electrocardiogram (ECG) using Fifth-order Spline Interpolation
John A. OJO; Temilade B. ADETOYI; Solomon A. Adeniran
2016-01-01
Baseline wandering can mask some important features of the Electrocardiogram (ECG) signal hence it is desirable to remove this noise for proper analysis and display of the ECG signal. This paper presents the implementation and evaluation of spline interpolation and linear phase FIR filtering methods to remove this noise. Spline interpolation method requires the QRS waves to be first detected and fifth-order (quintic) interpolation technique applied to determine the smo...
Interpolating solutions in cubic superstring field theory
Arroyo, E Aldo
2016-01-01
Performing a gauge transformation of an identity based solution, we construct a one-parameter family of solutions, and by evaluating the energy associated to these solutions, we show that depending on the value of the parameter, the solution interpolates between three distinct gauge orbits corresponding to the perturbative vacuum, the half brane and the tachyon vacuum solution.
Adaptive Predistortion Using Cubic Spline Nonlinearity Based Hammerstein Modeling
Wu, Xiaofang; Shi, Jianghong
In this paper, a new Hammerstein predistorter modeling for power amplifier (PA) linearization is proposed. The key feature of the model is that the cubic splines, instead of conventional high-order polynomials, are utilized as the static nonlinearities due to the fact that the splines are able to represent hard nonlinearities accurately and circumvent the numerical instability problem simultaneously. Furthermore, according to the amplifier's AM/AM and AM/PM characteristics, real-valued cubic spline functions are utilized to compensate the nonlinear distortion of the amplifier and the following finite impulse response (FIR) filters are utilized to eliminate the memory effects of the amplifier. In addition, the identification algorithm of the Hammerstein predistorter is discussed. The predistorter is implemented on the indirect learning architecture, and the separable nonlinear least squares (SNLS) Levenberg-Marquardt algorithm is adopted for the sake that the separation method reduces the dimension of the nonlinear search space and thus greatly simplifies the identification procedure. However, the convergence performance of the iterative SNLS algorithm is sensitive to the initial estimation. Therefore an effective normalization strategy is presented to solve this problem. Simulation experiments were carried out on a single-carrier WCDMA signal. Results show that compared to the conventional polynomial predistorters, the proposed Hammerstein predistorter has a higher linearization performance when the PA is near saturation and has a comparable linearization performance when the PA is mildly nonlinear. Furthermore, the proposed predistorter is numerically more stable in all input back-off cases. The results also demonstrate the validity of the convergence scheme.
3D Medical Image Interpolation Based on Parametric Cubic Convolution
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter, which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.
A Cubic B-Spline Approach for Inter-Transformation Between Potential Field and Gradient Data
Wang, B.; Gao, S. S.
2008-12-01
Traditionally, algorithms involving Fast Fourier Transforms (FFT) are used to calculate gradients from field data and vise versa. Because the popular FFT differentiation algorithms are prone to noise, expensive field campaigns are increasingly utilized to obtain gradient data. In areas with both field and gradient data, transformation facilitates comparison. In areas with only one kind of data, transformation facilitates interpretation by transforming the measured data into another form of data. We advance unified formulae for interpolation, differentiation and integration using cubic B-splines, and propose new space-domain approaches for 2D and 3D transformations from potential field data to potential-field gradient data and vice versa. We also advance spline-based continuation techniques. In the spline-based algorithms, the spacing can be either regular or irregular. Analyses using synthetic and real gravity and magnetic data show that the new algorithms have higher accuracy, are more noise-tolerant and thus provide better insights into understanding the nature of the sources than the traditional FFT techniques.
Application and Realization of the Computer Animation Design Based on Improved Cubic B-spline Curves
Directory of Open Access Journals (Sweden)
Ni Na
2015-01-01
Full Text Available Based on the application of the cubic B-spline curves in the computer animation design, taking into account the security and confidentiality of the information, this paper improves the animation design techniques by the use of the improved cubic B-spline curves. Finally, this paper provides the relevant C language programs of the animation design.
Image interpolation by two-dimensional parametric cubic convolution.
Shi, Jiazheng; Reichenbach, Stephen E
2006-07-01
Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] x [-2, 2] with constraints for biaxial symmetry, diagonal (or 90 degrees rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.
A Finite Element Cable Model and Its Applications Based on the Cubic Spline Curve
Institute of Scientific and Technical Information of China (English)
方子帆; 贺青松; 向兵飞; 肖化攀; 何孔德; 杜义贤
2013-01-01
For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.
Cubature Formula and Interpolation on the Cubic Domain
Institute of Scientific and Technical Information of China (English)
Huiyuan Li; Jiachang Sun; Yuan Xu
2009-01-01
Several cubature formulas on the cubic domains are derived using the dis-crete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Cheby-shev weight functions and associated interpolation polynomials on [-1,1]2, as well as new results on [-1,1]3. In particular, compact formulas for the fundamental interpo-lation polynomials are derived, based on n3/4 + (n2) nodes of a cubature formula on [-1,1]3.
Partially Blended Constrained Rational Cubic Trigonometric Fractal Interpolation Surfaces
Chand, A. K. B.; Tyada, K. R.
2016-08-01
Fractal interpolation is an advance technique for visualization of scientific shaped data. In this paper, we present a new family of partially blended rational cubic trigonometric fractal interpolation surfaces (RCTFISs) with a combination of blending functions and univariate rational trigonometric fractal interpolation functions (FIFs) along the grid lines of the interpolation domain. The developed FIFs use rational trigonometric functions pi,j(θ) qi,j(θ), where pi,j(θ) and qi,j(θ) are cubic trigonometric polynomials with four shape parameters. The convergence analysis of partially blended RCTFIS with the original surface data generating function is discussed. We derive sufficient data-dependent conditions on the scaling factors and shape parameters such that the fractal grid line functions lie above the grid lines of a plane Π, and consequently the proposed partially blended RCTFIS lies above the plane Π. Positivity preserving partially blended RCTFIS is a special case of the constrained partially blended RCTFIS. Numerical examples are provided to support the proposed theoretical results.
Barmpoutis, Angelos; Vemuri, Baba C; Shepherd, Timothy M; Forder, John R
2007-11-01
In this paper, we present novel algorithms for statistically robust interpolation and approximation of diffusion tensors-which are symmetric positive definite (SPD) matrices-and use them in developing a significant extension to an existing probabilistic algorithm for scalar field segmentation, in order to segment diffusion tensor magnetic resonance imaging (DT-MRI) datasets. Using the Riemannian metric on the space of SPD matrices, we present a novel and robust higher order (cubic) continuous tensor product of B-splines algorithm to approximate the SPD diffusion tensor fields. The resulting approximations are appropriately dubbed tensor splines. Next, we segment the diffusion tensor field by jointly estimating the label (assigned to each voxel) field, which is modeled by a Gauss Markov measure field (GMMF) and the parameters of each smooth tensor spline model representing the labeled regions. Results of interpolation, approximation, and segmentation are presented for synthetic data and real diffusion tensor fields from an isolated rat hippocampus, along with validation. We also present comparisons of our algorithms with existing methods and show significantly improved results in the presence of noise as well as outliers.
Theory, computation, and application of exponential splines
Mccartin, B. J.
1981-01-01
A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.
Study of Quintic Spline Interpolation and Generated Velocity Profile for High Speed Machining
Institute of Scientific and Technical Information of China (English)
ZHENG Jinxing; ZHANG Mingjun; MENG Qingxin
2006-01-01
Modern high speed machining (HSM) machine tools often operates at high speed and high feedrate with high accelerations, in order to deliver the rapid feed motion. This paper presents an interpolation algorithm to generate continuous quintic spline toolpaths, with a constant travel increment at each step, while the smoother accelerations and jerks of two-order curve are obtained. Then an approach for reducing the feedrate fluctuation in high speed spline interpolation is presented. The presented approach has been validated to quickly, reliably and effective with the simulation.
Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme
Energy Technology Data Exchange (ETDEWEB)
Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)
Research on Quadratic Spline Interpolation%二次样条插值研究
Institute of Scientific and Technical Information of China (English)
刘为; 高毅; 高尚
2011-01-01
The spline technology has applications widely in CAD, CAM, and computer graphics systems. The qualification of quadratic spline interpolation is discussed firstly. The solutions of quadratic spline interpolation on the 5 boundary conditions are given. At last, computation methods are illustrated by examples.%样条技术在计算机辅助设计,计算机辅助制造,和计算机图形系统得到了广泛应用.分析了二次样条函数插值的条件,分5种边值条件给出了二次样条插值的求解方法,最后给出实例验证求解方法.
Monotone data visualization using rational trigonometric spline interpolation.
Ibraheem, Farheen; Hussain, Maria; Hussain, Malik Zawwar
2014-01-01
Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.
Monotone Data Visualization Using Rational Trigonometric Spline Interpolation
Directory of Open Access Journals (Sweden)
Farheen Ibraheem
2014-01-01
Full Text Available Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.
Geometric Hermite Interpolation for Space Curves by B-Spline%空间曲线几何Hermite插值的B样条方法
Institute of Scientific and Technical Information of China (English)
朱春钢; 王仁宏
2005-01-01
在给定的GC2插值条件,利用de Boor的构造平面曲线的GC2-Hermite插值方法,构造了一条具有两个自由度的三次B样条插值曲线,并证明插值曲线是局部存在的且具有4阶精度.%This paper considers the space GC2 Hermite interpolation by cubic B-spline curve which is based on de Boor's idea for constructing the planar GC2 Hermite interpolation. In addition to position and tangent direction, the curvature vector is interpolated at each point. It is proved that under appropriate assumptions the interpolant exists locally with two degrees of freedom and the 4th order accuracy.
Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations
Energy Technology Data Exchange (ETDEWEB)
Kim, Sang Dong [KyungPook National Univ., Taegu (Korea, Republic of)
1996-12-31
In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).
Accurate B-spline-based 3-D interpolation scheme for digital volume correlation
Ren, Maodong; Liang, Jin; Wei, Bin
2016-12-01
An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.
Realization Methodology of a 5-axis Spline Interpolator in an Open CNC System
Institute of Scientific and Technical Information of China (English)
Wang Yongzhang; Ma Xiongbo; Chen Liangji; Han Zhenyu
2007-01-01
By making use of the advantages of non-uniform rational B-spline (NURBS) curves to represent spatial curves, an instruction format with double NURBS curves suitable for 5-axis coordinated real-time interpolation is presented to replace the current 5-axis coordinated linear interpolation method defective in low-speed, low-accuracy and enormous numerical control (NC) files in sculptured surface machining. A generation procedure of the NC files with the presented format is introduced and the method to realize the interpolation in an open computer numerical control (CNC) system is developed by ourselves. These illustrated the feasibility of the proposed method and its capability of avoiding all the shortages of 5-axis linear interpolation method.
Cubic Trigonometric B-spline Galerkin Methods for the Regularized Long Wave Equation
Irk, Dursun; Keskin, Pinar
2016-10-01
A numerical solution of the Regularized Long Wave (RLW) equation is obtained using Galerkin finite element method, based on Crank Nicolson method for the time integration and cubic trigonometric B-spline functions for the space integration. After two different linearization techniques are applied, the proposed algorithms are tested on the problems of propagation of a solitary wave and interaction of two solitary waves.
Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions
Institute of Scientific and Technical Information of China (English)
ZHU Meng-Hua; LIU Liang-Gang; QI Dong-Xu; YOU Zhong; XU Ao-Ao
2009-01-01
In this paper,the least square fitting method with the cubic B-spline basis hmctioas is derived to reduce the influence of statistical fluctuations in the gamma ray spectra.The derived procedure is simple and automatic.The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.
Application of Cubic Spline in the Implementation of Braces for the Case of a Child
Directory of Open Access Journals (Sweden)
Azmin Sham Rambely
2012-01-01
Full Text Available Problem statement: Orthodontic teeth movement is influenced by the characteristics of the applied force, including its magnitude and direction which normally based on the shape of ellipsoid, parabolic and U-shape that are symmetry. However, this will affect the movement of the whole set of tooth. Approach: This study intends to compare the form of general teeth with another method called cubic spline to get a minimum error in presenting the general form of teeth. Cubic spline method is applied in a mathematical model of a childâs teeth, which is produced through resignation of orthodontic wires. It is also meant to create a clear view towards the true nature of orthodontic wires. Results: Based on mathematical characteristics in the spline and the real data of a teethâs model, cubic spline shows to be very useful in reflecting the shape of a curve because the dots chosen are not totally symmetry. Conclusion/Recommendation: Therefore, symmetrical curve can be produced in teethâs shape which is basically asymmetry.
Indhumathi, C; Cai, Y Y; Guan, Y Q; Opas, M; Zheng, J
2012-01-01
Confocal laser scanning microscopy has become a most powerful tool to visualize and analyze the dynamic behavior of cellular molecules. Photobleaching of fluorochromes is a major problem with confocal image acquisition that will lead to intensity attenuation. Photobleaching effect can be reduced by optimizing the collection efficiency of the confocal image by fast z-scanning. However, such images suffer from distortions, particularly in the z dimension, which causes disparities in the x, y, and z directions of the voxels with the original image stacks. As a result, reliable segmentation and feature extraction of these images may be difficult or even impossible. Image interpolation is especially needed for the correction of undersampling artifact in the axial plane of three-dimensional images generated by a confocal microscope to obtain cubic voxels. In this work, we present an adaptive cubic B-spline-based interpolation with the aid of lookup tables by deriving adaptive weights based on local gradients for the sampling nodes in the interpolation formulae. Thus, the proposed method enhances the axial resolution of confocal images by improving the accuracy of the interpolated value simultaneously with great reduction in computational cost. Numerical experimental results confirm the effectiveness of the proposed interpolation approach and demonstrate its superiority both in terms of accuracy and speed compared to other interpolation algorithms.
Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William
2016-01-01
Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather
双二次B-样条插值图像缩放%Image resizing via bi-quadratic B-spline interpolation
Institute of Scientific and Technical Information of China (English)
李英明; 夏海宏
2011-01-01
双线性和各种双三次插值方法是图像缩放中常用方法,但是双二次插值函数却很少被人提起.本文提出了一种基于双二次B-样条局部插值的图像缩放方法,该算法在图像局部重构过程中对称地采用了4×4采样点,并通过对该函数进行重采样来实现图像的缩放,避免了二次函数在图像重构与采样中的相位失真问题,此算法是一个局部性算法,易于扩展.实验结果表明,本文算法得到的图像的峰值信噪比(PSNR)、MISSIM值比双线性插值、双三次卷积、Catmull-Rom三次插值、Dodgson插值算法都要好,接近于最好的双三次B-样条算法,视觉效果虽然不如双三次B-样条插值算法,但优于Dodgson方法,计算时间比双三次B-样条减少了近三分之一.由于该算法没有对图像边缘特征进行特殊处理,对于一些细节纹理比较丰富的图像,将进一步研究.%Bilinear interpolation and various bi-cubic interpolations are frequently adopted in image resizing. However the biquadratic function is rarely considered due to its phase distortion problem. In this paper, we propose an image resizing method via bi-quadratic B-spline interpolation, where 4x4 pixels are sampled symmetrically in the local image. The proposed algorithm is a local algorithm and can be easily extended. According to our experiment results, the proposed bi-quadratic B-spline interpolation algorithm has better image peak signal-to-noise ratio ( PSNR) and MISSIM than bi-linear interpolation, bi-cubic convolution, Catmull-Rom cubic interpolation, or the Dodgson interpolation algorithm. The results are comparable to the bi-cubic B-spline interpolation algorithm, though the visual effects are not as good as that, but still better than the Dodgson algorithm. The computing time is reduced by nearly one-third compared to the bi-cubic B-spline interpolation algorithm. Since the algorithm has not carried on the special handling to the image edge features
Intensity Conserving Spline Interpolation (ICSI): A New Tool for Spectroscopic Analysis
Klimchuk, James A; Tripathi, Durgesh
2015-01-01
The detailed shapes of spectral line profiles provide valuable information about the emitting plasma, especially when the plasma contains an unresolved mixture of velocities, temperatures, and densities. As a result of finite spectral resolution, the intensity measured by a spectrometer is the average intensity across a wavelength bin of non-zero size. It is assigned to the wavelength position at the center of the bin. However, the actual intensity at that discrete position will be different if the profile is curved, as it invariably is. Standard fitting routines (spline, Gaussian, etc.) do not account for this difference, and this can result in significant errors when making sensitive measurements. Detection of asymmetries in solar coronal emission lines is one example. Removal of line blends is another. We have developed an iterative procedure called Intensity Conserving Spline Interpolation (ICSI) that corrects for this effect. As its name implies, it conserves the observed intensity within each wavelength...
Modeling of type-2 fuzzy cubic B-spline surface for flood data problem in Malaysia
Bidin, Mohd Syafiq; Wahab, Abd. Fatah
2017-08-01
Malaysia possesses a low and sloping land areas which may cause flood. The flood phenomenon can be analyzed if the surface data of the study area can be modeled by geometric modeling. Type-2 fuzzy data for the flood data is defined using type-2 fuzzy set theory in order to solve the uncertainty of complex data. Then, cubic B-spline surface function is used to produce a smooth surface. Three main processes are carried out to find a solution to crisp type-2 fuzzy data which is fuzzification (α-cut operation), type-reduction and defuzzification. Upon conducting these processes, Type-2 Fuzzy Cubic B-Spline Surface Model is applied to visualize the surface data of the flood areas that are complex uncertainty.
Numerical Solution of One-dimensional Telegraph Equation using Cubic B-spline Collocation Method
Directory of Open Access Journals (Sweden)
J. Rashidinia
2014-02-01
Full Text Available In this paper, a collocation approach is employed for the solution of the one-dimensional telegraph equation based on cubic B-spline. The derived method leads to a tri-diagonal linear system. Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory. The obtained numerical results have been compared with the results obtained by some existing methods to verify the accurate nature of our method.
Explicit Gaussian quadrature rules for C^1 cubic splines with symmetrically stretched knot sequence
Ait-Haddou, Rachid
2015-06-19
We provide explicit expressions for quadrature rules on the space of C^1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.
Research on the Shortest Quadratic Spline Interpolation%最短二次样条插值研究
Institute of Scientific and Technical Information of China (English)
陈刚; 高尚
2011-01-01
The spline technology has applications widely in CAD, CAM, and computer graphics systems.The qualification of quadratic spline interpolation is discussed firstly.The solutions of quadratic spline interpolation on one kind of boundary conditions are given.Based on analysis of quadratic spline interpolation, the shortest quadratic spline interpolation is discussed.Furthermore, golden section method is put forward to solve this problem.At last, computation methods are illustrated by examples.%样条技术在计算机辅助设计,计算机辅助制造,和计算机图形系统得到了广泛应用.分析了二次样条函数插值的条件,给出了其中一种边值条件二次样条插值的求解方法.在分析了样条函数插值基础上,提出最短二次样条插值问题,并提出用黄金分割法解决该问题.最后给出了实例来说明求解方法.
Certified Approximation of Parametric Space Curves with Cubic B-spline Curves
Shen, Liyong; Gao, Xiao-Shan
2012-01-01
Approximating complex curves with simple parametric curves is widely used in CAGD, CG, and CNC. This paper presents an algorithm to compute a certified approximation to a given parametric space curve with cubic B-spline curves. By certified, we mean that the approximation can approximate the given curve to any given precision and preserve the geometric features of the given curve such as the topology, singular points, etc. The approximated curve is divided into segments called quasi-cubic B\\'{e}zier curve segments which have properties similar to a cubic rational B\\'{e}zier curve. And the approximate curve is naturally constructed as the associated cubic rational B\\'{e}zier curve of the control tetrahedron of a quasi-cubic curve. A novel optimization method is proposed to select proper weights in the cubic rational B\\'{e}zier curve to approximate the given curve. The error of the approximation is controlled by the size of its tetrahedron, which converges to zero by subdividing the curve segments. As an applic...
Surface evaluation with Ronchi test by using Malacara formula, genetic algorithms, and cubic splines
Cordero-Dávila, Alberto; González-García, Jorge
2010-08-01
In the manufacturing process of an optical surface with rotational symmetry the ideal ronchigram is simulated and compared with the experimental ronchigram. From this comparison the technician, based on your experience, estimated the error on the surface. Quantitatively, the error on the surface can be described by a polynomial e(ρ2) and the coefficients can be estimated from data of the ronchigrams (real and ideal) to solve a system of nonlinear differential equations which are related to the Malacara formula of the transversal aberration. To avoid the problems inherent in the use of polynomials it proposed to describe the errors on the surface by means of cubic splines. The coefficients of each spline are estimated from a discrete set of errors (ρi,ei) and these are evaluated by means of genetic algorithms to reproduce the experimental ronchigrama starting from the ideal.
A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation
Directory of Open Access Journals (Sweden)
S. Battal Gazi Karakoç
2016-02-01
Full Text Available The generalized equal width (GEW wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.
Institute of Scientific and Technical Information of China (English)
温伟斌; 蹇开林; 骆少明
2013-01-01
A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven-tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin-ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.
Basic Searching, Interpolating, and Curve-Fitting Algorithms in C++
2015-01-01
for best-fit equations. Functions for working with periodic equations are included. 15. SUBJECT TERMS interpolate , linear, cubic, hermite, polynomial ...Periodic Interpolations 17 11. Example: Determining Interpolation Performance 18 12. Example: Interpolating in Two Dimensions 19 13. Polynomial ...cubic Hermite spline is a third-degree- polynomial interpolating function that is uniquely determined by 2 endpoint positions ( 0p and 1p ) and
Comparison of interpolating methods for image resampling.
Parker, J; Kenyon, R V; Troxel, D E
1983-01-01
When resampling an image to a new set of coordinates (for example, when rotating an image), there is often a noticeable loss in image quality. To preserve image quality, the interpolating function used for the resampling should be an ideal low-pass filter. To determine which limited extent convolving functions would provide the best interpolation, five functions were compared: A) nearest neighbor, B) linear, C) cubic B-spline, D) high-resolution cubic spline with edge enhancement (a = -1), and E) high-resolution cubic spline (a = -0.5). The functions which extend over four picture elements (C, D, E) were shown to have a better frequency response than those which extend over one (A) or two (B) pixels. The nearest neighbor function shifted the image up to one-half a pixel. Linear and cubic B-spline interpolation tended to smooth the image. The best response was obtained with the high-resolution cubic spline functions. The location of the resampled points with respect to the initial coordinate system has a dramatic effect on the response of the sampled interpolating function the data are exactly reproduced when the points are aligned, and the response has the most smoothing when the resampled points are equidistant from the original coordinate points. Thus, at the expense of some increase in computing time, image quality can be improved by resampled using the high-resolution cubic spline function as compared to the nearest neighbor, linear, or cubic B-spline functions.
Extended cubic B-spline method for solving a linear system of second-order boundary value problems.
Heilat, Ahmed Salem; Hamid, Nur Nadiah Abd; Ismail, Ahmad Izani Md
2016-01-01
A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, [Formula: see text] and [Formula: see text], play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error is calculated. This method is tested on three examples. The examples suggest that this method produces comparable or more accurate results than cubic B-spline and some other methods.
Neural Network Methods for NURBS Curve and Surface Interpolation
Institute of Scientific and Technical Information of China (English)
秦开怀
1997-01-01
New algorithms based on artificial neural network models are presented for cubic NURBS curve and surface interpolation.When all th knot spans are identical,the NURBS curve interpolation procedure degenerates into that of uniform rational B-spline curves.If all the weights of data points are identical,then the NURBS curve interpolation procedure degenerates into the integral B-spline curve interpolation.
Cubic Shape Preserving Rational Spline and Its Offset Curve%保形三次有理样条及其等距曲线
Institute of Scientific and Technical Information of China (English)
刘文艳; 王强; 张养聪
2012-01-01
为了使有理插值样条及其等距曲线在工业设计、制造及计算机图形和CAGD领域有着更灵活更广泛的应用,构造含参数三次有理插值样条模型,生成插值有限个离散点的光滑曲线及其等距线,该模型可通过选取其中的形状参数使得曲线具有保形性并达到一阶连续.并可通过适当调整插值函数中的参数进行交互式的修改,以得到满意的曲线及等距线,并可结合细分算法达到要求的逼近精度.%In order to make rational interpolating spline and its equidistant curve to be more flexibly and more widely used in industrial design, manufacturing, computer graphics and CAGD fields, cubic rational interpolation spline model with parameters was constructed to generate a smooth interpolation curve and its equidistant line by finite number of discrete point data. In the model curve can be with shape retention and first - order continuity by select the shape parameters. The interactive modification can be carried out by appropriate adjustment of the parameters in the interpolation function, to obtain satisfied curve and its equidistant line, and with segmentation algorithm to meet the requirements of the approximation precision.
One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation
Institute of Scientific and Technical Information of China (English)
ZHANG Li; YANG Yan; LI Yuan-yuan; TAN Jie-qing
2014-01-01
A new method to the problem of fairing planar cubic B-spline curves is introduced in this paper. The method is based on weighted progressive iterative approximation (WPIA for short) and consists of following steps:finding the bad point which needs to fair, deleting the bad point, re-inserting a new data point to keep the structure of the curve and applying WPIA method with the new set of the data points to obtain the faired curve. The new set of the data points is formed by the rest of the original data points and the new inserted point. The method can be used for shape design and data processing. Numerical examples are provided to demonstrate the effectiveness of the method.
Numerical solution of the Black-Scholes equation using cubic spline wavelets
Černá, Dana
2016-12-01
The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.
Institute of Scientific and Technical Information of China (English)
侯朝胜; 李婧; 龙泉
2003-01-01
The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.
Energy Technology Data Exchange (ETDEWEB)
Castillo, Victor Manuel [Univ. of California, Davis, CA (United States)
1999-01-01
A collocation method using cubic splines is developed and applied to simulate steady and time-dependent, including turbulent, thermally convecting flows for two-dimensional compressible fluids. The state variables and the fluxes of the conserved quantities are approximated by cubic splines in both space direction. This method is shown to be numerically conservative and to have a local truncation error proportional to the fourth power of the grid spacing. A ''dual-staggered'' Cartesian grid, where energy and momentum are updated on one grid and mass density on the other, is used to discretize the flux form of the compressible Navier-Stokes equations. Each grid-line is staggered so that the fluxes, in each direction, are calculated at the grid midpoints. This numerical method is validated by simulating thermally convecting flows, from steady to turbulent, reproducing known results. Once validated, the method is used to investigate many aspects of thermal convection with high numerical accuracy. Simulations demonstrate that multiple steady solutions can coexist at the same Rayleigh number for compressible convection. As a system is driven further from equilibrium, a drop in the time-averaged dimensionless heat flux (and the dimensionless internal entropy production rate) occurs at the transition from laminar-periodic to chaotic flow. This observation is consistent with experiments of real convecting fluids. Near this transition, both harmonic and chaotic solutions may exist for the same Rayleigh number. The chaotic flow loses phase-space information at a greater rate, while the periodic flow transports heat (produces entropy) more effectively. A linear sum of the dimensionless forms of these rates connects the two flow morphologies over the entire range for which they coexist. For simulations of systems with higher Rayleigh numbers, a scaling relation exists relating the dimensionless heat flux to the two-seventh's power of the Rayleigh number
Energy Technology Data Exchange (ETDEWEB)
Castillo, V M
2005-01-12
A collocation method using cubic splines is developed and applied to simulate steady and time-dependent, including turbulent, thermally convecting flows for two-dimensional compressible fluids. The state variables and the fluxes of the conserved quantities are approximated by cubic splines in both space direction. This method is shown to be numerically conservative and to have a local truncation error proportional to the fourth power of the grid spacing. A ''dual-staggered'' Cartesian grid, where energy and momentum are updated on one grid and mass density on the other, is used to discretize the flux form of the compressible Navier-Stokes equations. Each grid-line is staggered so that the fluxes, in each direction, are calculated at the grid midpoints. This numerical method is validated by simulating thermally convecting flows, from steady to turbulent, reproducing known results. Once validated, the method is used to investigate many aspects of thermal convection with high numerical accuracy. Simulations demonstrate that multiple steady solutions can coexist at the same Rayleigh number for compressible convection. As a system is driven further from equilibrium, a drop in the time-averaged dimensionless heat flux (and the dimensionless internal entropy production rate) occurs at the transition from laminar-periodic to chaotic flow. This observation is consistent with experiments of real convecting fluids. Near this transition, both harmonic and chaotic solutions may exist for the same Rayleigh number. The chaotic flow loses phase-space information at a greater rate, while the periodic flow transports heat (produces entropy) more effectively. A linear sum of the dimensionless forms of these rates connects the two flow morphologies over the entire range for which they coexist. For simulations of systems with higher Rayleigh numbers, a scaling relation exists relating the dimensionless heat flux to the two-seventh's power of the Rayleigh number
Energy Technology Data Exchange (ETDEWEB)
Koo, Bon-Seung; Lee, Chung-Chan; Zee, Sung-Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
2006-07-01
Online digital core protection system(SCOPS) for a system-integrated modular reactor is being developed as a part of a plant protection system at KAERI. SCOPS calculates the minimum CHFR and maximum LPD based on several online measured system parameters including 3-level ex-core detector signals. In conventional ABB-CE digital power plants, cubic spline synthesis technique has been used in online calculations of the core axial power distributions using ex-core detector signals once every 1 second in CPC. In CPC, pre-determined cubic spline function sets are used depending on the characteristics of the ex-core detector responses. But this method shows an unnegligible power distribution error for the extremely skewed axial shapes by using restrictive function sets. Therefore, this paper describes the cubic spline method for the synthesis of an axial power distribution and it generates several new cubic spline function sets for the application of the core protection system, especially for the severely distorted power shapes needed reactor type.
Hardy, David J; Wolff, Matthew A; Xia, Jianlin; Schulten, Klaus; Skeel, Robert D
2016-03-21
The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle-mesh Ewald method falls short.
Chen, Xu; Xiang, Yang; Feng, Yu-Tao
2011-04-01
Spectral curvature destroys the co-registration of the spectra measured by dispersion imaging spectrometer. Using interpolation to re-sample the measured spectra at the non-offset mid-wavelengths can mitigate the spectral misregistration. It is very important to select an optimum interpolation method. The performances of six common interpolation methods are evaluated by comparing the residual errors in the corrected spectral radiance. The results indicate that, four-point cubic Lagrange interpolation and cubic spline interpolation are better than other four interpolation methods (linear Interpolation, three points quadratic polynomial interpolation, five points four-order Lagrange interpolation and cubic Hermite interpolation). For spectral offset of 10% deltalambda (deltalambda = 5 nm), the normalized errors in measured spectral radiance is PV = 0.06, that is reduced to PV interpolation with cubic Lagrange interpolation or cubic spline interpolation, but for other four methods they are PV > 0.035. Furthermore, for lower spectral resolution (deltalambda > 5 nm), cubic Lagrange interpolation is a little better than cubic spline interpolation; while for higher spectral resolution (deltalambda interpolation is a little better.
Cubic Spline Collocation Method for the Shallow Water Equations on the Sphere
Layton, Anita T.
2002-07-01
Spatial discretization schemes commonly used in global meteorological applications are currently limited to spectral methods or low-order finite-difference/finite-element methods. The spectral transform method, which yields high-order approximations, requires Legendre transforms, which have a computational complexity of O(N3), where N is the number of subintervals in one dimension. Thus, high-order finite-element methods may be a viable alternative to spectral methods. In this study, we present a new numerical method for solving the shallow water equations (SWE) in spherical coordinates. In this implementation, the SWE are discretized in time with the semi-implicit leapfrog method, and in space with the cubic spline collocation method on a skipped latitude-longitude grid. Numerical results for the Williamson et al. SWE test cases [D. L. Williamson, J. B. Blake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, J. Comput. Phys.102, 211 (1992)] are presented to demonstrate the stability and accuracy of the method. Results are also shown for an efficiency comparison between this method and a similar method in which spatial discretization is done on a uniform latitude-longitude grid.
Directory of Open Access Journals (Sweden)
H. S. Shukla
2015-01-01
Full Text Available In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs. The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54. Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
Directory of Open Access Journals (Sweden)
H. S. Shukla
2014-11-01
Full Text Available In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
Research on interpolation methods in medical image processing.
Pan, Mei-Sen; Yang, Xiao-Li; Tang, Jing-Tian
2012-04-01
Image interpolation is widely used for the field of medical image processing. In this paper, interpolation methods are divided into three groups: filter interpolation, ordinary interpolation and general partial volume interpolation. Some commonly-used filter methods for image interpolation are pioneered, but the interpolation effects need to be further improved. When analyzing and discussing ordinary interpolation, many asymmetrical kernel interpolation methods are proposed. Compared with symmetrical kernel ones, the former are have some advantages. After analyzing the partial volume and generalized partial volume estimation interpolations, the new concept and constraint conditions of the general partial volume interpolation are defined, and several new partial volume interpolation functions are derived. By performing the experiments of image scaling, rotation and self-registration, the interpolation methods mentioned in this paper are compared in the entropy, peak signal-to-noise ratio, cross entropy, normalized cross-correlation coefficient and running time. Among the filter interpolation methods, the median and B-spline filter interpolations have a relatively better interpolating performance. Among the ordinary interpolation methods, on the whole, the symmetrical cubic kernel interpolations demonstrate a strong advantage, especially the symmetrical cubic B-spline interpolation. However, we have to mention that they are very time-consuming and have lower time efficiency. As for the general partial volume interpolation methods, from the total error of image self-registration, the symmetrical interpolations provide certain superiority; but considering the processing efficiency, the asymmetrical interpolations are better.
Shishvan, Masoud Soleymani; Sattarvand, Javad
2012-12-01
In this paper a new method of modeling variable slope angles has been presented based on the spline interpolation method. Slope angle modeling and defining precedency of the blocks are the vital parts of almost any open pit optimization algorithm. Traditionally heuristic patterns such as 1:5 or 1:9 have been used to generate slope angles. Cone template based models were later employed in developing variable slope angles. They normally use a linear interpolation process for determination of slope angles between the given directions which leads to sharp and non-realistic pits. The other elliptical alternatives suffer from having limitations in defining slope angles in non-geographical directions. The method is capable to consider any number of slope angles in any desired direction as well as creating quite accurate and realistic pit shapes. Three major types of the spline interpolation including cubic, quadratic and cardinal are tested, however, the cubic form is preferred due to more realistic outcomes. Main steps of the method are described through a numerical case study.
Brown, Charles G., Jr.; Adcock, Aaron B.; Azevedo, Stephen G.; Liebman, Judith A.; Bond, Essex J.
2011-03-01
Some diagnostics at the National Ignition Facility (NIF), including the Gamma Reaction History (GRH) diagnostic, require multiple channels of data to achieve the required dynamic range. These channels need to be stitched together into a single time series, and they may have non-uniform and redundant time samples. We chose to apply the popular cubic smoothing spline technique to our stitching problem because we needed a general non-parametric method. We adapted one of the algorithms in the literature, by Hutchinson and deHoog, to our needs. The modified algorithm and the resulting code perform a cubic smoothing spline fit to multiple data channels with redundant time samples and missing data points. The data channels can have different, timevarying, zero-mean white noise characteristics. The method we employ automatically determines an optimal smoothing level by minimizing the Generalized Cross Validation (GCV) score. In order to automatically validate the smoothing level selection, the Weighted Sum-Squared Residual (WSSR) and zero-mean tests are performed on the residuals. Further, confidence intervals, both analytical and Monte Carlo, are also calculated. In this paper, we describe the derivation of our cubic smoothing spline algorithm. We outline the algorithm and test it with simulated and experimental data.
Energy Technology Data Exchange (ETDEWEB)
Brown, C; Adcock, A; Azevedo, S; Liebman, J; Bond, E
2010-12-28
Some diagnostics at the National Ignition Facility (NIF), including the Gamma Reaction History (GRH) diagnostic, require multiple channels of data to achieve the required dynamic range. These channels need to be stitched together into a single time series, and they may have non-uniform and redundant time samples. We chose to apply the popular cubic smoothing spline technique to our stitching problem because we needed a general non-parametric method. We adapted one of the algorithms in the literature, by Hutchinson and deHoog, to our needs. The modified algorithm and the resulting code perform a cubic smoothing spline fit to multiple data channels with redundant time samples and missing data points. The data channels can have different, time-varying, zero-mean white noise characteristics. The method we employ automatically determines an optimal smoothing level by minimizing the Generalized Cross Validation (GCV) score. In order to automatically validate the smoothing level selection, the Weighted Sum-Squared Residual (WSSR) and zero-mean tests are performed on the residuals. Further, confidence intervals, both analytical and Monte Carlo, are also calculated. In this paper, we describe the derivation of our cubic smoothing spline algorithm. We outline the algorithm and test it with simulated and experimental data.
Directory of Open Access Journals (Sweden)
Are eLosnegård
2013-07-01
Full Text Available Image-based tractography of white matter (WM fiber bundles in the brain using diffusion weighted MRI (DW-MRI has become a useful tool in basic and clinical neuroscience. However, proper tracking is challenging due to the anatomical complexity of fiber pathways, the coarse resolution of clinically applicable whole-brain in vivo imaging techniques, and the difficulties associated with verification. In this study we introduce a new tractography algorithm using splines (denoted Spline. Spline reconstructs smooth fiber trajectories iteratively, in contrast to most other tractography algorithms that create piecewise linear fiber tract segments, followed by spline fitting. Using DW-MRI recordings from eight healthy elderly people participating in a longitudinal study of cognitive aging, we compare our Spline algorithm to two state-of-the-art tracking methods from the TrackVis software suite. The comparison is done quantitatively using diffusion metrics (fractional anisotropy, FA, with both (i tract averaging, (ii longitudinal linear mixed-effects model fitting, and (iii detailed along-tract analysis. Further validation is done on recordings from a diffusion hardware phantom, mimicking a coronal brain slice, with a known ground truth. Results from the longitudinal aging study showed high sensitivity of Spline tracking to individual aging patterns of mean FA when combined with linear mixed-effects modelling, moderately strong differences in the along-tract analysis of specific tracts, whereas the tract-averaged comparison using simple linear OLS regression revealed less differences between Spline and the two other tractography algorithms. In the brain phantom experiments with a ground truth, we demonstrated improved tracking ability of Spline compared to the two reference tractography algorithms being tested.
Rational Cubics and Conics Representation: A Practical Approach
Directory of Open Access Journals (Sweden)
M. Sarfraz
2012-08-01
Full Text Available A rational cubic spline, with one family of shape parameters, has been discussed with the view to its application in Computer Graphics. It incorporates both conic sections and parametric cubic curves as special cases. The parameters (weights, in the description of the spline curve can be used to modify the shape of the curve, locally and globally, at the knot intervals. The rational cubic spline attains parametric smoothness whereas the stitching of the conic segments preserves visually reasonable smoothness at the neighboring knots. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as bits and pieces of a rational cubic spline.Key Words: Computer Graphics, Interpolation, Spline, Conic, Rational Cubic
Analysis of Spatial Interpolation in the Material-Point Method
DEFF Research Database (Denmark)
Andersen, Søren; Andersen, Lars
2010-01-01
This paper analyses different types of spatial interpolation for the material-point method The interpolations include quadratic elements and cubic splines in addition to the standard linear shape functions usually applied. For the small-strain problem of a vibrating bar, the best results are obta......This paper analyses different types of spatial interpolation for the material-point method The interpolations include quadratic elements and cubic splines in addition to the standard linear shape functions usually applied. For the small-strain problem of a vibrating bar, the best results...... are obtained using quadratic elements. It is shown that for more complex problems, the use of partially negative shape functions is inconsistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations...
Ahn, Kang-Hyun; Halpern, Howard J
2007-03-01
Spectral-spatial images reconstructed from a small number of projections suffer from streak artifacts that are seen as noise, particularly in the spectral dimension. Interpolation in projection space can reduce artifacts in the reconstructed images. The reduction of background artifacts improves lineshape fitting. In this work, we compared the performances of angular interpolation implemented using linear, cubic B-spline, and sinc methods. Line width maps were extracted from 4-D EPR images of phantoms using spectral fitting to evaluate each interpolation method and its robustness to noise. Results from experiment and simulation showed that the cubic B-spline, angular interpolation was preferable to either sinc or linear interpolation methods.
Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline
Directory of Open Access Journals (Sweden)
Cheng-ming Liu
2017-05-01
Full Text Available Image interpolation is a basic operation in image processing. Lots of methods have been proposed, including convolution-based methods, edge modeling methods, point spread function (PSF-based methods or learning-based methods. Most of them, however, present a high computational complexity and are not suitable for real time applications. However, fast methods are not able to provide artifacts-free images. In this paper we describe a new image interpolation method by using scanning line algorithm which can generate C - 1 curves or surfaces. The C - 1 interpolation can truncate the interpolation curve at big skipping; hence, the image edge can be kept. Numerical experiments illustrate the efficiency of the novel method.
Image Interpolation via Scanning Line Algorithm and Discontinuous B-Spline
Cheng-ming Liu; Ze-kun Wang; Hai-bo Pang; Jun-xiao Xue
2017-01-01
Image interpolation is a basic operation in image processing. Lots of methods have been proposed, including convolution-based methods, edge modeling methods, point spread function (PSF)-based methods or learning-based methods. Most of them, however, present a high computational complexity and are not suitable for real time applications. However, fast methods are not able to provide artifacts-free images. In this paper we describe a new image interpolation method by using scanning line algorit...
Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
Matt, Michael Andreas
2012-01-01
Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C1 splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C2 splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macro-elements based on the Alfeld split, where each tetrahedron
基于三次B样条的曲线逼近算法及其收敛性%Approximate algorithm of curves and its convergence based on cubic B-spline
Institute of Scientific and Technical Information of China (English)
蒋勇; 李玉梅
2013-01-01
为了改进传统的插值样条曲线算法不易于后期处理和实时局部修改、B样条算法不能满足精度要求的缺点,提出了一种基于三次B样条的曲线逼近算法[1].该算法以三次B样条为基础对曲线的逼近领域进行了研究,通过大量的数值实验证明了该算法的可行性及高效性.该算法通过结合插值样条与B样条的各种优点,有效避免了传统算法的不足.同时,对该算法的收敛性进行了理论证明.数值实验表明了该算法具有收敛速度快、精度高且编程易实现等优点,为曲线研究提供了可供参考的有效算法.%In order to improve the shortcomings of the traditional interpolation spline that is not easy to solve the problems at the post-processing and to do the local modification in time,and to improve the disadvantage of the approximate spline which can not meet the accuracy requirements,the approximate algorithm based on the cubic B-Spline is put forward[1].The algorithm is based on the cubic B-Spline and makes some research on the area of the curve approximate.A large number of numerical experiments are made to illustrate the feasibility and the efficiency of the algorithm.The algrithm combines the advantages of the interpolation spline and the B-Spline.The shortcomings of the traditional algrithrn are prevented effectively.At the same time,the theoretical proof is put forward to demonstrate the convergence of the algorithm.And the numerical experiments show that this algorithm has fast convergence speed and high precision.And its programming is easy to implement.A effective algorithm is put forward for the curve research which can be use as a reference.
Hintzen, N.T.; Piet, G.J.; Brunel, T.P.A.
2010-01-01
For control and enforcement purposes, all fishing vessels operating in European waters are equipped with satellite-based Vessel Monitoring by Satellite systems (VMS) recording their position at regular time intervals. VMS data are increasingly used by scientists to study spatial and temporal pattern
Institute of Scientific and Technical Information of China (English)
Zhu Yiqing; Hu Bin; Li Hui; Jiang Fengyun
2005-01-01
In this paper, the spatial-temporal gravity variation patterns of the northeastern margin of Qinghai-Xizang (Tibet) Plateau in 1992～ 2001 are modeled using bicubic spline interpolation functions and the relations of gravity change with seismicity and tectonic movement are discussed preliminarily. The results show as follows: ① Regionalgravitational field changes regularly and the gravity abnormity zone or gravity concentration zone appears in the earthquake preparation process; ② In the significant time period, the gravity variation shows different features in the northwest, southeast and northeast parts of the surveyed region respectively, with Lanzhou as its boundary; ③ The gravity variation distribution is basically identical to the strike of tectonic fault zone of the region, and the contour of gravity variation is closely related to the fault distribution.
Energy Technology Data Exchange (ETDEWEB)
Birchler, W.D.; Schilling, S.A.
2001-02-01
The purpose of this report is to demonstrate that modern computer-aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) systems can be used in the Department of Energy (DOE) Nuclear Weapons Complex (NWC) to design new and remodel old products, fabricate old and new parts, and reproduce legacy data within the inspection uncertainty limits. In this study, two two-dimensional splines are compared with several modern CAD curve-fitting modeling algorithms. The first curve-fitting algorithm is called the Wilson-Fowler Spline (WFS), and the second is called a parametric cubic spline (PCS). Modern CAD systems usually utilize either parametric cubic and/or B-splines.
Mittal, R. C.; Jain, R. K.
2012-12-01
In this paper, a numerical method is proposed to approximate the solution of the nonlinear parabolic partial differential equation with Neumann's boundary conditions. The method is based on collocation of cubic B-splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range. We apply cubic B-splines for spatial variable and its derivatives, which produce a system of first order ordinary differential equations. We solve this system by using SSP-RK3 scheme. The numerical approximate solutions to the nonlinear parabolic partial differential equations have been computed without transforming the equation and without using the linearization. Four illustrative examples are included to demonstrate the validity and applicability of the technique. In numerical test problems, the performance of this method is shown by computing L∞andL2error norms for different time levels. Results shown by this method are found to be in good agreement with the known exact solutions.
一种参数三次样条曲线光顺优化算法%An Optimal Fairing Algorithm for Parametric Cubic Spline Curves
Institute of Scientific and Technical Information of China (English)
章虎冬
2011-01-01
An optimal fairing algorithm for planar parametric cubic spline curves is proposed based on revising gene and revising angle. Faired point can be obtained by resolving a objective function of containing modifying gene λ and revising angle 9 and faired curves is obtained by interpolating the faired point. The purpose of this algorithm is to make the change of curvature of faired curves more gradual and its deviation from the initial curves smaller. It is shown that the algorithm is simply facile and needs a smaller calculation.%论文给出了一种基于修改因子和修改角度的平面参数三次样条曲线的优化光顺算法,该算法通过求解一个带有修改因子λ和修改角度θ的目标函数得到光顺后的型值点,插值光顺后的型值点得到光顺曲线.目的是使曲线的曲率变化均匀的同时,使光顺后的曲线与原曲线的偏差尽量小,此算法简单易行,计算量较小.
Quadratic vs cubic spline-wavelets for image representations and compression
Marais, P.C.; Blake, E.H.; Kuijk, A.A.M.
1997-01-01
The Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary transform data. The use of semi-orthogonal quadratic spline wavelets allows one
Quadratic vs cubic spline-wavelets for image representation and compression
Marais, P.C.; Blake, E.H.; Kuijk, A.A.M.
1994-01-01
The Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary ransform data. The use of semi-orthogonal quadratic spline wavelets allows one t
A kernel representation for exponential splines with global tension
Barendt, Sven; Fischer, Bernd; Modersitzki, Jan
2009-02-01
Interpolation is a key ingredient in many imaging routines. In this note, we present a thorough evaluation of an interpolation method based on exponential splines in tension. They are based on so-called tension parameters, which allow for a tuning of their properties. As it turns out, these interpolants have very many nice features, which are, however, not born out in the literature. We intend to close this gap. We present for the first time an analytic representation of their kernel which enables one to come up with a space and frequency domain analysis. It is shown that the exponential splines in tension, as a function of the tension parameter, bridging the gap between linear and cubic B-Spline interpolation. For example, with a certain tension parameter, one is able to suppress ringing artefacts in the interpolant. On the other hand, the analysis in the frequency domain shows that one derives a superior signal reconstruction quality as known from the cubic B-Spline interpolation, which, however, suffers from ringing artifacts. With the ability to offer a trade-off between opposing features of interpolation methods we advocate the use of the exponential spline in tension from a practical point of view and use the new kernel representation to qualify the trade-off.
Ozkaya, Sait Ismail
1995-08-01
Two short EXCEL function macros are presented for calculation of borehole deviation, true vertical thickness, and true stratigraphic thickness. The function macros can be used as regular EXCEL functions. The calling formula, arguments, and their type are described and application is demonstrated on an example data set. The borehole bearing and drift between any two observation points are estimated by fitting a cubic spline curve to three adjacent observation points at a time. The macro can cope with horizontal wells. The macro expects dip; dip direction at formation tops; and x, y, and z components of the distance from point P 1 to point P 2 where P 1 and P 2 are the intersections of the borehole with the top and bottom of a formation, respectively. The macro returns true stratigraphic thickness of formations. Coordinates of points P 1 and P 2 are obtained from the results returned by the macro.
A Taylor-Galerkin finite element method for the KdV equation using cubic B-splines
Energy Technology Data Exchange (ETDEWEB)
Canivar, Aynur [Cemal Mumtaz Teachers Training Anatolian High School, 26210 Eskisehir (Turkey); Sari, Murat, E-mail: msari@pau.edu.t [Department of Mathematics, Pamukkale University, Denizli 20070 (Turkey); Dag, Idris [Department of Computer Engineering, Eskisehir Osmangazi University, Eskisehir 26480 (Turkey)
2010-08-15
In this paper, to obtain accurate solutions of the Korteweg-de Vries (KdV) equation, a Taylor-Galerkin method is proposed based on cubic B-splines over finite elements. To tackle this a forward time-stepping technique is accepted in time. To see the accuracy of the proposed method, L{sub 2} and L{sub {infinity} }error norms are calculated in three test problems. The numerical results are found to be in good agreement with exact solutions and with the literature. The applied numerical method has also been shown to be unconditionally stable. In order to find out the physical behaviour of more intricate models, this procedure has been seen to have a great potentiality.
Fast and efficient evaluation of gravitational waveforms via reduced-order spline interpolation
Galley, Chad R
2016-01-01
Numerical simulations of merging black hole binaries produce the most accurate gravitational waveforms. The availability of hundreds of these numerical relativity (NR) waveforms, often containing many higher spherical harmonic modes, allows one to study many aspects of gravitational waves. Amongst these are the response of data analysis pipelines, the calibration of semi-analytical models, the building of reduced-order surrogates, the estimation of the parameters of detected gravitational waves, and the composition of public catalogs of NR waveform data. The large number of generated NR waveforms consequently requires efficient data storage and handling, especially since many more waveforms will be generated at an increased rate in the forthcoming years. In addition, gravitational wave data analyses often require the NR waveforms to be interpolated and uniformly resampled at high sampling rates. Previously, this resulted in very large data files (up to $\\sim$ several GB) in memory-intensive operations, which ...
Cubic spline symplectic algorithm for dynamic analysis of space truss structure%网架结构动力分析的三次样条辛算法
Institute of Scientific and Technical Information of China (English)
李纬华; 王堉; 罗恩
2013-01-01
According to the basic idea of dual-complementarity,the unconventional Hamilton-type variational principle in phase space for dynamic analysis of space truss structure was introduced,which can fully characterize this kind of dynamic initial-boundary-value problems.In addition,its Euler equation is of symplectic structure character.Based on this vairiational principle,a symplectic algorithm was presented,combining the finite element method in space domain with the time subdomain method,in which the cubic spline interpolation was applied as approximation.The results of numerical examples show that the method is a highly efficient method with better computational performance and superior ability of stability compared with Wilson-θ and Newmark-β methods.%根据对偶互补的思想,建立了网架结构动力学的相空间非传统Hamilton型变分原理.这种变分原理不仅能反映这种动力学初值-边值问题的全部特征,而且它的欧拉方程具有辛结构.基于该变分原理,空间域采用有限元法与时间子域采用三次样条函数插值的时间子域法相结合,构造了求解网架结构动力响应的一种辛算法,给出了逐步递推计算格式.数值算例结果表明,这种新方法的稳定性、计算精度和效率都明显高于Wilson-θ法和Newmark-β法.
Convexity of a Bivatiate Rational Interpolating Spline Funciton%一种二元有理插值样条函数的凸性
Institute of Scientific and Technical Information of China (English)
项梅灵; 唐月红
2012-01-01
通过研究一种基于函数值的(3,2)1阶二元有理插值样条函数中诸如边界插值、极限、解析和正则等性质,指出极限曲面是双曲抛物面,揭示了参数对这种插值曲面的影响.首先引入双8次矩阵表示的凸性判别函数,推导了判定插值曲面凸性的充要条件；然后根据该条件给出数值实例,展示如何适当选取参数实现有理插值样条曲面的局部保凸性.特别发现了这种插值曲面凸性在某些点处即使型值是凸的数据也是相对刚性的,并提出了插值曲面局部保凸的必要条件.最后还讨论了文献(Zhang Y,Duan Q,Twizell E H.Convexity control of a bivariate rational interpolating spline surfaces.Computers & Graphics,2007,31(5):679-687)中存在的部分计算问题.%The properties of a bivariate rational interpolating spline function of order (3,2)' , which is based on values of the function, including boundaries, limits, analysis, regularity and so forth are the key subject studied in this paper. First of all, the paper indicates that the limit surface is hyperbolic paraboloid and illuminates the influences of parameters on the rational interpolating spline surfaces. Secondly, the convex discriminant function expressed by dual 8 matrix has been introduced into the paper. Thirdly, the necessary and sufficient conditions for identifying the convexity of rational interpolation surfaces have been derived, while in accordance with which the examples, explaining how to choose appropriate parameters resulting in local convexity, are put forward to prove the validity of all above. Particularly, if is found that the convexity of the interpolation surfaces is relatively rigid at certain points, although the interpolated data is convex. Considering such situation, this paper has raised a necessary condition ensuring the local convexity of interpolation surfaces. What's more, this paper points out that some error results in literature [7] need to be discussed.
Curve interpolation based on Catmull-Clark subdivision scheme
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
An efficient algorithm for curve interpolation is proposed. The algorithm can produce a subdivision surface that can interpolate the predefined cubic B-spline curves by applying the Catmull-Clark scheme to a polygonal mesh containing "symmetric zonal meshes", which possesses some special properties. Many kinds of curve interpolation problems can be dealt with by this algorithm, such as interpolating single open curve or closed curve, a mesh of nonintersecting or intersecting curve. The interpolating surface is C2 everywhere excepting at a finite number of points. At the same time, sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of initial mesh, i.e. the surface is only C0 along the cubic B-spline curve that is defined by the tagged edges. Because of being simple and easy to implement, this method can be used for product shape design and graphic software development.
Lee, Seung Min; Choi, Eue Keun; Chung, Gih Sung; Oh, Seil; Park, Kwang Suk
2012-02-01
With the development of an implantable radio transmitter system, direct measurement of cardiac autonomic nervous activities (CANAs) became possible for ambulatory animals for a couple of months. However, measured CANAs include not only CANA but also cardiac electric activity (CEA) that can affect the quantification of CANAs. In this study, we propose a novel CEA removal method using moving standard deviation and cubic smoothing spline. This method consisted of two steps of detecting CEA segments and eliminating CEAs in detected segments. Using implanted devices, we recorded stellate ganglion nerve activity (SGNA), vagal nerve activity (VNA) and superior left ganglionated plexi nerve activity (SLGPNA) directly from four ambulatory dogs. The CEA-removal performance of the proposed method was evaluated and compared with commonly used high-pass filtration (HPF) for various heart rates and CANA amplitudes. Results tested with simulated CEA and simulated true CANA revealed stable and excellent performance of the suggested method compared to the HPF method. The averaged relative error percentages of the proposed method were less than 0.67%, 0.65% and 1.76% for SGNA, VNA and SLGPNA, respectively.
Institute of Scientific and Technical Information of China (English)
孙丽男; 张馥菊
2012-01-01
In order to improve the accuracy of water hammer equations, it is in this paper the cubic spline wavelet finite element method to solve the water hammer equation. This method meets the requirements of complex pipeline, but also with the characteristics of the cubic spline wavelet function to improve the accuracy, opened a new way and theoretical basis for the solution of the water hammer equations.%利用差分方法对一类输运问题在一维和二维空间中进行数值分析，得到相应数值解，并将数值解与解析解进行比较，且进一步分析了数值方法的有效性．
Survey: interpolation methods in medical image processing.
Lehmann, T M; Gönner, C; Spitzer, K
1999-11-01
Image interpolation techniques often are required in medical imaging for image generation (e.g., discrete back projection for inverse Radon transform) and processing such as compression or resampling. Since the ideal interpolation function spatially is unlimited, several interpolation kernels of finite size have been introduced. This paper compares 1) truncated and windowed sinc; 2) nearest neighbor; 3) linear; 4) quadratic; 5) cubic B-spline; 6) cubic; g) Lagrange; and 7) Gaussian interpolation and approximation techniques with kernel sizes from 1 x 1 up to 8 x 8. The comparison is done by: 1) spatial and Fourier analyses; 2) computational complexity as well as runtime evaluations; and 3) qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing. For local and Fourier analyses, a standardized notation is introduced and fundamental properties of interpolators are derived. Successful methods should be direct current (DC)-constant and interpolators rather than DC-inconstant or approximators. Each method's parameters are tuned with respect to those properties. This results in three novel kernels, which are introduced in this paper and proven to be within the best choices for medical image interpolation: the 6 x 6 Blackman-Harris windowed sinc interpolator, and the C2-continuous cubic kernels with N = 6 and N = 8 supporting points. For quantitative error evaluations, a set of 50 direct digital X rays was used. They have been selected arbitrarily from clinical routine. In general, large kernel sizes were found to be superior to small interpolation masks. Except for truncated sinc interpolators, all kernels with N = 6 or larger sizes perform significantly better than N = 2 or N = 3 point methods (p cubic 6 x 6 interpolator with continuous second derivatives, as defined in (24), can be recommended for most common interpolation tasks. It appears to be the fastest
Quartic Box-Spline Reconstruction on the BCC Lattice.
Kim, Minho
2013-02-01
This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice, the seven-direction quartic box-spline M7 that has the same approximation order as the eight-direction quintic box-spline M8 but a lower polynomial degree, smaller support, and is computationally more efficient. When applied to reconstruction with quasi-interpolation prefilters, M7 shows less aliasing, which is verified quantitatively by integral filter metrics and frequency error kernels. To visualize and analyze distributional aliasing characteristics, each spectrum is evaluated on the planes and lines with various orientations.
带多个形状参数的三次均匀B样条曲线的扩展%Extension of Uniform Cubic B-Spline Curves withMultiple Shape Parameters
Institute of Scientific and Technical Information of China (English)
夏成林; 邬弘毅; 郑兴国; 彭凯军
2011-01-01
通过构造两类带多个形状参数的调配函数,生成三次均匀B样条基函数的扩展.基于给出的调配函数定义了两类带多个形状参数的分段多项式曲线.这些曲线具有三次均匀B样条曲线的绝大多数重要性质,能达到GC1或GC2连续.改变形状参数的值可以独立地调控各子段的端点的位置及其切矢的长度,对曲线进行整体或局部调整,甚至直接插值任何所需的控制点.%Two classes of blending functions with multiple shape parameters are presented in this paper. They are the extension of uniform cubic B-spline basic functions. Based on the given blending functions, the piecewise polynomial curves with shape parameters are defined. These curves inherit the most properties of uniform cubic B-spline curves with GCl or GC2 continuity.The position and the length of tangent vector at the end points of curve segments can be independently controlled by changing the values of the shape parameters. These curves can be adjusted totally or locally and interpolated by any given control points.
C1 Hermite shape preserving polynomial splines in R3
Gabrielides, Nikolaos C.
2012-06-01
The C 2 variable degree splines1-3 have been proven to be an efficient tool for solving the curve shape-preserving interpolation problem in two and three dimensions. Based on this representation, the current paper proposes a Hermite interpolation scheme, to construct C 1 shape-preserving splines of variable degree. After this, a slight modification of the method leads to a C 1 shape-preserving Hermite cubic spline. Both methods can easily be developed within a CAD system, since they compute directly (without iterations) the B-spline control polygon. They have been implemented and tested within the DNV Software CAD/CAE system GeniE. [Figure not available: see fulltext.
RATIONAL QUADRATIC B-SPLINE INTERPOLATION OF FUNCTION SEGMENTS%函数的分段有理二次B样条插值
Institute of Scientific and Technical Information of China (English)
梁锡坤
2012-01-01
Based on the proper segmentation of complicated functions, the triangle convex hull of functions segment is introduced. We propose a scheme of control polygon determination by the tangent of the endpoints of the segment intervals. The algorithm of the segment rational quadratic B-spline interpolation of complicated functions is discussed in details. The interpolation keeps many important geometric features of the original function such as convexity, monotonicity and G1 continuity. The numerical experiments show that the algorithm provides an efficient approach to approximate representation of complicated functions.%0引 言 科学和工程计算中,函数的近似表示一直是一个重要课题.近似方法一般可归结为插值、逼近和拟合三种基本类型,经历长期发展,函数逼近方法[1-3]十分丰富.
二次B样条曲面顶点及法向插值%Interpolation of Vertices and Their Normal Vectors with Quadratic B-Spline Surfaces
Institute of Scientific and Technical Information of China (English)
李桂清; 李现民; 李华
2001-01-01
Interpolation to vertex positions is an essential issue in surface modeling, and interpolation to normal vectors has also important applications in some CAD/CAM areas. Properties of bi-quadratic B-spline surface are investigated by the subdivision approach, and the control mesh of bi-quadratic B-spline surface is constructed by employing Doo-Sabin subdivision to derive the parametric representation of interpolation surface. For enhancing the efficiency of handling mesh with larger scale data, we first partition the mesh into a number of sub-meshes and compute their corresponding control nets satisfying interpolatory conditions, then the sub-nets are integrated to form a whole net such that its bi-quadratic B-spline surface interpolates all given vertices and normal vectors.%顶点位置插值是自由曲面造型的基本方法，法向插值在一些CAD/CAM系统中也有重要应用．文中利用子分曲面理论研究双二次B样条曲面的性质，在此基础上利用Doo-Sabin子分模式构造插值顶点位置和法向的双二次B样条曲面控制网格，得到插值曲面的参数表示．为了提高效率，对规模较大的网格数据，先把它划分成若干片子网格，分别求出满足与子网格相关的插值条件的控制网格. 最后再把它们整合在一起形成完整的控制网格，使得相应的二次B样条曲面插值所有顶点及法向.
Bi-cubic non-uniform B-spline surface reconstruction for slice contours%断层轮廓的双三次非均匀B样条曲面重构
Institute of Scientific and Technical Information of China (English)
王瑜; 郑津津; 周洪军; 沈连婠
2011-01-01
A surface reconstruction method from the slice contours was proposed. First, feature points were extracted based on curvature feature, and they were resampled in order to get a unification of sampling points in each line (column). Then, the sampling points were interpolated to get a bi-cubic non-uniform B-spline surface. Finally, nodes were inserted on the surface based on distance feature at a certain control accuracy, and the new control points through the least-squares approximation method were calculated to get approximate surface within the permissible range error. Based on the characteristics of slice contours, B-spline cycle and non-cycle B-spline combined, and the calculation of closed and non-closed surface was discussed. It was found that the combination of interpolation and approximation makes the algorithm more rapid and practical.%针对断层图像数据,提出了一种曲面重构的方法.依据曲率特征首先提取各层特征点,对其重采样使每行(列)获得统一的采样点数;再对采样点插值得到非均匀双三次B样条曲面;最后,在一定控制精度下对曲面依据距离特征进行节点插入,通过最小二乘逼近法算出新的控制顶点,从而得到误差在容许范围内的逼近曲面.根据断层轮廓的特点,本算法综合运用了周期B样条和非周期B样条,讨论了封闭曲面和非封闭曲面的计算方法.另外插值和逼近的结合应用使该算法更快速、实用.
Penalized Spline: a General Robust Trajectory Model for ZIYUAN-3 Satellite
Pan, H.; Zou, Z.
2016-06-01
Owing to the dynamic imaging system, the trajectory model plays a very important role in the geometric processing of high resolution satellite imagery. However, establishing a trajectory model is difficult when only discrete and noisy data are available. In this manuscript, we proposed a general robust trajectory model, the penalized spline model, which could fit trajectory data well and smooth noise. The penalized parameter λ controlling the smooth and fitting accuracy could be estimated by generalized cross-validation. Five other trajectory models, including third-order polynomials, Chebyshev polynomials, linear interpolation, Lagrange interpolation and cubic spline, are compared with the penalized spline model. Both the sophisticated ephemeris and on-board ephemeris are used to compare the orbit models. The penalized spline model could smooth part of noise, and accuracy would decrease as the orbit length increases. The band-to-band misregistration of ZiYuan-3 Dengfeng and Faizabad multispectral images is used to evaluate the proposed method. With the Dengfeng dataset, the third-order polynomials and Chebyshev approximation could not model the oscillation, and introduce misregistration of 0.57 pixels misregistration in across-track direction and 0.33 pixels in along-track direction. With the Faizabad dataset, the linear interpolation, Lagrange interpolation and cubic spline model suffer from noise, introducing larger misregistration than the approximation models. Experimental results suggest the penalized spline model could model the oscillation and smooth noise.
Ozkaya, S. I.; Mattner, J.
1996-06-01
An EXCEL visual basic program is presented for modeling fault drag using cubic splines. The objective of the program is to estimate minimum dip and strike separation using dip measurements in the vicinity of a fault. The program is useful especially for estimating stratigraphic separation in the subsurface environment where only limited structural information is available from dipmeter logs. A modified cubic spline curve fitting procedure is used to model bedding trace within the fault drag zone. The solution procedure is based on the assumption that the dip angle is the same at equal distances away from the fault trace on a cross-section or map projection within the fault drag zone on the same side of the fault. On a cross-section perpendicular to the strike of a fault, the distance between the points of intersection of the fault trace with dragged bed and projection of the undisturbed bed gives half of the minimum dip separation. On a map projection, this distance is equal to half of the strike separation.
Spline energy method and its application in the structural analysis of antenna reflector
Wang, Deman; Wu, Qinbao
A method is proposed for analyzing combined structures consisting of shell and beam (rib) members. The cubic B spline function is used to interpolate the displacements and the total potential energy of the shell and the ribs. The equilibrium simultaneous equations can be obtained according to the principle of minimum potential energy.
Institute of Scientific and Technical Information of China (English)
祝恒佳; 严思杰; 刘学伟
2011-01-01
A method of modifying glass - shape curve based on cubic B - spline curve is studied. An algorithm of screening the effective data points in processing the sampling points is putted forward. As a result, the glass - shape curve can be generated by calculating the control points and interpolation. The curve can be modified directly by dragging the control point. And then calculate the space curve of the glass,and control the three axis linkage for molding movement. The algorithm effectively simplify the calculating process of modifying the glass - shape curve, and make the modifying convenience.%研究了一种基于三次B样条来进行镜框曲线修调策略.提出对镜框采样数据的有效型值点筛选算法,通过反求控制点、插值生成镜框平面曲线.直接通过拖动控制点来对平面曲线进行修调.进而计算镜框空间曲线,控制三轴联动来完成镜框成型运动.该算法能够有效简化曲线修调的计算过程,并使修调操作方便.
Assessing manual lifting tasks based on segment angle interpolations.
Chang, Chien-Chi; Xu, Xu; Faber, Gert S; Kingma, Idsart; Dennerlein, Jack
2012-01-01
This study investigates the effects of the number of interpolation points on the prediction accuracy of segment angle trajectory during lifting. Ten participants performed various lifting tasks while a motion tracking system recorded their movements. Two-point through ten-point equal time-spaced segment angles extracted from major segment trajectory data captured by the motion tracking system were used to re-generate the whole body lifting motion by using polynomial and cubic spline interpolation methods. The root mean square error (RMSE) between the reference (motion tracking system) and the estimated (interpolation method) segment angle trajectories were calculated to quantify the prediction accuracy. The results showed that the cubic spline interpolation will yield a smaller RMSE value than one based on the polynomial interpolation. While increasing the number of interpolation points can reduce the RMSE of the estimated segment angle trajectories, there was a diminishing advantage in continuing to add interpolation points. A sensitivity analysis suggests that if the estimation of the segment angles at each interpolation point deviates considerably from the real value, and cannot be controlled at a low level (interpolation points will not improve the estimation accuracy.
An Algorithm for Constructing Shape Preserving Cubic Spline Interpolation%保形三次B样条插值算法
Institute of Scientific and Technical Information of China (English)
方逵
2003-01-01
给定空间有序点列{Vi}ni=0,构造了一条三次B样条插值曲线,该曲线上的所有3n+1 个deBoor点由点列{Vi}ni=0直接计算产生.对于平面有序点列{Vi}ni=0,导出了该三次B样条插值曲线保形的一种算法,该算法中所有的deBoor点由点列{Vi}ni=0直接计算产生,避免了求解矢量方程.
The Convergence of Cubic Spline Interpolation%三次样条插值的收敛性
Institute of Scientific and Technical Information of China (English)
朱立勋; 魏萍
2006-01-01
本文在一些特殊条件下对三次样条插值的收敛性进行了讨论.给出了一个结论:设f(x)∈C[a,b],且f(x0)=f(xn),SΔn(x)是关于Δn的三次周期样条插值函数,对任何满足Δn0的分划序列Δn,limn∞‖SΔn(x)-f(x)‖=0成立的充分必要条件是f(x)∈LiP1,且当f(x)∈Lipk1时,有‖SΔn(x)-f(x)‖≤(5)/(4)kn.
A cubic interpolation pipeline for fast computation of 3D deformation fields modeled using B-splines
Castro-Pareja, Carlos R.; Shekhar, Raj
2006-02-01
Fast computation of 3D deformation fields is critical to bringing the application of automated elastic image registration algorithms to routine clinical practice. However, it lies beyond the computational power of current microprocessors; therefore requiring implementations using either massively parallel computers or application-specific hardware accelerators. The use of massively parallel computers in a clinical setting is not practical or cost-effective, therefore making the use of hardware accelerators necessary. We present a hardware pipeline that allows accelerating the computation of 3D deformation fields to speeds up to two orders of magnitude faster than software implementations on current workstations and about 64 times faster than other previously reported architectures. The pipeline implements a version of the free-form deformation calculation algorithm, which is optimized to minimize the number of arithmetic operations required to calculate the transformation of a given set of neighboring voxels, thereby achieving an efficient and compact implementation in hardware which allows its use as part of a larger system.
Data Visualization using Spline Functions
Directory of Open Access Journals (Sweden)
Maria Hussain
2013-10-01
Full Text Available A two parameter family of C1 rational cubic spline functions is presented for the graphical representation of shape preserving curve interpolation for shaped data. These parameters have a direct impact on the shape of the curve. Constraints are developed on one family of the parameters to visualize positive, monotone and convex data while other family of parameters can assume any positive values. The problem of visualization of constrained data is also addressed when the data is lying above a straight line and curve is required to lie on the same side of the line. The approximation order of the proposed rational cubic function is also investigated and is found to be O(h3 .
Spline Histogram Method for Reconstruction of Probability Density Functions of Clusters of Galaxies
Docenko, Dmitrijs; Berzins, Karlis
We describe the spline histogram algorithm which is useful for visualization of the probability density function setting up a statistical hypothesis for a test. The spline histogram is constructed from discrete data measurements using tensioned cubic spline interpolation of the cumulative distribution function which is then differentiated and smoothed using the Savitzky-Golay filter. The optimal width of the filter is determined by minimization of the Integrated Square Error function. The current distribution of the TCSplin algorithm written in f77 with IDL and Gnuplot visualization scripts is available from www.virac.lv/en/soft.html.
Spline histogram method for reconstruction of probability density function of clusters of galaxies
Docenko, D; Docenko, Dmitrijs; Berzins, Karlis
2003-01-01
We describe the spline histogram algorithm which is useful for visualization of the probability density function setting up a statistical hypothesis for a test. The spline histogram is constructed from discrete data measurements using tensioned cubic spline interpolation of the cumulative distribution function which is then differentiated and smoothed using the Savitzky-Golay filter. The optimal width of the filter is determined by minimization of the Integrated Square Error function. The current distribution of the TCSplin algorithm written in f77 with IDL and Gnuplot visualization scripts is available from http://www.virac.lv/en/soft.html
About a family of C2 splines with one free generating function
Directory of Open Access Journals (Sweden)
Igor Verlan
2005-01-01
Full Text Available The problem of interpolation of discrete set of data on the interval [a, b] representing the function f is investigated. A family of C*C splines with one free generating function is introduced in order to solve this problem. Cubic C*C splines belong to this family. The required conditions which must satisfy the generating function in order to obtain explicit interpolants are presented and examples of generating functions are given. Mathematics Subject Classification: 2000: 65D05, 65D07, 41A05, 41A15.
Directory of Open Access Journals (Sweden)
Hannu Olkkonen
2013-01-01
Full Text Available In this work we introduce a new family of splines termed as gamma splines for continuous signal approximation and multiresolution analysis. The gamma splines are born by -times convolution of the exponential by itself. We study the properties of the discrete gamma splines in signal interpolation and approximation. We prove that the gamma splines obey the two-scale equation based on the polyphase decomposition. to introduce the shift invariant gamma spline wavelet transform for tree structured subscale analysis of asymmetric signal waveforms and for systems with asymmetric impulse response. Especially we consider the applications in biomedical signal analysis (EEG, ECG, and EMG. Finally, we discuss the suitability of the gamma spline signal processing in embedded VLSI environment.
Control theory and splines, applied to signature storage
Enqvist, Per
1994-01-01
In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix.
Maltsev, I A; Tupitsyn, I I; Shabaev, V M; Kozhedub, Y S; Plunien, G; Stoehlker, Th
2013-01-01
A new approach for solving the time-dependent two-center Dirac equation is presented. The method is based on using the finite basis set of cubic Hermite splines on a two-dimensional lattice. The Dirac equation is treated in rotating reference frame. The collision of U92+ (as a projectile) and U91+ (as a target) is considered at energy E_lab=6 MeV/u. The charge transfer probabilities are calculated for different values of the impact parameter. The obtained results are compared with the previous calculations [I. I. Tupitsyn et al., Phys. Rev. A 82, 042701 (2010)], where a method based on atomic-like Dirac-Sturm orbitals was employed. This work can provide a new tool for investigation of quantum electrodynamics effects in heavy-ion collisions near the supercritical regime.
Application of Piecewise Cubic B-Spline%过两端点分段三次 B 样条方法应用研究*
Institute of Scientific and Technical Information of China (English)
王争争
2015-01-01
通过引入约束点 P0和常量 r，构建过两端点分段三次B样条曲线并推出衔接点光滑衔接条件。应用过两端点分段三次B样条方法可以构建直线、三角形、四边形及蛋形画法，并通过消齿光顺得到理想效果。实现图形的平移、缩放和旋转，通过逆时针、顺时针旋转计算消除偏差，保形效果理想。按顺时针方向生成闭曲线并记录轨迹点位置数据，方便平面上闭曲线对象间关系的计算，并得到布尔运算结果。应用该方法可以构建空间图形，实现颜色渐变效果理想。%By introducing the constraint point P0 and constant r ,two endpoints piecewise cubic B spline curve is built and some smooth cohesion terms are introduced .Application of two endpoints piecewise cubic B spline method can build straight lines ,triangles ,quadrilateral and egg painting .Through the elimination of tooth smoothing ,ideal effect is got . Translation ,scaling and rotation of graphics are achieved and eliminated by counterclockwise ,clockwise calculation devia‐tion ,conformal effect is ideal .Clockwise to generate closed curve trajectory point location and record data ,convenient plane closed curve calculation of relations between objects ,Boolean calculation results are obtained .The method can build space graphics ,make color gradient effect ideal .
Nakashima, Eiji
2015-07-01
Using the all solid cancer mortality data set of the Life Span Study (LSS) cohort from 1950 to 2003 (LSS Report 14) data among atomic bomb survivors, excess relative risk (ERR) statistical analyses were performed using the second degree polynomial and the threshold and restricted cubic spline (RCS) dose response models. For the RCS models with 3 to 7 knots of equally spaced percentiles with margins in the dose range greater than 50 mGy, the dose response was assumed to be linear at less than 70 to 90 mGy. Due to the skewed dose distribution of atomic bomb survivors, the current knot system for the RCS analysis results in a detailed depiction of the dose response as less than approximately 0.5 Gy. The 6 knot RCS models for the all-solid cancer mortality dose response of the whole dose or less than 2 Gy were selected with the AIC model selection criterion and fit significantly better (p < 0.05) than the linear (L) model. The usual RCS includes the L-global model but not the quadratic (Q) nor linear-quadratic (LQ) global models. The authors extended the RCS to include L or LQ global models by putting L or LQ constraints on the cubic spline in the lower and upper tails, and the best RCS model selected with AIC criterion was the usual RCS with L-constraints in both the lower and upper tails. The selected RCS had a linear dose-response model in the lower dose range (i.e., < 0.2-0.3 Gy) and was compatible with the linear no-threshold (LNT) model in this dose range. The proposed method is also useful in describing the dose response of a specific cancer or non-cancer disease incidence/mortality.
Institute of Scientific and Technical Information of China (English)
李军成
2011-01-01
The traditional method for constructing identical slope surface is under the premise that exact expression of lead curve is known. But in practical engineering, the exact expression of lead curve is hard to obtain, and only some measured data points of the lead curve are given. For solving that problem, a method of constructing the identical slope surface in engineering is presented in this paper. Firstly, cubic parametric spline interpolation curve is constructed according to the measured data points, which is regarded as the lead curve. Then, the parametric equation of identical slope gradient surface is constructed based on the forming principle of that surface. Lastly, an example is presented to show the method is feasible and effectual.%传统的同坡曲面构造方法都是在导线方程为已知的前提下进行的.然而在实际工程中,导线方程往往是很难得到的,只能通过测量得知导线通过一列数据点.针对这一问题,给出了一种实际工程中同坡曲面的构造方法,该法首先根据测量数据点,利用三次参数样条曲线插值方法构造出同坡曲面的导线方程,然后再从同坡曲面的形成原理入手建立其参数方程,最后通过实例表明该方法是可行有效的.
Institute of Scientific and Technical Information of China (English)
成贤锴; 顾国刚; 陈琦; 于涌
2014-01-01
It is difficult and inefficient for an industrial robot to move along a particular complex track by teaching programming, for the control system is closed and independent. Thus, waiting process trajectory is planned in the image of workpiece surface. According to cubic B-spline interpolation algorithm, it needs some data processing to the planned trajectory path. Then, the format of data points converts to robot lan-guage by off-line programming. Complex curvilinear motion of industrial robot divides to linear motion and circular motion. During the experiment, the robot moves smoothly, and actual trajectory and planning traj-ectory are highly consistent. And the experimental results prove that the method is feasible.%工业机器人的控制系统是封闭且独立的，通过示教方式来在线编程是很难完成复杂的曲线运动，效率较低。为此在工件面型图像中对待加工轨迹进行规划，根据三次B样条曲线插值算法对规划好的加工路径轨迹进行数据处理，通过离线编程把加工轨迹数据点格式转换成机器人程序文件，把复杂的曲线运动分解成直线运动和圆弧运动，从而实现工业机器人的复杂曲线运动。实验过程中机器人运动流畅没有停顿，实际运动轨迹和规划运动轨迹吻合得很好，证明该方法有效可行。
Barton, Michael
2016-07-21
We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature rules we recently derived (Bartoň and Calo, 2016) act on spaces of the smallest odd degrees and, therefore, are still slightly sub-optimal. In this work, we derive optimal rules directly for even-degree spaces and therefore further improve our recent result. We use optimal quadrature rules for spaces over two elements as elementary building blocks and use recursively the homotopy continuation concept described in Bartoň and Calo (2016) to derive optimal rules for arbitrary admissible numbers of elements.We demonstrate the proposed methodology on relevant examples, where we derive optimal rules for various even-degree spline spaces. We also discuss convergence of our rules to their asymptotic counterparts, these are the analogues of the midpoint rule of Hughes et al. (2010), that are exact and optimal for infinite domains.
Constrained reverse diffusion for thick slice interpolation of 3D volumetric MRI images.
Neubert, Aleš; Salvado, Olivier; Acosta, Oscar; Bourgeat, Pierrick; Fripp, Jurgen
2012-03-01
Due to physical limitations inherent in magnetic resonance imaging scanners, three dimensional volumetric scans are often acquired with anisotropic voxel resolution. We investigate several interpolation approaches to reduce the anisotropy and present a novel approach - constrained reverse diffusion for thick slice interpolation. This technique was compared to common methods: linear and cubic B-Spline interpolation and a technique based on non-rigid registration of neighboring slices. The methods were evaluated on artificial MR phantoms and real MR scans of human brain. The constrained reverse diffusion approach delivered promising results and provides an alternative for thick slice interpolation, especially for higher anisotropy factors.
Energy Technology Data Exchange (ETDEWEB)
M Ali, M. K., E-mail: majidkhankhan@ymail.com, E-mail: eutoco@gmail.com; Ruslan, M. H., E-mail: majidkhankhan@ymail.com, E-mail: eutoco@gmail.com [Solar Energy Research Institute (SERI), Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Muthuvalu, M. S., E-mail: sudaram-@yahoo.com, E-mail: jumat@ums.edu.my; Wong, J., E-mail: sudaram-@yahoo.com, E-mail: jumat@ums.edu.my [Unit Penyelidikan Rumpai Laut (UPRL), Sekolah Sains dan Teknologi, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah (Malaysia); Sulaiman, J., E-mail: ysuhaimi@ums.edu.my, E-mail: hafidzruslan@eng.ukm.my; Yasir, S. Md., E-mail: ysuhaimi@ums.edu.my, E-mail: hafidzruslan@eng.ukm.my [Program Matematik dengan Ekonomi, Sekolah Sains dan Teknologi, Universiti Malaysia Sabah, 88400 Kota Kinabalu, Sabah (Malaysia)
2014-06-19
The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m{sup 2} and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R{sup 2}), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.
M Ali, M. K.; Ruslan, M. H.; Muthuvalu, M. S.; Wong, J.; Sulaiman, J.; Yasir, S. Md.
2014-06-01
The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m2 and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R2), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.
Howarth, Samuel J; Callaghan, Jack P
2010-12-01
Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11-90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7 mm (LCS); 0.29 mm (spline); 0.42 mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3 mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200 ms. Spline interpolation was superior for shorter durations.
Cubic Spline - wavelet Finite Element Method for Solving the Water Hammer Equation%三次样条小波有限元法求解水锤方程
Institute of Scientific and Technical Information of China (English)
陈辉
2012-01-01
In order to improve the accuracy of water hammer equations, it is in this paper the cubic spline wavelet finite element method to solve the water hammer equation. This method meets the requirements of complex pipeline, but also with the characteristics of the cubic spline wavelet function to improve the accuracy, opened a new way and theoretical basis for the solution of the water hammer equations.%为了提高水锤方程的求解精确度，采用三次样条小波有限元法求解水锤方程，此法既能满足复杂管道的要求，又能借助三次样条小波函数的特点提高计算精度．为水锤方程的解法开辟了一条新的途径和理论依据．
Directory of Open Access Journals (Sweden)
Xiaogang Ji
2014-01-01
Full Text Available In the process of curves and surfaces fairing with multiresolution analysis, fairing accuracy will be determined by final fairing scale. On the basis of Dyadic wavelet fairing algorithm (DWFA, arbitrary resolution wavelet fairing algorithm (ARWFA, and corresponding software, accuracy control of multiresolution fairing was studied for the uncertainty of fairing scale. Firstly, using the idea of inverse problem for reference, linear hypothesis was adopted to predict the corresponding wavelet scale for any given fairing error. Although linear hypothesis has error, it can be eliminated by multiple iterations. So faired curves can be determined by a minimum number of control vertexes and have the best faring effect under the requirement of accuracy. Secondly, in consideration of efficiency loss caused by iterative algorithm, inverse calculation of fairing scale was presented based on the least squares fitting. With the increase of order of curves, inverse calculation accuracy becomes higher and higher. Verification results show that inverse calculation scale can meet the accuracy requirement when fitting curve is sextic. In the whole fairing process, because there is no approximation algorithm such as interpolation and approximation, faired curves can be reconstructed again exactly. This algorithm meets the idea and essence of wavelet analysis well.
Tai, Chiew-Lan; Wang, Guo-Jin
2004-12-01
This paper presents a new interpolation method that enables the construction of C2 cubic polynomial spline curves without solving a global system of equations, while providing slackness/continuity control and convexity preserving ability. The basic idea is to blend a cubic B-spline curve with a singularly parametrized sequence of connected line segments. A global slackness parameter controls the tautness, specifically the distance between the interpolating curve and the linear interpolant. The order of continuity at each knot is controlled via multiple knot insertions so that cusps and straight-line segments can be conveniently prescribed. In addition, a method for selecting local slackness values to produce G1 convexity preserving curve is presented. With the low-degree polynomials and direct computation of control vertices, this local method is computationally simple and is useful for interactive shape design and computer graphics applications.
Institute of Scientific and Technical Information of China (English)
吴宪祥; 郭宝龙; 王娟
2009-01-01
针对移动机器人路径规划问题,提出了一种基于粒了群三次样条优化的路径规划方法.借助三次样条连接描述路径,这样将路径规划问题转化为三次样条曲线的参数优化问题.借助粒了群优化算法快速收敛和全局寻优特性实现最优路径规划.实验结果表明:所提算法町以快速有效地实现障碍环境下机器人的无碰撞路径规划,规划路径平滑,利于机器人的运动控制.%A novel algorithm based on particle swarm optimization (PSO) of cubic splines is proposed for mobile robot path planning. The path is described by string of cubic splines, thus the path planning is equivalent to parameter optimization of particular cubic splines. PSO is introduced to get the optimal path for its fast convergence and global search character. Ex-perimental results show that a collision-avoidance path can be found fleetly and effectively among obstacles by the proposed algorithm. The planned path is smooth which is useful for robot motion control.
Evaluation of solid–liquid interface profile during continuous casting by a spline based formalism
Indian Academy of Sciences (India)
S K Das
2001-08-01
A numerical framework has been applied which comprises of a cubic spline based collocation method to determine the solid–liquid interface profile (solidification front) during continuous casting process. The basis function chosen for the collocation algorithm to be employed in this formalism, is a cubic spline interpolation function. An iterative solution methodology has been developed to track the interface profile for copper strand of rectangular transverse section for different casting speeds. It is based on enthalpy conservation criteria at the solidification interface and the trend is found to be in good agreement with the available information in the literature although a point to point mapping of the profile is not practically realizable. The spline based collocation algorithm is found to be a reasonably efficient tool for solidification front tracking process, as a good spatial derivative approximation can be achieved incorporating simple modelling philosophy which is numerically robust and computationally cost effective.
B-spline image model for energy minimization-based optical flow estimation.
Le Besnerais, Guy; Champagnat, Frédéric
2006-10-01
Robust estimation of the optical flow is addressed through a multiresolution energy minimization. It involves repeated evaluation of spatial and temporal gradients of image intensity which rely usually on bilinear interpolation and image filtering. We propose to base both computations on a single pyramidal cubic B-spline model of image intensity. We show empirically improvements in convergence speed and estimation error and validate the resulting algorithm on real test sequences.
Mathematical research on spline functions
Horner, J. M.
1973-01-01
One approach in spline functions is to grossly estimate the integrand in J and exactly solve the resulting problem. If the integrand in J is approximated by Y" squared, the resulting problem lends itself to exact solution, the familiar cubic spline. Another approach is to investigate various approximations to the integrand in J and attempt to solve the resulting problems. The results are described.
Institute of Scientific and Technical Information of China (English)
李军成; 刘成志; 易叶青
2016-01-01
针对三次 Cardinal 样条与 Catmull-Rom 样条的不足，提出带形状因子的 C2连续五次 Cardinal 样条与Catmull-Rom样条。首先构造一组带2个形状因子的五次Cardinal样条基函数；然后基于该组基函数定义带形状因子的五次 Cardinal 样条曲线与曲面，并讨论五次 Cardinal 样条函数的保单调插值；最后研究对应的一元与二元五次Catmull-Rom样条插值函数，并给出最优一元与二元五次Catmull-Rom样条插值函数的确定方法。实例结果表明，五次Cardinal样条与Catmull-Rom样条无需任何条件即可达到C2连续，且其形状还可通过自带的形状因子进行灵活地调整，利用最优五次Catmull-Rom样条插值函数可获得满意的插值效果。%In view of the deficiency of the cubic Cardinal spline and Catmull-Rom spline, theC2 continuous quintic Cardinal spline and Catmull-Rom spline with shape factors are presented in this paper. First, a class of quitic Cardinal spline basis functions with two shape factors is constructed. Then, the quintic Cardinal spline curves and surfaces with shape factors are defined on base of the proposed basis functions, and the monotonicity-preserving interpolation with the quintic Cardinal spline function is discussed. Finally, the corresponding one dimensional and two dimensional quintic Catmull-Rom spline interpolation functions are studied, and the method of determining the optimal one dimensional and two dimensional quintic Cat-mull-Rom spline interpolation functions are given. Example results show that, the quintic Cardinal spline and Catmull-Rom spline can not only beC2 continuous without any conditions, but also can be flexibly ad-justed by the shape factors. Satisfactory interpolation results can be obtained by using the optimal quintic Catmull-Rom spline interpolation functions.
三次B样条曲线拟合的虹膜定位%Iris Localization Algorithm Based on Cubic B-spline Curve Fitting
Institute of Scientific and Technical Information of China (English)
叶永强; 沈建新; 周啸; 张敏
2011-01-01
采用圆检测定位虹膜内外边界的方法是当前虹膜定位的主流算法.当虹膜图像分辨率很高时,圆曲线不能准确地拟合虹膜真实边界,特别是受瞳孔收缩影响很大的内边界.而采用三次B样条曲线能够很好地拟合内边界.为了提高定位效率,首先运用质心探测方法分割出瞳孔区域,然后在瞳孔区域中搜索内边界点,采用三次B样条曲线精确拟合内边界；最后利用Canny算子检测外边界,并采用圆曲线的最小二乘拟合外边界.运用Bath大学虹膜库中的1000幅虹膜图像对该定位算法进行测试,内边界定位时间0.0203s、准确率99.2％；外边界定位时间2.0277s,准确率98.9％,满足准确、高效的定位要求.%The current important methods of iris localization are based on circle detection. But they could not fit the real boundary well when iris images are high-resolution, especially the inner boundary under the influence of pupil constriction. Proposed method based on cubic B-spline curve can figure out this problem. It locates the inner boundary area first, and then the outer boundary. To improve the efficiency and robustness for inner boundary localization, this paper has proposed a method to segment the pupil area first based centroid detection, then search inner edge in the segmented area. The outer boundary area is then determined by using Ihe parameter relations between inner and outer boundary. Finally, using canny operator delects the outer edge, and the outer boundary is fitted in the Least-square circle sense. The Experiment results based on the iris database of Bath University, with 99.2% accuracy and 0.022s positioning time of inner boundary, 98.9% and 2.027s of outer show that the proposed approach is efficient and robust.
Numerical solution of Poisson equation by quintic B-spline interpolation%均匀二型剖分下的二元五次B样条基函数及其应用
Institute of Scientific and Technical Information of China (English)
张胜刚; 宋明威; 王仁宏; 李国荣; 唐晓; 刘启贵
2012-01-01
1975年王仁宏建立了任意剖分下多元样条函数的基本理论框架,即所谓光滑余因子方法.多元样条在函数逼近、计算机辅助几何设计、有限元及小波等领域中均有重要的应用.由于某些特殊剖分如均匀剖分的可研究性,1984年王仁宏给出均匀二型剖分下的二元三次一阶光滑样条空间S1((△(2)mn))的维数及其B样条基函数,在计算机辅助几何设计,微分方程数值解等方面应用广泛.在研究光滑余因子方法的基础上,分析均匀二型剖分下的二元五次三阶光滑样条空间(S35)((△(2)mn))函数空间,给出了(S35)((△(2)mn))的维数及其B样条基函数,满足曲面拟合和微分方程数值解等应用中对更高阶光滑性的要求.基于该组基函数,提出一种Poisson方程的数值解方法,通过数值实例检验该方法的精度.%Multivariate splines have wide applications in approximation theory, computer aided geometric design(CAGD) and finite element method. In 1975, Ren-Hong Wang established a new approach to study the basic theory on multivariate spline functions on arbitrary partition by presenting the so called Smoothing cofactor-conformality method. As the large applications in CAGD et al. , Ren-Hong Wang discussed the dimension and B-spline basis of the C1 cubic spline spaces on type-2 triangulation partition, which is denoted by S31(△(2)mn). Accordingly we analyze the C3 quintic spline spaces on type-2 triangulation partition S53 (△(2)mn). The dimension and one group of B spline basis of S53(△(2)mn)are given. High derivatives is satisfied in applications. Based on the basis one numerical scheme is proposed to simulate the Poisson equation. Numerical examples are given to show the validity of the scheme.
Xu, Xu; Chang, Chien-Chi; Faber, Gert S; Kingma, Idsart; Dennerlein, Jack T
2010-07-20
Video-based field methods that estimate L5/S1 net joint moments from kinematics based on interpolation in the sagittal plane of joint angles alone can introduce a significant error on the interpolated joint angular trajectory when applied to asymmetric dynamic lifts. Our goal was to evaluate interpolation of segment Euler angles for a wide range of dynamic asymmetric lifting tasks using cubic spline methods by comparing the interpolated values with the continuous measured ones. For most body segments, the estimated trajectories of segment Euler angles have less than 5 degrees RMSE (in each dimension) with 5-point cubic spline interpolation when there is no measurement error of interpolation points. Sensitivity analysis indicates that when the measurement error exists, the root mean square error (RMSE) of estimated trajectories increases. Comparison among different lifting conditions showed that lifting a load from a high initial position yielded a smaller RMSE than lifting from a low initial position. In conclusion, interpolation of segment Euler angles can provide a robust estimation of segment angular trajectories during asymmetric lifting when measurement error of interpolation points can be controlled at a low level.
Vibration Analysis of Rectangular Plates with One or More Guided Edges via Bicubic B-Spline Method
Directory of Open Access Journals (Sweden)
W.J. Si
2005-01-01
Full Text Available A simple and accurate method is proposed for the vibration analysis of rectangular plates with one or more guided edges, in which bicubic B-spline interpolation in combination with a new type of basis cubic B-spline functions is used to approximate the plate deflection. This type of basis cubic B-spline functions can satisfy simply supported, clamped, free, and guided edge conditions with easy numerical manipulation. The frequency characteristic equation is formulated based on classical thin plate theory by performing Hamilton's principle. The present solutions are verified with the analytical ones. Fast convergence, high accuracy and computational efficiency have been demonstrated from the comparisons. Frequency parameters for 13 cases of rectangular plates with at least one guided edge, which are possible by approximate or numerical methods only, are presented. These results are new in literature.
Baldi, Antonio; Bertolino, Filippo
2013-10-01
It is well known that displacement components estimated using digital image correlation are affected by a systematic error due to the polynomial interpolation required by the numerical algorithm. The magnitude of bias depends on the characteristics of the speckle pattern (i.e., the frequency content of the image), on the fractional part of displacements and on the type of polynomial used for intensity interpolation. In literature, B-Spline polynomials are pointed out as being able to introduce the smaller errors, whereas bilinear and cubic interpolants generally give the worst results. However, the small bias of B-Spline polynomials is partially counterbalanced by a somewhat larger execution time. We will try to improve the accuracy of lower order polynomials by a posteriori correcting their results so as to obtain a faster and more accurate analysis.
Regional Ionosphere Mapping with Kriging and B-spline Methods
Grynyshyna-Poliuga, O.; Stanislawska, I. M.
2013-12-01
This work demonstrates the concept and practical examples of mapping of regional ionosphere, based on GPS observations from the EGNOS Ranging and Integrity Monitoring Stations (RIMS) network and permanent stations near to them. Interpolation/prediction techniques, such as kriging (KR) and the cubic B-spline, which are suitable for handling multi-scale phenomena and unevenly distributed data, were used to create total electron content (TEC) maps. Their computational efficiency (especially the B-spline) and the ability to handle undersampled data (especially kriging) are particularly attractive. The data sets have been collect into seasonal bins representing June, December solstices and equinox (March, September). TEC maps have a spatial resolution of 2.50 and 2.50 in latitude and longitude, respectively, and a 15-minutes temporal resolution. The time series of the TEC maps can be used to derive average monthly maps describing major ionospheric trends as a function of time, season, and spatial location.
带有切线多边形的三次B样条的α扩展曲线%α extension of the cubic B-spline curve with given tangent polygon
Institute of Scientific and Technical Information of China (English)
王成伟
2011-01-01
为了使三次均匀B样条的α扩展曲线与给定多边形相切,构造了一种与给定多边形相切的三次均匀B样条曲线的α扩展的算法.在算法中,所有的三次均匀B样条的α扩展曲线的控制点可以通过对多边形的顶点简单计算产生.所构造的曲线对多边形具有保形性,曲线可以局部修改.最后给出了2个算例.%In order to a expansion of the cubic uniform B-spline curve tangent to the given polygon,in this paper, an algorithm for constructing α extension of the cubic uniform B-spine curve which is tangent to the given polygon is described. The control points of α extension of the cubic uniform B-spine curve to be constructed are computed simply by the vertices of the given polygon. The constructed curve is shape-preserving to the polygon. The local modification to a extension of the cubic uniform B-spine curve can be completed by simply adjusting the corresponding control parameters. Two examples are included.
Subpixel shift with Fourier transform to achieve efficient and high-quality image interpolation
Chen, Qin-Sheng; Weinhous, Martin S.
1999-05-01
A new approach to image interpolation is proposed. Different from the conventional scheme, the interpolation of a digital image is achieved with a sub-unity coordinate shift technique. In the approach, the original image is first shifted by sub-unity distances matching the locations where the image values need to be restored. The original and the shifted images are then interspersed together, yielding an interpolated image. High quality sub-unity image shift which is crucial to the approach is accomplished by implementing the shift theorem of Fourier transformation. It is well known that under the Nyquist sampling criterion, the most accurate image interpolation can be achieved with the interpolating function (sinc function). A major drawback is its computation efficiency. The present approach can achieve an interpolation quality as good as that with the sinc function since the sub-unity shift in Fourier domain is equivalent to shifting the sinc function in spatial domain, while the efficiency, thanks to the fast Fourier transform, is very much improved. In comparison to the conventional interpolation techniques such as linear or cubic B-spline interpolation, the interpolation accuracy is significantly enhanced. In order to compensate for the under-sampling effects in the interpolation of 3D medical images owing to a larger inter-slice distance, proper window functions were recommended. The application of the approach to 2- and 3-D CT and MRI images produced satisfactory interpolation results.
B-splines on 3-D tetrahedron partition in four-directional mesh
Institute of Scientific and Technical Information of China (English)
SUN; Jiachang
2001-01-01
［1］ de Boor, C., Hllig, K., Riemannschneider, S. D., Box Splines, New York: Springer-Verlag, 1993.［2］ Dahmen, W., Micchelli, C. A., Recent Process in Multivariate Splines, Interpolating Cardinal Splines as Their Degree Tends to Infinity (ed. Ward, J.), New York: Academic Press, 1983, 27.［3］ de Boor, C., Topics in multivariate approximation theory, in Topics in Numerical Analysis, Lecture Notes in Mathematics (ed. Turner, P. R.), Vol. 965, New York: Springer-Verlag, 1982, 39.［4］ de Boor, C., B-form basics, in Geometric Modelling (ed. Farin, G.), Philadephia: SIAM, 1987, 131.［5］ Chui, C. K., Wang, R. H., Spaces of bivariate cubic and quartic splines on type-1 triangulations, J. Math. Anal. Appl., 1984, 101: 540.［6］ Jia, R. Q., Approximation order from certain spaces of smooth bivariate splines on a three-direction mesh, Trans. AMS, 1986, 295: 199.［7］ Dahmen, W., On multivariate B-splines, SIAM J. Numer. Anal., 1980, 17: 179.［8］ Sun Jiachang, The B-net structure and recurrence algorithms for B-splines on a three direction mesh, Mathematica Numerica Sinica, 1990, 12: 365.［9］ Sun Jiachang, Some results on the field of spline theory and its applications, Contemporary Mathematics, 1994, 163: 127.［10］ Sun Jiachang, Dual bases and quasi-interpolation of B-splines on S13 with three direction meshes, Acta Mathematicae Applicatae Sinica, 1991, 14: 170.［11］ Wang, R. H., He, T. X., Liu, X. Y. Et al., An integral method for constructing bivariate spline functions, J. Comp. Math., 1989, 7: 244.［12］ Wang, R. H., Shi, X. Q., A kind of C interpolation in the n-dimensional finite element method, J. Math. Res. And Exp., 1989, 9: 173.［13］ Shi, X. Q., Wang, R. H., The existence conditions of space S12(Δn), Chinese Science Bulletin, 1989, 34: 2015.
基于三次B样条函数的话务量预测模型%Traffic Prediction Model Based on Cubic B Spline Interpolation
Institute of Scientific and Technical Information of China (English)
熊春波; 郭军峰
2009-01-01
针对某移动通信服务公司话务量预测的实际问题,利用三次B样条函数插值方法,建立了工作日和假日话务量预测模型,求解得出了移动电话的话务量随时间变化的规律性,并在某通信服务公司的话务量预测中得到了具体应用,结果是有效的.
Cubic B-spline interpolation for one-dimensional search method%一维搜索问题的三次B样条插值法
Institute of Scientific and Technical Information of China (English)
罗煦琼
2008-01-01
基于一元三次B样条函数插值, 给出了一种求解一维搜索问题的新算法和数值实验结果. 结果表明,新算法能很快地求出全局最优解, 且剖分数越大, 精度越高.
一个关于三次样条插值收敛性的证明%The Convergence of Cubic Spline Interpolation
Institute of Scientific and Technical Information of China (English)
朱立勋; 安玉萍
2007-01-01
在一些特殊条件下,对三次样条插值的收敛性进行了讨论.给出了一个结论:设f(x)∈C[a,b],且f(x0)＝f(xn),SΔn(x)是关于Δn的三次周期样条插值函数,对任何满足的(Δ－)n→0分划序列Δn,limn→∞‖SΔn(x)-f(x)‖＝0成立的充分必要条件是f(x)∈Lip1,且当f(x)∈Lipk1时,有‖SΔn(x)-f(x)‖(5)/(4)k(Δ－)n.
带法向约束的3次均匀B样条曲线插值%Cubic uniform B-spline curves interpolation with normal constrains
Institute of Scientific and Technical Information of China (English)
胡巧莉; 寿华好
2014-01-01
基于3次均匀B样条曲线段的端点性质,及其与控制顶点构成的三角形的几何关系,提出了一种插值给定顶点与法向约束的3次均匀B样条曲线构造算法.与以往B样条曲线的顶点法向插值算法不同的是,本算法结合由控制顶点构成的三角形的几何性质求解新添加的控制顶点,可生成严格插值型值点并且在型值点处法向与给定法向无偏移的B样条曲线.
Institute of Scientific and Technical Information of China (English)
梁锡坤
2011-01-01
为了丰富和发展B样条曲线理论,利用曲线线性组合的思想,将3次均匀B样条曲线进行了拓展,并讨论了拓展曲线的性质.研究表明,拓展曲线的基具有较简单的表达式;拓展曲线包含了原曲线的基本形式,比原曲线具有更强的描述能力,且保持曲线次数不变.利用曲线的形状因子可以调整曲线的局部形状;同时得到了一种闭曲线表示的新途径.%In order to develop the theory of B-spline curve, the representation of cubic uniform B-spline curve is extended to a general form based on linear combination of curves.Moreover, some properties of the extended curve are discussed in details.The research shows that the basis of the generalized curve is relative simple, and the extended curve includes the original B-spline curve and shows much better shape-control capability than the original curve.Meanwhile, the extended curve keeps the same degree of original one.It is easy to find that the curve can be reshape by adjusting the shape factor.Also, a new method of the representation of closed curve is given.
Wei Zeng; Muhammad Razib; Abdur Bin Shahid
2015-01-01
Conventional splines offer powerful means for modeling surfaces and volumes in three-dimensional Euclidean space. A one-dimensional quaternion spline has been applied for animation purpose, where the splines are defined to model a one-dimensional submanifold in the three-dimensional Lie group. Given two surfaces, all of the diffeomorphisms between them form an infinite dimensional manifold, the so-called diffeomorphism space. In this work, we propose a novel scheme to model finite dimensional...
Fuzzy linguistic model for interpolation
Energy Technology Data Exchange (ETDEWEB)
Abbasbandy, S. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34194-288 (Iran, Islamic Republic of); Adabitabar Firozja, M. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of)
2007-10-15
In this paper, a fuzzy method for interpolating of smooth curves was represented. We present a novel approach to interpolate real data by applying the universal approximation method. In proposed method, fuzzy linguistic model (FLM) applied as universal approximation for any nonlinear continuous function. Finally, we give some numerical examples and compare the proposed method with spline method.
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
Variational Splines and Paley--Wiener Spaces on Combinatorial Graphs
Pesenson, Isaac
2011-01-01
Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of interpolating variational splines on a graph is shown. As an application of variational splines, the paper presents a reconstruction algorithm of Paley-Wiener functions on graphs from their uniqueness sets.
Institute of Scientific and Technical Information of China (English)
肖静
2014-01-01
In accurate modeling of three-dimensional, the result was affected by the underground coal faults, rock, undulat⁃ing terrain and other factors, so the modeling accuracy was not high. To improve the accuracy of three-dimensional model⁃ing of coal, an algorithm of three-dimensional coal seam modeling with pseudo point elimination and four fields spline inter⁃polation was proposed, the pseudo point was pretreated, and the isolated point was removed, the remaining non-isolated point was used for establishing the basic model and rebuilding the model, the spline interpolation method was used for the four domains of non-isolated point modeling, modeling, the modeling domain was divided into the starting field, extending the domain, stable domain and the convergence domain, in different domains, different modeling point of matching weight⁃ed interpolation was processed, filtering through four domains were combined to achieve the four domains spline interpola⁃tion, it played a role of smoothing filter in modeling, thus the accuracy of three-dimensional modeling was greatly im⁃proved. Simulation results show that the new algorithm has good robustness for external faults, rock, undulating terrain, the 3D modeling accuracy was improved and the computation is less.%三维煤层精确建模受地下断层、岩层、地势起伏等因素的影响，建模精度不高。为提高三维煤层建模的精度，提出一种基于伪点剔除与四域样条插值的三维煤层精确建模算法，通过伪点剔除方法对建模点进行预处理，筛选出其中的孤立点，进行剔除，其余非孤立点用于基本模型建立和基于映射的模型重构，采用四域样条插值方法对非孤立点进行建模，在建模中，将建模域分为起始域、延伸域、稳定域、收敛域共四个域，在不同域中，对不同的建模点进行匹配加权插值处理，经过四域联合滤波，实现四域样条插值，对建模效果起到平滑
Directory of Open Access Journals (Sweden)
Wei Zeng
2015-04-01
Full Text Available Conventional splines offer powerful means for modeling surfaces and volumes in three-dimensional Euclidean space. A one-dimensional quaternion spline has been applied for animation purpose, where the splines are defined to model a one-dimensional submanifold in the three-dimensional Lie group. Given two surfaces, all of the diffeomorphisms between them form an infinite dimensional manifold, the so-called diffeomorphism space. In this work, we propose a novel scheme to model finite dimensional submanifolds in the diffeomorphism space by generalizing conventional splines. According to quasiconformal geometry theorem, each diffeomorphism determines a Beltrami differential on the source surface. Inversely, the diffeomorphism is determined by its Beltrami differential with normalization conditions. Therefore, the diffeomorphism space has one-to-one correspondence to the space of a special differential form. The convex combination of Beltrami differentials is still a Beltrami differential. Therefore, the conventional spline scheme can be generalized to the Beltrami differential space and, consequently, to the diffeomorphism space. Our experiments demonstrate the efficiency and efficacy of diffeomorphism splines. The diffeomorphism spline has many potential applications, such as surface registration, tracking and animation.
Institute of Scientific and Technical Information of China (English)
蔡利栋
2001-01-01
The profit-and-loss revision technique may improve the accuracy of approximation to raw image data undergone a cubic B-spline smoothing. Comments are made on this technique from the viewpoint of image smoothing and restoration, giving highlights on the equivalence between spline smoothing and diffusion smoothing, and between profit-and-loss revision and inverse diffusion restoration; formulating the revision operators into a series of renewal recursions together with an estimation to the order of their deviations from the raw data; and exposing the numerical instability of both simple and renewal recursion of the profit and loss revision. Finally, a discussion is further made on the feasibility of applying the profit-and-loss revision to edge detection for images in the presence of noise.%以三阶B-样条作数据磨光时，引入盈亏修正可以在磨光的同时提高逼近原始数据的精度.通过从图象的平滑与恢复处理的角度出发来对盈亏修正技术进行评注，并进一步阐明了样条磨光与扩散平滑、盈亏修正与反扩散恢复在离散条件下的等价关系，给出了用于修正的更新迭代算子序列以及相应的偏差阶数估计，并且指出了盈亏修正的简单迭代和更新迭代都是数值上绝对不稳定的计算；最后讨论了盈亏修正技术在图象边缘探测中的适用性.
Institute of Scientific and Technical Information of China (English)
郭啸; 韩旭里; 黄琳
2016-01-01
给出了形状可调的四次Hermite插值样条曲线的构造方法.四次样条曲线可提供额外的自由度用于调整曲线具有合理形状.利用导矢逼近使得四次Hermite样条曲线具有与三次B样条曲线相似的形状.通过最小化曲线间的导矢误差给出了确定自由度的方法,提出了四次Hermite插值样条曲线的构造方法.该方法增加了自由度控制曲线形状能更好满足保形要求.最后以实例对构造的四次Hermite样条曲线和标准三次Hermite插值样条曲线进行了比较.
Institute of Scientific and Technical Information of China (English)
邹洁云; 陈苏婷
2014-01-01
暴雨洪涝灾害更是种十分常见的自然灾害，所以对其风险评估刻不容缓。该文利用到江苏1957-2007年的降水资料，将整个评估流程划分为四个部分，致灾因子危险性、孕灾环境敏感性、承灾体易损性和抗灾因子安全性，其中自然灾害中导致灾害直接发生的因素即是致灾因子，因此对致灾因子的正确评估对整个评估起着举足轻重的作用。其中选取样条插值法中的张力样条函数来处理致灾因子部分，能形成一个比较光滑的曲线，比较真实的符合降雨情况，然后结合灾害评估方法、层次分析法、ArcGIS空间处理方法、加权综合评价法，以县为单位，公里为栅格进行评估。结果表明江苏省的自然风险呈从南至北逐渐增加，风险较高地区主要集中在苏北例如宿迁、徐州、淮安等城市一带，其结果与历年灾情相符合。%Rainstorm and flood risk is very common kind of natural disaster,so urgent assessment of its risks.This paper use Jiangsu rainfall data 1957-2007 ,and it will evaluate the whole process is divided into four parts,hazard risk,suffering flexibility,pregnant disaster environmental sensitivity,disaster resisting security,among other factors,hazards are the factors directly occur cause natural disasters , so the correct assessment of hazard assessment for the entire play a decisive role.The paper selected spline interpolation method tension spline function to handle with hazards section, the advantage in tension spline function with convexity,can form a relatively smooth curve, more in line with actual rainfall.Then it combined with disaster assessment method, AHP, ARCGIS spa-tial processing method, weighted comprehensive evaluation method, the county as a unit, kilometers assess raster. The results showed that natural risks of Jiangsu Province increased gradually from south to north, mainly in the higher risk areas such as northern Jiangsu Suqian
Mautz, R.; Ping, J.; Heki, K.; Schaffrin, B.; Shum, C.; Potts, L.
2005-05-01
Wavelet expansion has been demonstrated to be suitable for the representation of spatial functions. Here we propose the so-called B-spline wavelets to represent spatial time-series of GPS-derived global ionosphere maps (GIMs) of the vertical total electron content (TEC) from the Earth’s surface to the mean altitudes of GPS satellites, over Japan. The scalar-valued B-spline wavelets can be defined in a two-dimensional, but not necessarily planar, domain. Generated by a sequence of knots, different degrees of B-splines can be implemented: degree 1 represents the Haar wavelet; degree 2, the linear B-spline wavelet, or degree 4, the cubic B-spline wavelet. A non-uniform version of these wavelets allows us to handle data on a bounded domain without any edge effects. B-splines are easily extended with great computational efficiency to domains of arbitrary dimensions, while preserving their properties. This generalization employs tensor products of B-splines, defined as linear superposition of products of univariate B-splines in different directions. The data and model may be identical at the locations of the data points if the number of wavelet coefficients is equal to the number of grid points. In addition, data compression is made efficient by eliminating the wavelet coefficients with negligible magnitudes, thereby reducing the observational noise. We applied the developed methodology to the representation of the spatial and temporal variations of GIM from an extremely dense GPS network, the GPS Earth Observation Network (GEONET) in Japan. Since the sampling of the TEC is registered regularly in time, we use a two-dimensional B-spline wavelet representation in space and a one-dimensional spline interpolation in time. Over the Japan region, the B-spline wavelet method can overcome the problem of bias for the spherical harmonic model at the boundary, caused by the non-compact support. The hierarchical decomposition not only allows an inexpensive calculation, but also
Spline model of the high latitude scintillation based on in situ satellite data
Priyadarshi, S.; Wernik, A. W.
2013-12-01
We present a spline model for the high latitude ionospheric scintillation using satellite in situ measurements made by the Dynamic Explorer 2 (DE 2) satellite. DE 2 satellite measurements give observations only along satellite orbit but our interpolation model fills the gaps between the satellite orbits. This analytical model is based on products of cubic B-splines and coefficients determined by least squares fit to the binned data and constrained to make the fit periodic in 24 hours of geomagnetic local time, periodic in 360 degrees of invariant longitude, in geomagnetic indices and solar radio flux. Discussion of our results clearly shows the seasonal and diurnal behavior of ionospheric parameters important in scintillation modeling for different geophysical and solar activity conditions. We also show that results obtained from our analytical model match observations obtained from in situ measurements. Shishir Priyadarshi Space Research Centre, Poland
A further assessment of interpolation schemes for window deformation in PIV
Kim, Byoung Jae; Sung, Hyung Jin
2006-09-01
We have evaluated the performances of the following seven interpolation schemes used for window deformation in particle image velocimetry (PIV): the linear, quadratic, B-spline, cubic, sinc, Lagrange, and Gaussian interpolations. Artificially generated images comprised particles of diameter in a range 1.1 ≤ d p ≤ 10.0 pixel were investigated. Three particle diameters were selected for detailed evaluation: d p = 2.2, 3.3, and 4.4 pixel with a constant particle concentration 0.02 particle/pixel2. Two flow patterns were considered: uniform and shear flow. The mean and random errors, and the computation times of the interpolation schemes were determined and compared.
Spectral Gauss quadrature method with subspace interpolation for Kohn-Sham Density functional theory
Wang, Xin
Algorithms with linear-scaling ( (N)) computational complexity for Kohn-Sham density functional theory (K-S DFT) is crucial for studying molecular systems beyond thousands of atoms. Of the (N) methods that use a polynomial-based approximation of the density matrix, the linear-scaling spectral Gauss quadrature (LSSGQ) method (Suryanarayana et al., JMPS, 2013) has been shown to exhibit the fastest convergence. The LSSGQ method requires a Lanczos procedure at every node in a real-space mesh, leading to a large computational pre-factor. We propose a new interpolation scheme specific to the LSSGQ method that lift the need to perform a Lanczos procedure at every node in the real-mesh. This interpolation will be referred to as subspace interpolation. The key idea behind subspace interpolation is that there is a large overlap in the Krylov-subspaces produced by the Lanczos procedures of nodes that are close in real-space. The subspace interpolation scheme takes advantage of the block-Lanczos procedure to group the Krylov-subspaces from a few representative nodes to approximate the density matrix over a large collection of nodes. Subspace interpolation outperforms cubic-spline interpolation by several orders of magnitude.
Coelho, Antonio Augusto Rodrigues
2016-01-01
This paper introduces the Fuzzy Logic Hypercube Interpolator (FLHI) and demonstrates applications in control of multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) processes with Hammerstein nonlinearities. FLHI consists of a Takagi-Sugeno fuzzy inference system where membership functions act as kernel functions of an interpolator. Conjunction of membership functions in an unitary hypercube space enables multivariable interpolation of N-dimensions. Membership functions act as interpolation kernels, such that choice of membership functions determines interpolation characteristics, allowing FLHI to behave as a nearest-neighbor, linear, cubic, spline or Lanczos interpolator, to name a few. The proposed interpolator is presented as a solution to the modeling problem of static nonlinearities since it is capable of modeling both a function and its inverse function. Three study cases from literature are presented, a single-input single-output (SISO) system, a MISO and a MIMO system. Good results are obtained regarding performance metrics such as set-point tracking, control variation and robustness. Results demonstrate applicability of the proposed method in modeling Hammerstein nonlinearities and their inverse functions for implementation of an output compensator with Model Based Predictive Control (MBPC), in particular Dynamic Matrix Control (DMC). PMID:27657723
Zhang, Zhimin; Tomlinson, John; Martin, Clyde
1994-01-01
In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.
Allen, Robert C; Rutan, Sarah C
2011-10-31
Simulated and experimental data were used to measure the effectiveness of common interpolation techniques during chromatographic alignment of comprehensive two-dimensional liquid chromatography-diode array detector (LC×LC-DAD) data. Interpolation was used to generate a sufficient number of data points in the sampled first chromatographic dimension to allow for alignment of retention times from different injections. Five different interpolation methods, linear interpolation followed by cross correlation, piecewise cubic Hermite interpolating polynomial, cubic spline, Fourier zero-filling, and Gaussian fitting, were investigated. The fully aligned chromatograms, in both the first and second chromatographic dimensions, were analyzed by parallel factor analysis to determine the relative area for each peak in each injection. A calibration curve was generated for the simulated data set. The standard error of prediction and percent relative standard deviation were calculated for the simulated peak for each technique. The Gaussian fitting interpolation technique resulted in the lowest standard error of prediction and average relative standard deviation for the simulated data. However, upon applying the interpolation techniques to the experimental data, most of the interpolation methods were not found to produce statistically different relative peak areas from each other. While most of the techniques were not statistically different, the performance was improved relative to the PARAFAC results obtained when analyzing the unaligned data.
Optimization and dynamics of protein-protein complexes using B-splines.
Gillilan, Richard E; Lilien, Ryan H
2004-10-01
A moving-grid approach for optimization and dynamics of protein-protein complexes is introduced, which utilizes cubic B-spline interpolation for rapid energy and force evaluation. The method allows for the efficient use of full electrostatic potentials joined smoothly to multipoles at long distance so that multiprotein simulation is possible. Using a recently published benchmark of 58 protein complexes, we examine the performance and quality of the grid approximation, refining cocrystallized complexes to within 0.68 A RMSD of interface atoms, close to the optimum 0.63 A produced by the underlying MMFF94 force field. We quantify the theoretical statistical advantage of using minimization in a stochastic search in the case of two rigid bodies, and contrast it with the underlying cost of conjugate gradient minimization using B-splines. The volumes of conjugate gradient minimization basins of attraction in cocrystallized systems are generally orders of magnitude larger than well volumes based on energy thresholds needed to discriminate native from nonnative states; nonetheless, computational cost is significant. Molecular dynamics using B-splines is doubly efficient due to the combined advantages of rapid force evaluation and large simulation step sizes. Large basins localized around the native state and other possible binding sites are identifiable during simulations of protein-protein motion. In addition to providing increased modeling detail, B-splines offer new algorithmic possibilities that should be valuable in refining docking candidates and studying global complex behavior.
A Unified Representation Scheme for Solid Geometric Objects Using B-splines (extended Abstract)
Bahler, D.
1985-01-01
A geometric representation scheme called the B-spline cylinder, which consists of interpolation between pairs of uniform periodic cubic B-spline curves is discussed. This approach carries a number of interesting implications. For one, a single relatively simple database schema can be used to represent a reasonably large class of objects, since the spline representation is flexible enough to allow a large domain of representable objects at very little cost in data complexity. The model is thus very storage-efficient. A second feature of such a system is that it reduces to one the number of routines which the system must support to perform a given operation on objects. Third, the scheme enables easy conversion to and from other representations. The formal definition of the cylinder entity is given. In the geometric properties of the entity are explored and several operations on such objects are defined. Some general purpose criteria for evaluating any geometric representation scheme are introduced and the B-spline cylinder scheme according to these criteria is evaluated.
Finite element method of spline for R-B equation%R-B方程样条有限元法
Institute of Scientific and Technical Information of China (English)
乃明; 胡兵; 闵心畅
2012-01-01
A finite element method is given based on cubic spline interpolation for R-B equation, and the numerical scheme is derived. Further more, the corresponding existence and uniqueness of the solution of this scheme are proved. Meanwhile, the convergence analysis is presented.%作者对R-B方程提出了基于三次样条插值的有限元法,给出了具体的计算格式,证明了该离散格式解的存在唯一性和稳定性,并给出了收敛性分析.
Tricubic polynomial interpolation.
Birkhoff, G
1971-06-01
A new triangular "finite element" is described; it involves the 12-parameter family of all quartic polynomial functions that are "tricubic" in that their variation is cubic along any parallel to any side of the triangle. An interpolation scheme is described that approximates quite accurately any smooth function on any triangulated domain by a continuously differentiable function, tricubic on each triangular element.
Point based interactive image segmentation using multiquadrics splines
Meena, Sachin; Duraisamy, Prakash; Palniappan, Kannappan; Seetharaman, Guna
2017-05-01
Multiquadrics (MQ) are radial basis spline function that can provide an efficient interpolation of data points located in a high dimensional space. MQ were developed by Hardy to approximate geographical surfaces and terrain modelling. In this paper we frame the task of interactive image segmentation as a semi-supervised interpolation where an interpolating function learned from the user provided seed points is used to predict the labels of unlabeled pixel and the spline function used in the semi-supervised interpolation is MQ. This semi-supervised interpolation framework has a nice closed form solution which along with the fact that MQ is a radial basis spline function lead to a very fast interactive image segmentation process. Quantitative and qualitative results on the standard datasets show that MQ outperforms other regression based methods, GEBS, Ridge Regression and Logistic Regression, and popular methods like Graph Cut,4 Random Walk and Random Forest.6
Color management with a hammer: the B-spline fitter
Bell, Ian E.; Liu, Bonny H. P.
2003-01-01
To paraphrase Abraham Maslow: If the only tool you have is a hammer, every problem looks like a nail. We have a B-spline fitter customized for 3D color data, and many problems in color management can be solved with this tool. Whereas color devices were once modeled with extensive measurement, look-up tables and trilinear interpolation, recent improvements in hardware have made B-spline models an affordable alternative. Such device characterizations require fewer color measurements than piecewise linear models, and have uses beyond simple interpolation. A B-spline fitter, for example, can act as a filter to remove noise from measurements, leaving a model with guaranteed smoothness. Inversion of the device model can then be carried out consistently and efficiently, as the spline model is well behaved and its derivatives easily computed. Spline-based algorithms also exist for gamut mapping, the composition of maps, and the extrapolation of a gamut. Trilinear interpolation---a degree-one spline---can still be used after nonlinear spline smoothing for high-speed evaluation with robust convergence. Using data from several color devices, this paper examines the use of B-splines as a generic tool for modeling devices and mapping one gamut to another, and concludes with applications to high-dimensional and spectral data.
Segmented Regression Based on B-Splines with Solved Examples
Directory of Open Access Journals (Sweden)
Miloš Kaňka
2015-12-01
Full Text Available The subject of the paper is segmented linear, quadratic, and cubic regression based on B-spline basis functions. In this article we expose the formulas for the computation of B-splines of order one, two, and three that is needed to construct linear, quadratic, and cubic regression. We list some interesting properties of these functions. For a clearer understanding we give the solutions of a couple of elementary exercises regarding these functions.
Realization of a 5-axis NURBS Interpolation with Controlled Angular Velocity
Institute of Scientific and Technical Information of China (English)
LIU Yuan; LI Hui; WANG Yongzhang
2012-01-01
5-axis machine tool plays an important role in high-speed and high-precision computer numerical control (CNC) machining of workpieces with complex shapes.A non-uniform rational B-spline (NURBS) interpolation format for 5-axis machining is proposed to adapt to the high speed machining (HSM).With this interpolation format,angles between orientation vectors are chosen as parameters of orientation B-spline constructed by an open controller to achieve reasonable orientation vectors in real-time interpolation process.Coordinated motion between linear axes and rotary axes is achieved by building a polynomial spline which relates interpolation arc lengths of position spline to angles of orientation spline.Algorithm routine of this interpolation format and its realization methods in the supported controller are discussed in detail.Finally,performance of the proposed NURBS interpolation format is demonstrated by a practical example.
Directory of Open Access Journals (Sweden)
Peng Liu
2016-01-01
Full Text Available A new model for the free transverse vibration of axially functionally graded (FG tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.
Mahmoudzadeh, Amir Pasha; Kashou, Nasser H
2013-01-01
Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR) grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order) and to compare the effect of cost functions (least squares (LS), normalized mutual information (NMI), normalized cross correlation (NCC), and correlation ratio (CR)) for optimized automatic image registration (OAIR) on 3D spoiled gradient recalled (SPGR) magnetic resonance images (MRI) of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.
Directory of Open Access Journals (Sweden)
Amir Pasha Mahmoudzadeh
2013-01-01
Full Text Available Interpolation has become a default operation in image processing and medical imaging and is one of the important factors in the success of an intensity-based registration method. Interpolation is needed if the fractional unit of motion is not matched and located on the high resolution (HR grid. The purpose of this work is to present a systematic evaluation of eight standard interpolation techniques (trilinear, nearest neighbor, cubic Lagrangian, quintic Lagrangian, hepatic Lagrangian, windowed Sinc, B-spline 3rd order, and B-spline 4th order and to compare the effect of cost functions (least squares (LS, normalized mutual information (NMI, normalized cross correlation (NCC, and correlation ratio (CR for optimized automatic image registration (OAIR on 3D spoiled gradient recalled (SPGR magnetic resonance images (MRI of the brain acquired using a 3T GE MR scanner. Subsampling was performed in the axial, sagittal, and coronal directions to emulate three low resolution datasets. Afterwards, the low resolution datasets were upsampled using different interpolation methods, and they were then compared to the high resolution data. The mean squared error, peak signal to noise, joint entropy, and cost functions were computed for quantitative assessment of the method. Magnetic resonance image scans and joint histogram were used for qualitative assessment of the method.
基于样条插值的非线性滤波器的分析与设计%Analysis and Design of Non-linear filters Based on Cubic Spline Function
Institute of Scientific and Technical Information of China (English)
伍小芹; 张宏科; 邓家先
2011-01-01
在理论分析和实际应用中,信号分析具有重要的理论意义和实际应用价值.非平稳信号的分析及处理一直是学术和工程界关注的热点问题之一.由于传统数据分析方法受线性或者平稳性假设的限制,无法有效地应用于图像处理、语音处理及雷达信号处理等实际应用中.本文通过对非线性、非平稳数据的建模,研究了适合非平稳数据分析的经验数据分解算法.建立了可行的经验数据分解滤波器的设计准则,并利用三次样条插值预测滤波器的参数.使用超光谱图像数据进行测试分析,在一次经验数据分解后,分析了高频子带数值在规定范围内的概率分布及相应的熵值.实验结果表明:经验数据分解算法产生的高频系数在0附近更集中,这对图像压缩有利,从而证明经验数据分解是一种对非平稳数据有效的分析方法.%Signal analysis has important theoretical and practical application. Non-stationary signal analysis and processing is one of the hot topics in the scientific and engineering research area. Because of the limit of linearity and stationarity assumption, the traditional methods can not be effectively used in image processing, speech processing and radar signal processing. A model suiting for nonlinear and non-stationary is established. The empirical data decomposition algorithm is discussed. A suitable design criteria is established. The use of cubic spline functions to predict the parameters of the predictive filter is discussed. Making a test on spectrum image data with empirical data decomposition. The system is simulated in Matlab. The probability distribution of the samples in high-frequency subbands whose values are within the specified range and the corresponding entropy are analyzed through simulation. The results show that the high-frequency coefficients produed by empirical data decomposition algorithm is more concentrated than those of 5/3 wavelet and 9
Interpolating point spread function anisotropy
Gentile, M; Meylan, G
2012-01-01
Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging...
Log-cubic method for generation of soil particle size distribution curve.
Shang, Songhao
2013-01-01
Particle size distribution (PSD) is a fundamental physical property of soils. Traditionally, the PSD curve was generated by hand from limited data of particle size analysis, which is subjective and may lead to significant uncertainty in the freehand PSD curve and graphically estimated cumulative particle percentages. To overcome these problems, a log-cubic method was proposed for the generation of PSD curve based on a monotone piecewise cubic interpolation method. The log-cubic method and commonly used log-linear and log-spline methods were evaluated by the leave-one-out cross-validation method for 394 soil samples extracted from UNSODA database. Mean error and root mean square error of the cross-validation show that the log-cubic method outperforms two other methods. What is more important, PSD curve generated by the log-cubic method meets essential requirements of a PSD curve, that is, passing through all measured data and being both smooth and monotone. The proposed log-cubic method provides an objective and reliable way to generate a PSD curve from limited soil particle analysis data. This method and the generated PSD curve can be used in the conversion of different soil texture schemes, assessment of grading pattern, and estimation of soil hydraulic parameters and erodibility factor.
Interpolating point spread function anisotropy
Gentile, M.; Courbin, F.; Meylan, G.
2013-01-01
Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will not benefit from that scaling effect and will require very accurate modeling and correction. While numerous methods have been devised to carry out the PSF correction itself, modeling of the PSF shape and its spatial variations across the instrument field of view has, so far, attracted much less attention. This step is nevertheless crucial because the PSF is only known at star positions while the correction has to be performed at any position on the sky. A reliable interpolation scheme is therefore mandatory and a popular approach has been to use low-order bivariate polynomials. In the present paper, we evaluate four other classical spatial interpolation methods based on splines (B-splines), inverse distance weighting (IDW), radial basis functions (RBF) and ordinary Kriging (OK). These methods are tested on the Star-challenge part of the GRavitational lEnsing Accuracy Testing 2010 (GREAT10) simulated data and are compared with the classical polynomial fitting (Polyfit). In all our methods we model the PSF using a single Moffat profile and we interpolate the fitted parameters at a set of required positions. This allowed us to win the Star-challenge of GREAT10, with the B-splines method. However, we also test all our interpolation methods independently of the way the PSF is modeled, by interpolating the GREAT10 star fields themselves (i.e., the PSF parameters are known exactly at star positions). We find in that case RBF to be the clear winner, closely followed by the other local methods, IDW and OK. The global methods, Polyfit and B-splines, are largely behind, especially in fields with (ground-based) turbulent PSFs. In fields with non-turbulent PSFs, all interpolators reach a variance on PSF systematics σ2sys better than the 1
Occlusion-Aware View Interpolation
Directory of Open Access Journals (Sweden)
Janusz Konrad
2009-01-01
Full Text Available View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
Occlusion-Aware View Interpolation
Directory of Open Access Journals (Sweden)
Ince Serdar
2008-01-01
Full Text Available Abstract View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
Stein, A.
1991-01-01
The theory and practical application of techniques of statistical interpolation are studied in this thesis, and new developments in multivariate spatial interpolation and the design of sampling plans are discussed. Several applications to studies in soil science are presented.Sampling s
The Order of Monotone Piecewise Cubic Interpolation.
1981-08-02
diedi+1) onto the boundary of 1,; Figure 2-4: Step 3 of the Two-Sweep Algoritm . -7- Forward Sweep. On the Backward Sweep, only the first component...short-coming of the Two-Sweep Algoritm is that it may move a point (di 1 ) much farther than necessary when projecting it into i. This problem is
Interpolation based consensus clustering for gene expression time series.
Chiu, Tai-Yu; Hsu, Ting-Chieh; Yen, Chia-Cheng; Wang, Jia-Shung
2015-04-16
Unsupervised analyses such as clustering are the essential tools required to interpret time-series expression data from microarrays. Several clustering algorithms have been developed to analyze gene expression data. Early methods such as k-means, hierarchical clustering, and self-organizing maps are popular for their simplicity. However, because of noise and uncertainty of measurement, these common algorithms have low accuracy. Moreover, because gene expression is a temporal process, the relationship between successive time points should be considered in the analyses. In addition, biological processes are generally continuous; therefore, the datasets collected from time series experiments are often found to have an insufficient number of data points and, as a result, compensation for missing data can also be an issue. An affinity propagation-based clustering algorithm for time-series gene expression data is proposed. The algorithm explores the relationship between genes using a sliding-window mechanism to extract a large number of features. In addition, the time-course datasets are resampled with spline interpolation to predict the unobserved values. Finally, a consensus process is applied to enhance the robustness of the method. Some real gene expression datasets were analyzed to demonstrate the accuracy and efficiency of the algorithm. The proposed algorithm has benefitted from the use of cubic B-splines interpolation, sliding-window, affinity propagation, gene relativity graph, and a consensus process, and, as a result, provides both appropriate and effective clustering of time-series gene expression data. The proposed method was tested with gene expression data from the Yeast galactose dataset, the Yeast cell-cycle dataset (Y5), and the Yeast sporulation dataset, and the results illustrated the relationships between the expressed genes, which may give some insights into the biological processes involved.
Polynomial interpolation methods for viscous flow calculations
Rubin, S. G.; Khosla, P. K.
1977-01-01
Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.
Polynomial interpolation methods for viscous flow calculations
Rubin, S. G.; Khosla, P. K.
1977-01-01
Higher-order collocation procedures which result in block-tridiagonal matrix systems are derived from (1) Taylor series expansions and from (2) polynomial interpolation, and the relationships between the two formulations, called respectively Hermite and spline collocation, are investigated. A Hermite block-tridiagonal system for a nonuniform mesh is derived, and the Hermite approach is extended in order to develop a variable-mesh sixth-order block-tridiagonal procedure. It is shown that all results obtained by Hermite development can be recovered by appropriate spline polynomial interpolation. The additional boundary conditions required for these higher-order procedures are also given. Comparative solutions using second-order accurate finite difference and spline and Hermite formulations are presented for the boundary layer on a flat plate, boundary layers with uniform and variable mass transfer, and the viscous incompressible Navier-Stokes equations describing flow in a driven cavity.
A family of locally adjustable cubic algebraic-trigonometric interpolation spline%一类局部可调的三次代数三角插值样条
Institute of Scientific and Technical Information of China (English)
杨炼; 李军成; 匡小兰
2013-01-01
在空间Ω=span{1,t,sint,cost,sin2t,cos 2t}中提出了一种新的带形状参数的三次代数三角插值样条,该样条具有许多与三次B样条类似的性质.所构造的曲线曲面无需解方程组或插入某些节点即可直接插值某些控制顶点.曲线能精确表示直线段、椭圆(圆)弧、抛物线弧以及圆柱螺旋、三角函数曲线等一些超越曲线,相应的张量积曲面能精确表示一些二次曲面和超越曲面,如球面、圆柱面和螺旋柱面等.通过改变基函数中的全局参数的取值可整体调节曲线曲面的形状,并利用奇异混合技术在三次代数三角插值样条中引入局部参数,使曲线曲面的形状能局部调节.几何造型实例表明,三次代数三角插值样条可作为几何造型的一种新的有效模型.
三次B样条参数曲线插补算法及其特性分析%Interpolation Algorithm and Characteristic Analysis for Cubic B-spline Curves
Institute of Scientific and Technical Information of China (English)
徐绍华; 田新诚; 方磊
2007-01-01
插补算法是数控系统的核心技术之一,插补算法的选择及算法特性直接影响到数控系统的控制精度、速度及加工能力等.文章介绍了两种三次B样条参数曲线插补算法,研究分析了算法的位置控制精度、插补速度稳定性等技术特性,对两种插补算法进行了对比,给出了插补算法的选取原则.
Institute of Scientific and Technical Information of China (English)
刘洪臣; 冯勇; 杨旭强
2007-01-01
亚像元动态成像技术是实现遥感器高分辨、小型化的有效方法.将双三次B样条曲面插值方法应用于亚像元动态成像,利用待插值点周围邻域范围内16个像素点做一张B样条曲面,取曲面中点的值作为待插值点的像素值.文中推导了双三次B样条曲面插值亚像元图像的插值算式,对所提方法进行了计算机仿真研究,并与其他几种常用插值方法进行了性能比较,结果表明,本文算法得到的高分辨率图像效果更佳.
Institute of Scientific and Technical Information of China (English)
胡志刚
2000-01-01
运用三次均匀B样条曲线插值法分段构造凸轮曲线,给出任意插值点的三次均匀B样条闭曲线的B特征多边形顶点的反算公式,并导出由三次均匀B样条闭曲线构成的对心直动从动件盘形凸轮轮廓曲线上任一点处的压力角计算公式.
Institute of Scientific and Technical Information of China (English)
陈娟; 李崇君
2015-01-01
薄板弯曲单元被广泛地应用到工程问题的有限元计算中.然而,由于协调的薄板弯曲位移型单元要求挠度和转角(即位移的函数值和导数值)都是连续的,导致很难直接构造协调的位移型薄板单元.在数学上,样条是满足一定协调性的分片光滑的多项式,有限元的形函数可以视为样条函数.本文基于三角形面积坐标和B网方法,利用三次样条Hermite插值基重构了两个协调的薄板弯曲单元.由于单元形函数是基于四边形构造的,避免了等参变换,可以有效地降低网格畸变对计算精度的影响.
基于周期性延伸的三次B样条闭曲线插值%Interpolation of Cubic B-spline Closed Curve Based on Periodic Extension
Institute of Scientific and Technical Information of China (English)
李学艺; 王钊; 连小珉; 曾庆良
2009-01-01
针对闭曲线具有可周期性延伸的特点,提出了一种基于求解双列带阵线性方程组的三次B样条完全闭曲线插算法.通过节点向量和控制点在曲线闭合点两端的周期性延伸,使插值曲线在闭合点实现了理论上的完全封闭.针对曲线插值线性方程组中系数矩阵具有不完全带阵的特点,提出了一种双列带阵线性方程组求解算法.应用实例表明,算法性能稳定、效率高、可插值任意形状的复杂闭曲线,适于处理大数据量闭曲线插值运算.
The Real-time Interpolation of Cubic B-spline Curves Based on TMS320F2812%基于TMS320F2812的三次B样条曲线实时插补
Institute of Scientific and Technical Information of China (English)
李广涛; 薛重德; 侯小强
2008-01-01
为提高数控系统实时插补的准确性、加工速度和加工精度,采用在每个插补周期中保持进给速度不变的三次B样条曲线参变量非均匀变化实时插补算法.利用数字信号处理器(DSP)进行三次B样条曲线实时插补,可缩短插补计算时间;通过设定DSP的定时器中断来实现各轴控制脉冲的发送,可实现最大限度地减少折线状的插补轨迹的目的.结果表明,该算法能使所有的插补点都在理论曲线上,可以保证运动控制系统的高速高精度要求.
基于三次B样条插值的形状错误隐藏算法%Spatial shape error concealment method based on cubic B-spline interpolation
Institute of Scientific and Technical Information of China (English)
符祥; 郭宝龙; 杨占龙
2008-01-01
分析了基于Bézier插值的视频对象形状错误隐藏方法的不足,即计算附加控制点的过程复杂,隐藏结果受附加控制点影响大.针对这一问题,提出了一种基于三次B样条插值的错误隐藏算法.对三次B样条插值的矩阵公式进行了改进,保证目标轮廓的平滑性;直接对已知轮廓点插值,克服了传统方法的不足.与传统方法对比实验表明,新算法简单易实现,有较好的实用意义.
A Local Representation of General Cubic B-Spline Interactive Interpolation%一般三次B样条交互插值的一种局部表示法
Institute of Scientific and Technical Information of China (English)
贾根莲; 包利亚; 杜新俊
2000-01-01
交互插值三次B样条曲线曲面在辅助几何设计中使用很多,但控制点和插值点之间的变化关系一直是讨论的关键.本文就一般三次B样条曲线交互性插值中控制点和插值点之间的关系进行了讨论,并提出了一个实用的局部表示法来实现曲线的交互插值.
Institute of Scientific and Technical Information of China (English)
党耀国; 张娟; 陈兴怡
2015-01-01
针对具有时滞特征的输入输出系统,建立了灰色时滞GDM(1,2)模型.并结合三次样条插值和粒子群优化算法,求解出模型的3个参数[a,b,τ].相对于先利用灰关联分析确定出时滞参数τ再求解灰预测模型的方法,把时滞参数r融入模型中求解,避免了参数求解过程中的误差传递;并且还消除了时滞参数τ必须为整数的限制,使模型更加贴合现实中滞后期数不一定为整数的实际情况.最后将模型应用于公路旅客周转量的预测问题,实例表明该模型在具有时滞特征的输入输出系统预测中具有较高的精度.
High-speed real-time interpolation of cubic uniform B-spline curve%三次均匀B样条曲线高速实时插补研究
Institute of Scientific and Technical Information of China (English)
赵彤; 吕强; 张辉; 杨开明
2008-01-01
为满足复杂曲线高速和高精度的加工要求,研究了具有轨迹预读功能的三次均匀B样条曲线速度规划和插补算法.提出了"重叠拼接法",实现了相邻两条B样条曲线段的光滑连接;推导了插补钳制速度的计算公式,保证了加工精度,满足了系统的动态响应能力.在引入"规划单元"概念的基础上,将速度规划和插补设计成B样条曲线插值、规划单元划分、速度规划、规划单元插补四个并行计算的线程,解决了三次均匀B样条曲线高速加工的插补实时性问题.最后,在GT100数控系统中验证了算法的有效性.
Matrix Representation for Cubic B-spline Interpolation Curve and Surface%三次均匀B样条插值曲线和曲面的矩阵形式
Institute of Scientific and Technical Information of China (English)
符祥; 郭宝龙
2007-01-01
根据三次B样条曲线(CB)的矩阵形式灵活的特点、CB曲线的端点性质和插值曲线在连接点应满足的连续性条件,推导出CB插值(CBI)曲线的矩阵形式,并进一步推广,得到了双CBI曲面的矩阵形式.生成了平面和空间插值曲线、闭合插值曲线和插值面片.与传统方法进行了比较,结果表明,本文方法有较大的优越性和较好的实用价值.
Institute of Scientific and Technical Information of China (English)
罗煦琼; 刘利斌
2008-01-01
讨论了Ly(x):=y"(x)-p(x)y'(x)-q(x)y(x)=g(x)的两点边值问题的三次B样条插值解法.证明了该方法具有二阶收敛性和很好的稳定性.数值实验结果表明,该三次B样条方法比文献[8]和文献[9]的精度更高.
Institute of Scientific and Technical Information of China (English)
星蓉生; 潘日晶
2014-01-01
基于渐进迭代逼近算法生成插值数据点及其切矢的三次均匀B样条曲线.其基本思想是用偶数项控制顶点来对应拟合数据点,用奇数项控制顶点控制相应切矢逼近,根据迭代公式不断调整控制顶点,当迭代次数趋于无穷时,一系列迭代曲线的极限曲线插值于给定的数据点及其相应的切矢.用该方法构造插值曲线是一个迭代过程,不必解线性方程组.
Terrain Reconstruction Algorithm Based on Bi-cubic B-spline Interpolation%基于双三次B-样条插值的大地形重构
Institute of Scientific and Technical Information of China (English)
张立民; 邹容平; 李一平; 陈敏
2007-01-01
提出一种基于双三次B-样条的DEM地形数据重构算法.根据用户对不同地形区域关注程度的不同而采用不同的地形分辨率,可有效地降低计算机负荷.采用该算法可以有效地对关注度较高的区域进行地形重构,提高该区域的地形分辨率.实践结果表明,该算法满足大地形视景仿真系统的需要.
Institute of Scientific and Technical Information of China (English)
陈守年; 王硕桂
2009-01-01
插补技术是数控技术中的核心技术,插补算法的选择直接影响到数控系统的加工精度和速度.充分运用GT400-SV运动控制卡开放式数控系统具有的双CPU的优点,综合考虑加工精度和加工速度的要求,采用累加弦长的三次B样条曲线插补算法,并利用VC 6.0编写插补程序,在固高二维运动平台上得到了实际验证.并对插补精度和效率进行优化.
非均匀三次B样条曲线插值的Jacobi-PIA算法%Jacobi-PIA Algorithm for Non-uniform Cubic B-Spline Curve Interpolation
Institute of Scientific and Technical Information of China (English)
刘晓艳; 邓重阳
2015-01-01
为了求解非均匀三次B样条曲线插值问题,基于解线性方程组的Jacobi迭代方法提出一种渐进迭代插值算法——Jacobi-PIA算法.该算法以待插值点为初始控制多边形得到第0层的三次B样条曲线,递归地求得插值给定点集的三次B样条曲线;在每个迭代过程中,定义待插值点与第k层的三次B样条曲线上对应点的差向量乘以该点对应的B样条系数的倒数为偏移向量,第k层的控制顶点加上对应的偏移向量得到第k+1层的三次B样条曲线的控制顶点.由于Jacobi-PIA算法在更新控制顶点时减少了一个减法运算,因而运算量更少.理论分析表明该算法是收敛的.数值算例结果表明,Jacobi-PIA算法的收敛速度优于经典的渐进迭代插值算法,与最优权因子对应的带权渐进迭代插值算法基本相同.
Institute of Scientific and Technical Information of China (English)
宣伯凯; 杨鹏; 孙昊; 冀云
2008-01-01
由工业PC机+运动控制卡组成的数控平台具有多轴联动功能,能够完成具有复杂曲面的足底矫形器的加工.为提高足底矫形器的加工质量,将三次B样条的方法引入加工过程.B样条方法能很好的表示自由曲线曲面的形状.通过反算控制顶点的方法,使构造的轮廓曲线能精确控制到模型每个数据点,还原曲线的原形.在教据点间进行插值,计算容易曲线光滑.为提高生产效率,在加工过程中采用连续插补的方式.多点加工一次完成减少了运行过程中电机的起停频率,不仅缩短运行时间而且能减小系统震荡.
Institute of Scientific and Technical Information of China (English)
李广涛; 薛重德; 侯小强; 孟建民
2009-01-01
为充分利用PC机资源,提高数控加工精度,介绍了基于TMS320F2812数字信号处理器(DSP)的多轴运动控制卡的设计方法以及三次B样条曲线恒速进给实时插补方案在控制卡上的应用.结果表明,该方法能有效地简化插补过程中的轨迹计算,显著缩短插补计算时间,使所有的插补点都在理论曲线上;只要合理决定曲线参变量,完全可以保证运动控制系统的高速高精度要求.
The study of cubic uniform rational B-spline interpolation algorithm%三次均匀有理B样条曲线插补算法的研究
Institute of Scientific and Technical Information of China (English)
陈伟华; 张铁
2010-01-01
插补算法是机器人系统实现运动控制的核心模块,对三次均匀有理B样条曲线的插补算法进行了研究.基于三次非均匀有理B样条曲线(NURBS),得出三次均匀有理B样条曲线的表达式.反算B样务曲线的控制顶点中发现规律,采用一种简单快捷的方法求取控制顶点,这使插补算法计算简单,更易于计算机编程.并且在算法中考虑到运动控制加减速的问题,这使插补算法符合实际,实用性强.最后采用三次均匀有理B样条曲线对螺旋线进行插补,仿真结果良好.
On the efficiency and accuracy of interpolation methods for spectral codes
Hinsberg, van M.A.T.; Thije Boonkkamp, ten J.H.M.; Toschi, F.; Clercx, H.J.H.
2012-01-01
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline-based interpolation method for spectral codes is presented. The theory links the order of the interpolation method with its spectral properties. In this way m
Energy Technology Data Exchange (ETDEWEB)
2013-08-29
An analytical model is developed to evaluate the design of a spline coupling. For a given torque and shaft misalignment, the model calculates the number of teeth in contact, tooth loads, stiffnesses, stresses, and safety factors. The analytic model provides essential spline coupling design and modeling information and could be easily integrated into gearbox design and simulation tools.
An Optimized Spline-Based Registration of a 3D CT to a Set of C-Arm Images.
Jonić, S; Thévenaz, P; Zheng, G; Nolte, L-P; Unser, M
2006-01-01
We have developed an algorithm for the rigid-body registration of a CT volume to a set of C-arm images. The algorithm uses a gradient-based iterative minimization of a least-squares measure of dissimilarity between the C-arm images and projections of the CT volume. To compute projections, we use a novel method for fast integration of the volume along rays. To improve robustness and speed, we take advantage of a coarse-to-fine processing of the volume/image pyramids. To compute the projections of the volume, the gradient of the dissimilarity measure, and the multiresolution data pyramids, we use a continuous image/volume model based on cubic B-splines, which ensures a high interpolation accuracy and a gradient of the dissimilarity measure that is well defined everywhere. We show the performance of our algorithm on a human spine phantom, where the true alignment is determined using a set of fiducial markers.
Age-period-cohort models using smoothing splines: a generalized additive model approach.
Jiang, Bei; Carriere, Keumhee C
2014-02-20
Age-period-cohort (APC) models are used to analyze temporal trends in disease or mortality rates, dealing with linear dependency among associated effects of age, period, and cohort. However, the nature of sparseness in such data has severely limited the use of APC models. To deal with these practical limitations and issues, we advocate cubic smoothing splines. We show that the methods of estimable functions proposed in the framework of generalized linear models can still be considered to solve the non-identifiability problem when the model fitting is within the framework of generalized additive models with cubic smoothing splines. Through simulation studies, we evaluate the performance of the cubic smoothing splines in terms of the mean squared errors of estimable functions. Our results support the use of cubic smoothing splines for APC modeling with sparse but unaggregated data from a Lexis diagram.
Energy Technology Data Exchange (ETDEWEB)
Maiden, D E
1998-10-01
A method for constructing bicubic interpolation polynomials for the pressure P and internal energy E that are thermodynamically consistent at the mesh ponts and continuous across mesh boundaries is presented. The slope boundary conditions for the pressure and energy are derived from finite differences of the data and from Maxwell's consistency relation. Monotonicity of the sound speed and the specific heat is obtained by a bilinear interpolation of the slopes of the tabulated data. Monotonicity of the functions near steep gradients may be achieved by mesh refinement or by using a non-consistent bilinear to the data. Mesh refinement is very efficient for uniform-linear or uniform-logarithmic spaced data because a direct table lookup can be used. The direct method was compared to binary search and was 37 percent faster for logarithmic-spaced data and 106 percent faster for linear-spaced data. This improvement in speed is very important in the radiation-transport opacity-lookup part of the calculation. Interpolation in P-E space, with mesh refinement, can be made simple, robust, and conserve energy. In the final analysis the interpolation of the free energy and entropy (Maiden and Cook) remains a competitor.
An interpolation method for stream habitat assessments
Sheehan, Kenneth R.; Welsh, Stuart A.
2015-01-01
Interpolation of stream habitat can be very useful for habitat assessment. Using a small number of habitat samples to predict the habitat of larger areas can reduce time and labor costs as long as it provides accurate estimates of habitat. The spatial correlation of stream habitat variables such as substrate and depth improves the accuracy of interpolated data. Several geographical information system interpolation methods (natural neighbor, inverse distance weighted, ordinary kriging, spline, and universal kriging) were used to predict substrate and depth within a 210.7-m2 section of a second-order stream based on 2.5% and 5.0% sampling of the total area. Depth and substrate were recorded for the entire study site and compared with the interpolated values to determine the accuracy of the predictions. In all instances, the 5% interpolations were more accurate for both depth and substrate than the 2.5% interpolations, which achieved accuracies up to 95% and 92%, respectively. Interpolations of depth based on 2.5% sampling attained accuracies of 49–92%, whereas those based on 5% percent sampling attained accuracies of 57–95%. Natural neighbor interpolation was more accurate than that using the inverse distance weighted, ordinary kriging, spline, and universal kriging approaches. Our findings demonstrate the effective use of minimal amounts of small-scale data for the interpolation of habitat over large areas of a stream channel. Use of this method will provide time and cost savings in the assessment of large sections of rivers as well as functional maps to aid the habitat-based management of aquatic species.
Institute of Scientific and Technical Information of China (English)
吴泽福
2012-01-01
Based on the comparision of basic static estimate methods of term structure of interest rate (TSIR), we improved B-spline function estimate method, which involved optimization on estimation programmes, node numbers choice, and node placement design. To overcome the subjective effect of B-spline node distribution and C2 smoothness condition of discount function, we introduced negative exponential smoothness cubic Li-spline optimization technology with minimum constraint function of estimation error from quadratic sum to absolute value and minimum volatility of discount function, to increase the estimation reliability and prediction ability of short-term interest rate's volatility structure mutation, improve the advantage on depicting the long-term interest rate volatility trend, and reduce the excessive volatility of discount function.%通过对比国内外利率期限结构静态估计模型的优劣,分析节点数目变化和定位改进B样条函数对利率期限结构静态估计的误差,构建最小化定价误差的节点组合布局搜索程序,并引入负指数平滑立方L1样条优化模型,将误差函数最小化结构从平方和最小化转化为误差距离最小化,权衡拟合误差绝对距离最小化与贴现函数波动性约束,克服B样条函数对节点数目与定位的人工干预和放宽对贴现函数的二阶平滑要求,保留B样条函数刻画中长期利率波动趋势的优势,增强对短期利率波动结构突变的估计和预测能力,提高定价精确度和缓解利率期限结构曲线的过度波动问题.
Some extremal properties of multivariate polynomial splines in the metric Lp (Rd )
Institute of Scientific and Technical Information of China (English)
刘永平; 许贵桥
2001-01-01
We constructed a kind of continuous multivariate spline operators as the approximation tools of the multivariate functions on the Bd instead of the usual multivariate cardinal interpolation oper-ators of splines, and obtained the approximation error by this kind of spline operators. Meantime, by the results, we also obtained that the spaces of multivariate polynomial splines are weakly asymptoti-cally optimal for the Kolmogorov widths and the linear widths of some anisotropic Sobolev classes of smooth functions on Bd in the metric Lp(Bd).
INTERPOLATION WITH RESTRICTED ARC LENGTH
Institute of Scientific and Technical Information of China (English)
Petar Petrov
2003-01-01
For given data (ti,yi), I= 0,1,…,n,0 = t0 ＜t1 ＜…＜tn = 1we study constrained interpolation problem of Favard type inf{‖f"‖∞|f∈W2∞[0,1],f(ti)=yi,i=0,…,n,l(f;[0,1])≤l0}, wherel(f";[0,1])=∫1 0 / 1+f'2(x)dx is the arc length off in [0,1]. We prove the existence of a solution f* of the above problem, that is a quadratic spline with a second derivative f"* , which coincides with one of the constants - ‖f"*‖∞,0,‖f"*‖∞ between every two consecutive knots. Thus, we extend a result ofKarlin concerning Favard problem, to the case of restricted length interpolation.
Comparing interpolation techniques for annual temperature mapping across Xinjiang region
Ren-ping, Zhang; Jing, Guo; Tian-gang, Liang; Qi-sheng, Feng; Aimaiti, Yusupujiang
2016-11-01
Interpolating climatic variables such as temperature is challenging due to the highly variable nature of meteorological processes and the difficulty in establishing a representative network of stations. In this paper, based on the monthly temperature data which obtained from the 154 official meteorological stations in the Xinjiang region and surrounding areas, we compared five spatial interpolation techniques: Inverse distance weighting (IDW), Ordinary kriging, Cokriging, thin-plate smoothing splines (ANUSPLIN) and Empirical Bayesian kriging(EBK). Error metrics were used to validate interpolations against independent data. Results indicated that, the ANUSPLIN performed best than the other four interpolation methods.
Energy Technology Data Exchange (ETDEWEB)
MACKAY, W.W.; LUCCIO, A.U.
2006-06-23
It is important to have symplectic maps for the various electromagnetic elements in an accelerator ring. For some tracking problems we must consider elements which evolve during a ramp. Rather than performing a computationally intensive numerical integration for every turn, it should be possible to integrate the trajectory for a few sets of parameters, and then interpolate the transport map as a function of one or more parameters, such as energy. We present two methods for interpolation of symplectic matrices as a function of parameters: one method is based on the calculation of a representation in terms of a basis of group generators [2, 3] and the other is based on the related but simpler symplectification method of Healy [1]. Both algorithms guarantee a symplectic result.
Loop Subdivision Surface Based Progressive Interpolation
Institute of Scientific and Technical Information of China (English)
Fu-Hua (Frank) Cheng; Feng-Tao Fan; Shu-Hua Lai; Cong-Lin Huang; Jia-Xi Wang; Jun-Hai Yong
2009-01-01
A new method for constructing interpolating Loop subdivision surfaces is presented. The new method is an extension of the progressive interpolation technique for B-splines. Given a triangular mesh M, the idea is to iteratively upgrade the vertices of M to generate a new control mesh M such that limit surface of M would interpolate M. It can be shown that the iterative process is convergent for Loop subdivision surfaces. Hence, the method is well-defined. The new method has the advantages of both a local method and a global method, i.e., it can handle meshes of any size and any topology while generating smooth interpolating subdivision surfaces that faithfully resemble the shape of the given meshes. The meshes considered here can be open or closed.
Energy Technology Data Exchange (ETDEWEB)
Zainudin, Mohd Lutfi, E-mail: mdlutfi07@gmail.com [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Institut Matematik Kejuruteraan (IMK), Universiti Malaysia Perlis, 02600 Arau, Perlis (Malaysia); Saaban, Azizan, E-mail: azizan.s@uum.edu.my [School of Quantitative Sciences, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu, E-mail: mohdnazari@perlis.uitm.edu.my [Faculty of Applied Science, Universiti Teknologi Mara, 02600 Arau, Perlis (Malaysia)
2015-12-11
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device’s development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
Zainudin, Mohd Lutfi; Saaban, Azizan; Bakar, Mohd Nazari Abu
2015-12-01
The solar radiation values have been composed by automatic weather station using the device that namely pyranometer. The device is functions to records all the radiation values that have been dispersed, and these data are very useful for it experimental works and solar device's development. In addition, for modeling and designing on solar radiation system application is needed for complete data observation. Unfortunately, lack for obtained the complete solar radiation data frequently occur due to several technical problems, which mainly contributed by monitoring device. Into encountering this matter, estimation missing values in an effort to substitute absent values with imputed data. This paper aimed to evaluate several piecewise interpolation techniques likes linear, splines, cubic, and nearest neighbor into dealing missing values in hourly solar radiation data. Then, proposed an extendable work into investigating the potential used of cubic Bezier technique and cubic Said-ball method as estimator tools. As result, methods for cubic Bezier and Said-ball perform the best compare to another piecewise imputation technique.
A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation
Directory of Open Access Journals (Sweden)
Mingzhu Li
2014-01-01
Full Text Available The main aim of this work is to consider a meshfree algorithm for solving Burgers’ equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.
Cylindrical Helix Spline Approximation of Spatial Curves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we present a new method for approximating spatial curves with a G1 cylindrical helix spline within a prescribed tolerance. We deduce the general formulation of a cylindrical helix,which has 11 freedoms. This means that it needs 11 restrictions to determine a cylindrical helix. Given a spatial parametric curve segment, including the start point and the end point of this segment, the tangent and the principal normal of the start point, we can always find a cylindrical segment to interpolate the given direction and position vectors. In order to approximate the known parametric curve within the prescribed tolerance, we adopt the trial method step by step. First, we must ensure the helix segment to interpolate the given two end points and match the principal normal and tangent of the start point, and then, we can keep the deviation between the cylindrical helix segment and the known curve segment within the prescribed tolerance everywhere. After the first segment had been formed, we can construct the next segment. Circularly, we can construct the G1 cylindrical helix spline to approximate the whole spatial parametric curve within the prescribed tolerance. Several examples are also given to show the efficiency of this method.
Vibration Analysis of Beams by Spline Finite Element
Institute of Scientific and Technical Information of China (English)
YANG Hao; SUN Li
2011-01-01
In this paper,the spline finite element method is developed to investigate free vibration problems of beams.The cubic B-spline functions are used to construct the displacement field.The assembly of elements and the introduction of boundary conditions follow the standard finite element procedure.The results under various boundary conditions are compared with those obtained by the exact method and the finite difference method.It shows that the results are in excellent agreement with the analytical results and much more accurate than the results obtained by the finite difference method,especially for higher order modes.
Energy Technology Data Exchange (ETDEWEB)
Araujo, Carlos Eduardo S. [Universidade Federal de Campina Grande, PB (Brazil). Programa de Recursos Humanos 25 da ANP]. E-mail: carlos@dme.ufcg.edu.br; Silva, Rosana M. da [Universidade Federal de Campina Grande, PB (Brazil). Dept. de Matematica e Estatistica]. E-mail: rosana@dme.ufcg.edu.br
2004-07-01
This work presents an implementation of a synthetic model of a channel found in oil reservoir. The generation these models is one of the steps to the characterization and simulation of the equal probable three-dimensional geological scenery. O implemented model was obtained from fitting techniques of geometric modeling of curves and surfaces to the geological parameters (width, thickness, sinuosity and preferential direction) that defines the form to be modeled. The parameter sinuosity is related with the parameter wave length and the local amplitude of the channel, the parameter preferential direction indicates the way of the flow and the declivity of the channel. The modeling technique used to represent the surface of the channel is the sweeping technique, the consist in effectuate a translation operation from a curve along a guide curve. The guide curve, in our implementation, was generated by the interpolation of points obtained form sampled values or simulated of the parameter sinuosity, using the cubic splines of Bezier technique. A semi-ellipse, determinate by the parameter width and thickness, representing a transversal section of the channel, is the transferred curve through the guide curve, generating the channel surface. (author)
A Hybrid Interpolation for Reconstructing Near-Surface Model%混合插值法重构近地表模型
Institute of Scientific and Technical Information of China (English)
魏亦文; 王彦春
2012-01-01
When both the number of control points and the size of grid become large, TPS based reconstruction of near-surface model is often very time-consuming. Therefore, such method affects the efficiency of building near-surface model in the static correction. To address this problem, a hybrid interpolation combining TPS with cubic spline interpolation is used for reconstructing near surface model. Firstly, not only recursive LU decomposition but also GPU based LU decomposition is used to solve large linear system of equations. And then, TPS interpolation function is created. Secondly, the grid is rarefied with appropriate steps in the X and Y directions and then, TPS interpolation function is evaluated on the sparse grid. Based on which cubic spline interpolation function is created and then, it calculates the value of the other points. Finally, OpenGL visualizes the 3D near-surface model. The experimental results show that this algorithm speeds up the reconstruction of near-surface model and approximates the TPS interpolation in accuracy.%当控制点多和网格稠密时,基于薄板样条(TPS)插值的近地表模型重构往往很耗时,影响了静校正中近地表建模的效率.针对此问题,采用一种TPS插值和三次样条插值相结合的混合插值法重构近地表模型.首先利用矩阵递归LU分解及GPU加速的LU分解算法求解大型线性方程组,建立TPS插值函数；然后在X和Y方向上使用适当的步长对网格进行抽稀,运用TPS插值函数计算稀疏网格点的值,再通过稀疏网格点建立三次样条插值函数并计算剩余网格点的值；最后用OpenGL实现近地表模型的三维可视化.实验结果表明,文中算法提高了近地表模型重构的速度,其精度接近TPS插值精度.
DEFF Research Database (Denmark)
Engell-Nørregård, Morten Pol; Erleben, Kenny
dimensional 2D/3D deformable model. Our activation splines are easy to set up and can be used for physics based animation of deformable models such as snake motion and locomotion of characters. Our approach generalises easily to both 2D and 3D simulations and is applicable in physics based games or animations...
1981-05-01
try todefine a complex planar spline by holomorphic elements like polynomials, then by the well known identity theorem (e.g. Diederich- Remmert [9, p...R. Remmert : Funktionentheorie I, Springer, Berlin, Heidelberg, New York, 1972, 246 p. 10 0. Lehto - K.I. Virtanen: Quasikonforme AbbildunQen, Springer
Interchangeable spline reference guide
Energy Technology Data Exchange (ETDEWEB)
Dolin, R.M.
1994-05-01
The WX-Division Integrated Software Tools (WIST) Team evolved from two previous committees, First was the W78 Solid Modeling Pilot Project`s Spline Subcommittee, which later evolved into the Vv`X-Division Spline Committee. The mission of the WIST team is to investigate current CAE engineering processes relating to complex geometry and to develop methods for improving those processes. Specifically, the WIST team is developing technology that allows the Division to use multiple spline representations. We are also updating the contour system (CONSYS) data base to take full advantage of the Division`s expanding electronic engineering process. Both of these efforts involve developing interfaces to commercial CAE systems and writing new software. The WIST team is comprised of members from V;X-11, -12 and 13. This {open_quotes}cross-functional{close_quotes} approach to software development is somewhat new in the Division so an effort is being made to formalize our processes and assure quality at each phase of development. Chapter one represents a theory manual and is one phase of the formal process. The theory manual is followed by a software requirements document, specification document, software verification and validation documents. The purpose of this guide is to present the theory underlying the interchangeable spline technology and application. Verification and validation test results are also presented for proof of principal.
Norton, Andrew H.
1991-01-01
Local spline approximants offer a means for constructing finite difference formulae for numerical solution of PDEs. These formulae seem particularly well suited to situations in which the use of conventional formulae leads to non-linear computational instability of the time integration. This is explained in terms of frequency responses of the FDF.
Knot Optimization for Biharmonic B-splines on Manifold Triangle Meshes.
Hou, Fei; He, Ying; Qin, Hong; Hao, Aimin
2017-09-01
Biharmonic B-splines, proposed by Feng and Warren, are an elegant generalization of univariate B-splines to planar and curved domains with fully irregular knot configuration. Despite the theoretic breakthrough, certain technical difficulties are imperative, including the necessity of Voronoi tessellation, the lack of analytical formulation of bases on general manifolds, expensive basis re-computation during knot refinement/removal, being applicable for simple domains only (e.g., such as euclidean planes, spherical and cylindrical domains, and tori). To ameliorate, this paper articulates a new biharmonic B-spline computing paradigm with a simple formulation. We prove that biharmonic B-splines have an equivalent representation, which is solely based on a linear combination of Green's functions of the bi-Laplacian operator. Consequently, without explicitly computing their bases, biharmonic B-splines can bypass the Voronoi partitioning and the discretization of bi-Laplacian, enable the computational utilities on any compact 2-manifold. The new representation also facilitates optimization-driven knot selection for constructing biharmonic B-splines on manifold triangle meshes. We develop algorithms for spline evaluation, data interpolation and hierarchical data decomposition. Our results demonstrate that biharmonic B-splines, as a new type of spline functions with theoretic and application appeal, afford progressive update of fully irregular knots, free of singularity, without the need of explicit parameterization, making it ideal for a host of graphics tasks on manifolds.
USING SPLINE FUNCTIONS FOR THE SUBSTANTIATION OF TAX POLICIES BY LOCAL AUTHORITIES
Directory of Open Access Journals (Sweden)
Otgon Cristian
2011-07-01
-order, Hermite spline and cubic splines of class C2 .
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...
Shape preserving rational bi-cubic function
Directory of Open Access Journals (Sweden)
Malik Zawwar Hussain
2012-11-01
Full Text Available The study is dedicated to the development of shape preserving interpolation scheme for monotone and convex data. A rational bi-cubic function with parameters is used for interpolation. To preserve the shape of monotone and convex data, the simple data dependent constraints are developed on these parameters in each rectangular patch. The developed scheme of this paper is confined, cheap to run and produce smooth surfaces.
Penalized Splines for Smooth Representation of High-dimensional Monte Carlo Datasets
Whitehorn, Nathan; Lafebre, Sven
2013-01-01
Detector response to a high-energy physics process is often estimated by Monte Carlo simulation. For purposes of data analysis, the results of this simulation are typically stored in large multi-dimensional histograms, which can quickly become both too large to easily store and manipulate and numerically problematic due to unfilled bins or interpolation artifacts. We describe here an application of the penalized spline technique to efficiently compute B-spline representations of such tables and discuss aspects of the resulting B-spline fits that simplify many common tasks in handling tabulated Monte Carlo data in high-energy physics analysis, in particular their use in maximum-likelihood fitting.
Interpolation functors and interpolation spaces
Brudnyi, Yu A
1991-01-01
The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the r...
Usando splines cúbicas na modelagem matemática da evolução populacional de Pirapora/MG
Directory of Open Access Journals (Sweden)
José Sérgio Domingues
2014-08-01
Full Text Available O objetivo desse trabalho é obter um modelo matemático para a evolução populacional da cidade de Pirapora/MG, baseando-se apenas nos dados de censos e contagens populacionais do Instituto Brasileiro de Geografia e Estatística (IBGE. Para isso, é utilizada a interpolação por splines cúbicas, pois as técnicas de interpolação linear e polinomial, e também o modelo logístico, não se ajustam bem a essa população. Os dados analisados não são equidistantes, então, utiliza-se como amostra anos separados com passo h de 10 anos. Os valores descartados inicialmente e as estimativas populacionais para esse município, descritos pela Fundação João Pinheiro, serviram para validação do modelo construído, e para a estimativa das diferenças percentuais de previsão, que não ultrapassaram os 2,21%. Ao se considerar que o padrão de evolução populacional de 2000 a 2010 se manterá até 2020, estima-se as populações da cidade de 2011 a 2020, cuja diferença percentual média foi de apenas 0,49%. Conclui-se que o modelo se ajusta muito bem aos dados, e que estimativas populacionais em qualquer ano de 1970 e 2020 são confiáveis. Além disso, o modelo permite a visualização prática de uma aplicação dessa técnica na modelagem populacional, e, portanto, também pode ser utilizada para fins didáticos.Palavras-chave: Splines cúbicas. Interpolação. Modelagem matemática. Evolução populacional. Pirapora.Using cubic splines on mathematical modeling of the population evolution of Pirapora/MGThe main objective of this paper is to obtain a mathematical model for the evolution of the population in Pirapora/MG, based only on data from censuses and population counts from Brazilian Institute of Geography and Statistics (IBGE. For this, the cubic spline interpolation is used because the technique of linear and polynomial interpolation, and also the logistic model do not fit well with this population. The analyzed data are not equidistant
Spline trigonometric bases and their properties
Strelkov, N. A.
2001-08-01
A family of pairs of biorthonormal systems is constructed such that for each p\\in(1,\\infty) one of these systems is a basis in the space L_p(a,b), while the other is the dual basis in L_q(a,b) (here 1/p+1/q=1). The functions in the first system are products of trigonometric and algebraic polynomials; the functions in the second are products of trigonometric polynomials and the derivatives of B-splines. The asymptotic behaviour of the Lebesgue functions of the constructed systems is investigated. In particular, it is shown that the dominant terms of pointwise asymptotic expansions for the Lebesgue functions have everywhere (except at certain singular points) the form 4/\\pi^2\\ln n (that is, the same as in the case of an orthonormal trigonometric system). Interpolation representations with multiple nodes for entire functions of exponential type \\sigma are obtained. These formulae involve a uniform grid; however, by contrast with Kotel'nikov's theorem, where the mesh of the grid is \\pi/\\sigma and decreases as the type of the entire function increases, in the representations obtained the nodes of interpolation can be kept independent of \\sigma, and their multiplicity increases as the type of the interpolated function increases. One possible application of such representations (particularly, their multidimensional analogues) is an effective construction of asymptotically optimal approximation methods by means of scaling and argument shifts of a fixed function (wavelets, grid projection methods, and so on).
基于B样条空间等距线的机器人轨迹优化算法%Robot Trajectory Optimization Algorithm Based on Spatial Offset B-Spline
Institute of Scientific and Technical Information of China (English)
胡绳荪; 庹宇鲲; 申俊琦; 陈昌亮; 谷文; 李坚
2015-01-01
针对J形坡口焊接机器人轨迹示教中理论轨迹与实际轨迹偏差较大的问题,利用实际轨迹的空间等距线逼近下一道焊接轨迹,并设计了相贯线轨迹等距线的B样条逼近算法. 算法主要包括:基于等曲线弧长准则对原B样条曲线取样;利用向心算法计算取样点的等距点;计算插值于该等距点的3次B样条曲线;在给定的全局误差限内去除多余控制顶点. 试验结果表明:等距点的向心算法可以有效解决相贯线曲线局部修改后主法向量发散的问题;全局插值方法可以保留原曲线修改特征;全局误差限下去除多余控制顶点可以减少B样条曲线控制顶点数目.%For the problem of the large deviation between the theoretical trajectory and the real trajectory of the J-groove joint welding robot during trajectory teaching, a solution is proposed using the offset spline of the real trajec-tory to approximate the next welding trajectory. An approximation algorithm for offset B-spline of intersecting splines is designed, which includes the following steps: sampling the original B-spline with the uniform curve arc length crite-rion; calculating the offset points of the sample points with the centripetal algorithm; fitting a cubic B-spline with global interpolation; removing most control points under the global error bound. The experimental results are as fol-lows: the centripetal algorithm could solve the problem of the divergence of the principal normal vectors after local modification on the intersecting curve; the algorithm of global interpolating could retain the modification features of the original trajectory; the algorithm of removing control points under global error bound could remove most control points effectively and reduce the number of control points of B-spline.
Directory of Open Access Journals (Sweden)
S. Abhishek
2016-07-01
Full Text Available It is well understood that in any data acquisition system reduction in the amount of data reduces the time and energy, but the major trade-off here is the quality of outcome normally, lesser the amount of data sensed, lower the quality. Compressed Sensing (CS allows a solution, for sampling below the Nyquist rate. The challenging problem of increasing the reconstruction quality with less number of samples from an unprocessed data set is addressed here by the use of representative coordinate selected from different orders of splines. We have made a detailed comparison with 10 orthogonal and 6 biorthogonal wavelets with two sets of data from MIT Arrhythmia database and our results prove that the Spline coordinates work better than the wavelets. The generation of two new types of splines such as exponential and double exponential are also briefed here .We believe that this is one of the very first attempts made in Compressed Sensing based ECG reconstruction problems using raw data.
Generalized Additive Models, Cubic Splines and Penalized Likelihood.
1987-05-22
in case control studies ). All models in the table include dummy variable to account for the matching. The first 3 lines of the table indicate that OA...Ausoc. Breslow, N. and Day, N. (1980). Statistical methods in cancer research, volume 1- the analysis of case - control studies . International agency
APPLICATION OF CUBIC SPLINE FOR DESIGNING HEADWEAR FROM MATRIX ELEMENTS
Андросова, Галина; Браилов, Иван; Черепанова, Светлана; Бахтурина, Елена
2009-01-01
Рассмотрено проектирование объемных поверхностей из матричных элементов на примере головного убора. Осуществлено построение развертки поверхности, описание ее контура кубическим сплайном, вписывание в ее контур матричных элементов. Разработан алгоритм проектирования головного убора из матричных элементов.Es wird die Projektierung der Volumenoberfläche aus der Matrixelementen am Beispiel von der Kopfbedeckung betrachtet. Es wird die Struktur der Abtastung der Oberfläche, die Beschreibung ihrer...
Hilbertian kernels and spline functions
Atteia, M
1992-01-01
In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type. Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.
Splines and variational methods
Prenter, P M
2008-01-01
One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text's first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimension
Splines and the Galerkin method for solving the integral equations of scattering theory
Brannigan, M.; Eyre, D.
1983-06-01
This paper investigates the Galerkin method with cubic B-spline approximants to solve singular integral equations that arise in scattering theory. We stress the relationship between the Galerkin and collocation methods.The error bound for cubic spline approximates has a convergence rate of O(h4), where h is the mesh spacing. We test the utility of the Galerkin method by solving both two- and three-body problems. We demonstrate, by solving the Amado-Lovelace equation for a system of three identical bosons, that our numerical treatment of the scattering problem is both efficient and accurate for small linear systems.
Numerical solution of functional integral equations by using B-splines
Directory of Open Access Journals (Sweden)
Reza Firouzdor
2014-05-01
Full Text Available This paper describes an approximating solution, based on Lagrange interpolation and spline functions, to treat functional integral equations of Fredholm type and Volterra type. This method can be extended to functional dierential and integro-dierential equations. For showing eciency of the method we give some numerical examples.
Straight-sided Spline Optimization
DEFF Research Database (Denmark)
Pedersen, Niels Leergaard
2011-01-01
and the subject of improving the design. The present paper concentrates on the optimization of splines and the predictions of stress concentrations, which are determined by finite element analysis (FEA). Using design modifications, that do not change the spline load carrying capacity, it is shown that large...
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...
Two-dimensional cubic convolution.
Reichenbach, Stephen E; Geng, Frank
2003-01-01
The paper develops two-dimensional (2D), nonseparable, piecewise cubic convolution (PCC) for image interpolation. Traditionally, PCC has been implemented based on a one-dimensional (1D) derivation with a separable generalization to two dimensions. However, typical scenes and imaging systems are not separable, so the traditional approach is suboptimal. We develop a closed-form derivation for a two-parameter, 2D PCC kernel with support [-2,2] x [-2,2] that is constrained for continuity, smoothness, symmetry, and flat-field response. Our analyses, using several image models, including Markov random fields, demonstrate that the 2D PCC yields small improvements in interpolation fidelity over the traditional, separable approach. The constraints on the derivation can be relaxed to provide greater flexibility and performance.
使用B样条无单元法进行梯形盖板受力分析%Stress Analysis of Trapezoidal Slabs by Using B-spline Meshless Method
Institute of Scientific and Technical Information of China (English)
李彬
2013-01-01
To meet the needs of stress analysis and evaluation of trapezoidal slabs of skew culvert,this paper puts forward a B-spline meshless method based on moderately thick slab theory.By using dual quartic and dual cubic B-spline to make interpolation for the deflection and the turning angle respectively,this paper deduces the stiffness matrix and equivalent load formulations,introduces the method of setting boundary condition by using penalty function,enumerates the key points of using both Matlab and Spline Toolbox in order to achieve this method,and gives numerical verification result.The results from research and calculation show that this method proposed has advantages such as concise formulation,simple post-processing,high precision and efficiency,and can facilitate the development of relevant specialized analysis program.%为满足对斜交涵洞梯形盖板进行受力分析与评估的需要,提出基于中厚板理论的B样条无单元方法.实现中对挠度和转角分别采用双四次和双三次B样条进行插值,使用变分原理推导相应的刚度矩阵和等效荷载列式,介绍利用罚函数施加边界条件的方法,列举使用Matlab及Spline Toolbox实现该方法时的一些要点,提供了数值验证结果.研究及计算结果表明,该方法列式简洁、后处理方便、精度好、效率高,为相关专用分析程序的开发提供一条方便的途径.
An adaptive interpolation scheme for molecular potential energy surfaces
Kowalewski, Markus; Larsson, Elisabeth; Heryudono, Alfa
2016-08-01
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
An adaptive interpolation scheme for molecular potential energy surfaces
Kowalewski, Markus; Heryudono, Alfa
2016-01-01
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior is evaluated for a model function in 2, 3 and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
Estimating monthly temperature using point based interpolation techniques
Saaban, Azizan; Mah Hashim, Noridayu; Murat, Rusdi Indra Zuhdi
2013-04-01
This paper discusses the use of point based interpolation to estimate the value of temperature at an unallocated meteorology stations in Peninsular Malaysia using data of year 2010 collected from the Malaysian Meteorology Department. Two point based interpolation methods which are Inverse Distance Weighted (IDW) and Radial Basis Function (RBF) are considered. The accuracy of the methods is evaluated using Root Mean Square Error (RMSE). The results show that RBF with thin plate spline model is suitable to be used as temperature estimator for the months of January and December, while RBF with multiquadric model is suitable to estimate the temperature for the rest of the months.
1986-08-01
basic B-spline theory by studying the spline space 5k.t, i.e.. the collection of all functions s of the form s = , Bika , (3.1) for a suitable...B-spline coefficients to be zero. More than that. I will assume that t, lim t, :( ( 2) This assumption is convenient since it ensures that every IR...procedure. we arrive at the formula s Bilo which shows that k- 1, Algorithm 9. From given constant polynomials a’" aj, i k- I, (which determine s Bika
Numerical Integration Based on Bivariate Quartic Quasi-Interpolation Operators
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we propose a method to deal with numerical integral by using two kinds of C2 quasi-interpolation operators on the bivariate spline space, and also discuss the convergence properties and error estimates. Moreover, the proposed method is applied to the numerical evaluation of 2-D singular integrals. Numerical experiments will be carried out and the results will be compared with some previously published results.
Institute of Scientific and Technical Information of China (English)
辜旭赞; 张兵; 王明欢
2011-01-01
In this paper, from the Navier-Stokes primitive equations and Eulerian operator, forecasting equations are deduced with 2-order time and space differential remainder by Taylor series expansion, and incorporated to the Bicubic Numerical Model (BiNM for short), which is with a quasi-Lagrangian integration scheme of fitting cubic spline/bicubic surface to all physical variables in atmospheric equation sets on spherical discrete meshes. Their first-order and second-order derivatives as well as their upstream points were determined, and discrete time integration was performed in cubic space for the governing equations, I.e.With a new algorithm of "fitting bicubic surface - time step integration - fitting bicubic surface -......". Then,BiNM's mathematical foundation of numerical analysis was discussed for the cubic spline and its mathematical polar characters. It was pointed out that, as a spectrum model, BiNM shows mathematical "convergence" of the cubic spline and the bicubic surface contracting to the original function as well as its first-order and second-order derivatives, with the "optimality" of the second-order derivative of the cubic spline being optimal approximation to that of the original function. It was indicated that Hermite bicubic patches are equivalent in performing operation to the secondary derivative "mesh" variables. It was identified that the slope and curvature of the centred difference are respectively three-point smooth of that of the cubic spline. Using a global BiNM with latitude-longitude grids, and keeping the non-static and total field compressible, adiabatic and non-frictional, and running the so called "shallow atmosphere" equations in the spherical coordinate, and along with a quasi -Lagrangian time integration scheme, an ideal global simulation case was shown by adopting the re-analysis data of NCEP for getting an initial model atmosphere. Lastly, we had to say that, because atmospheric motion can be essentially non-linear, future Bi
Spatial interpolation of monthly mean climate data for China
Hong, Yan; Nix, Henry A.; Hutchinson, Mike F.; Booth, Trevor H.
2005-08-01
Spline interpolation techniques are used to develop a gridded climate database for China at a resolution of 0.01° in latitude and longitude. A digital elevation model (DEM) was developed at the same resolution to improve the accuracy of interpolation based upon the general spatial dependence of climate on topography. Climate data for the period 1971-2000 from meteorological stations in China were used to develop thin-plate smoothing spline surfaces for monthly mean temperature and precipitation. A regularly gridded climate database was produced by coupling the spline surfaces with the underlying DEM. The summary statistics show interpolation errors for monthly temperatures varying within 0.42-0.83 °C and 8-13% for monthly precipitation. These estimates are superior to results produced by methods commonly used in China. The fine-resolution spatial climate database has many potential applications in natural resource management. For example, it can be used as a baseline for climate change studies, in which potential distributions of flora and fauna can be predicted under the impact of climate change and priority areas for biodiversity conservation can be identified.
Servo-controlling structure of five-axis CNC system for real-time NURBS interpolating
Chen, Liangji; Guo, Guangsong; Li, Huiying
2017-07-01
NURBS (Non-Uniform Rational B-Spline) is widely used in CAD/CAM (Computer-Aided Design / Computer-Aided Manufacturing) to represent sculptured curves or surfaces. In this paper, we develop a 5-axis NURBS real-time interpolator and realize it in our developing CNC(Computer Numerical Control) system. At first, we use two NURBS curves to represent tool-tip and tool-axis path respectively. According to feedrate and Taylor series extension, servo-controlling signals of 5 axes are obtained for each interpolating cycle. Then, generation procedure of NC(Numerical Control) code with the presented method is introduced and the method how to integrate the interpolator into our developing CNC system is given. And also, the servo-controlling structure of the CNC system is introduced. Through the illustration, it has been indicated that the proposed method can enhance the machining accuracy and the spline interpolator is feasible for 5-axis CNC system.
ANALISIS REGRESI NONPARAMETRIK SPLINE MULTIVARIAT UNTUK PEMODELAN INDIKATOR KEMISKINAN DI INDONESIA
Directory of Open Access Journals (Sweden)
DESAK AYU WIRI ASTITI
2016-08-01
Full Text Available The aim of this study is to obtain statistics models which explain the relationship between variables that influence the poverty indicators in Indonesia using multivariate spline nonparametric regression method. Spline is a nonparametric regression estimation method that is automatically search for its estimation wherever the data pattern move and thus resulting in model which fitted the data. This study, uses data from survey of Social Economy National (Susenas and survey of Employment National (Sakernas of 2013 from the publication of the Central Bureau of Statistics (BPS. This study yields two models which are the best model from two used response variables. The criterion uses to select the best model is the minimum Generalized Cross Validation (GCV. The best spline model obtained is cubic spline model with five optimal knots.
Triangular bubble spline surfaces.
Kapl, Mario; Byrtus, Marek; Jüttler, Bert
2011-11-01
We present a new method for generating a [Formula: see text]-surface from a triangular network of compatible surface strips. The compatible surface strips are given by a network of polynomial curves with an associated implicitly defined surface, which fulfill certain compatibility conditions. Our construction is based on a new concept, called bubble patches, to represent the single surface patches. The compatible surface strips provide a simple [Formula: see text]-condition between two neighboring bubble patches, which are used to construct surface patches, connected with [Formula: see text]-continuity. For [Formula: see text], we describe the obtained [Formula: see text]-condition in detail. It can be generalized to any [Formula: see text]. The construction of a single surface patch is based on Gordon-Coons interpolation for triangles.Our method is a simple local construction scheme, which works uniformly for vertices of arbitrary valency. The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves. Several examples of [Formula: see text], [Formula: see text] and [Formula: see text]-surfaces are presented, which have been generated by using our method. The obtained surfaces are visualized with reflection lines to demonstrate the order of smoothness.
Dominant point detecting based non-uniform B-spline approximation for grain contour
Institute of Scientific and Technical Information of China (English)
ZHAO XiuYang; YIN YanSheng; YANG Bo
2007-01-01
Three-dimension reconstruction from serial sections has been used in the last decade to obtain information concerning three-dimensional microstructural geometry. One of the crucial steps of three-dimension reconstruction is getting compact and fairing grain contours. Based on the achievement of closed raw contours of ceramic composite grains by using wavelet and level set, an adaptive method is adopted for the polygonal approximation of the digitized raw contours. Instead of setting a fixed length of support region in advance, the novel method computes the suitable length of support region for each point to find the best estimated curvature. The dominant points are identified as the points with local maximum estimated curvatures. Periodic closed B-spline approximation is used to find the most compact B-spline grain boundary contours within the given tolerance. A flexible distance selection approach is adopted to obtain the common knot vector of serial contours consisting of less knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Finally, a B-spline surface interpolating the serial contours is generated via B-spline surface skinning.
Dominant point detecting based non-uniform B-spline approximation for grain contour
Institute of Scientific and Technical Information of China (English)
2007-01-01
Three-dimension reconstruction from serial sections has been used in the last decade to obtain information concerning three-dimensional microstructural ge-ometry. One of the crucial steps of three-dimension reconstruction is getting compact and fairing grain contours. Based on the achievement of closed raw con-tours of ceramic composite grains by using wavelet and level set, an adaptive method is adopted for the polygonal approximation of the digitized raw contours. Instead of setting a fixed length of support region in advance, the novel method computes the suitable length of support region for each point to find the best es-timated curvature. The dominant points are identified as the points with local maximum estimated curvatures. Periodic closed B-spline approximation is used to find the most compact B-spline grain boundary contours within the given tolerance. A flexible distance selection approach is adopted to obtain the common knot vector of serial contours consisting of less knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Finally, a B-spline surface interpolating the serial contours is generated via B-spline surface skinning.
Space cutter compensation method for five-axis nonuniform rational basis spline machining
Directory of Open Access Journals (Sweden)
Yanyu Ding
2015-07-01
Full Text Available In view of the good machining performance of traditional three-axis nonuniform rational basis spline interpolation and the space cutter compensation issue in multi-axis machining, this article presents a triple nonuniform rational basis spline five-axis interpolation method, which uses three nonuniform rational basis spline curves to describe cutter center location, cutter axis vector, and cutter contact point trajectory, respectively. The relative position of the cutter and workpiece is calculated under the workpiece coordinate system, and the cutter machining trajectory can be described precisely and smoothly using this method. The three nonuniform rational basis spline curves are transformed into a 12-dimentional Bézier curve to carry out discretization during the discrete process. With the cutter contact point trajectory as the precision control condition, the discretization is fast. As for different cutters and corners, the complete description method of space cutter compensation vector is presented in this article. Finally, the five-axis nonuniform rational basis spline machining method is further verified in a two-turntable five-axis machine.
Michel, Volker
2013-01-01
Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelet...
An Optimized Spline-Based Registration of a 3D CT to a Set of C-Arm Images
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We have developed an algorithm for the rigid-body registration of a CT volume to a set of C-arm images. The algorithm uses a gradient-based iterative minimization of a least-squares measure of dissimilarity between the C-arm images and projections of the CT volume. To compute projections, we use a novel method for fast integration of the volume along rays. To improve robustness and speed, we take advantage of a coarse-to-fine processing of the volume/image pyramids. To compute the projections of the volume, the gradient of the dissimilarity measure, and the multiresolution data pyramids, we use a continuous image/volume model based on cubic B-splines, which ensures a high interpolation accuracy and a gradient of the dissimilarity measure that is well defined everywhere. We show the performance of our algorithm on a human spine phantom, where the true alignment is determined using a set of fiducial markers.
Directory of Open Access Journals (Sweden)
Ilyasov R. H.
2014-10-01
Full Text Available The energy market shows strong exposure to seasonal fluctuations. A striking example of the impact of seasonality is the dynamics of the production of natural and associated gas in Russia. We use two approaches to the identification and analysis of seasonality: classical econometric based on different smoothing procedure; spline method uses an approximation of the economic dynamics of cubic splines and phase analysis. In the comparison of the two methods are used to identify the benefits of using spline functions when modeling economic dynamics and phase analysis of seasonality
Improvement of energy model based on cubic interpolation curve
Institute of Scientific and Technical Information of China (English)
Li Peipei; Li Xuemei; and Wei Yu
2012-01-01
In CAGD and CG, energy model is often used to control the curves and surfaces shape. In curve/surface modeling, we can get fair curve/surface by minimizing the energy of curve/surface. However, our research indicates that in some cases we can＇t get fair curves/surface using the current energy model. So an improved energy model is presented in this paper. Examples are also included to show that fair curves can be obtained using the improved energy model.
Examination of the Circle Spline Routine
Dolin, R. M.; Jaeger, D. L.
1985-01-01
The Circle Spline routine is currently being used for generating both two and three dimensional spline curves. It was developed for use in ESCHER, a mesh generating routine written to provide a computationally simple and efficient method for building meshes along curved surfaces. Circle Spline is a parametric linear blending spline. Because many computerized machining operations involve circular shapes, the Circle Spline is well suited for both the design and manufacturing processes and shows promise as an alternative to the spline methods currently supported by the Initial Graphics Specification (IGES).
Interpolation of climate variables and temperature modeling
Samanta, Sailesh; Pal, Dilip Kumar; Lohar, Debasish; Pal, Babita
2012-01-01
Geographic Information Systems (GIS) and modeling are becoming powerful tools in agricultural research and natural resource management. This study proposes an empirical methodology for modeling and mapping of the monthly and annual air temperature using remote sensing and GIS techniques. The study area is Gangetic West Bengal and its neighborhood in the eastern India, where a number of weather systems occur throughout the year. Gangetic West Bengal is a region of strong heterogeneous surface with several weather disturbances. This paper also examines statistical approaches for interpolating climatic data over large regions, providing different interpolation techniques for climate variables' use in agricultural research. Three interpolation approaches, like inverse distance weighted averaging, thin-plate smoothing splines, and co-kriging are evaluated for 4° × 4° area, covering the eastern part of India. The land use/land cover, soil texture, and digital elevation model are used as the independent variables for temperature modeling. Multiple regression analysis with standard method is used to add dependent variables into regression equation. Prediction of mean temperature for monsoon season is better than winter season. Finally standard deviation errors are evaluated after comparing the predicted temperature and observed temperature of the area. For better improvement, distance from the coastline and seasonal wind pattern are stressed to be included as independent variables.
A Parallel Nonrigid Registration Algorithm Based on B-Spline for Medical Images
Directory of Open Access Journals (Sweden)
Xiaogang Du
2016-01-01
Full Text Available The nonrigid registration algorithm based on B-spline Free-Form Deformation (FFD plays a key role and is widely applied in medical image processing due to the good flexibility and robustness. However, it requires a tremendous amount of computing time to obtain more accurate registration results especially for a large amount of medical image data. To address the issue, a parallel nonrigid registration algorithm based on B-spline is proposed in this paper. First, the Logarithm Squared Difference (LSD is considered as the similarity metric in the B-spline registration algorithm to improve registration precision. After that, we create a parallel computing strategy and lookup tables (LUTs to reduce the complexity of the B-spline registration algorithm. As a result, the computing time of three time-consuming steps including B-splines interpolation, LSD computation, and the analytic gradient computation of LSD, is efficiently reduced, for the B-spline registration algorithm employs the Nonlinear Conjugate Gradient (NCG optimization method. Experimental results of registration quality and execution efficiency on the large amount of medical images show that our algorithm achieves a better registration accuracy in terms of the differences between the best deformation fields and ground truth and a speedup of 17 times over the single-threaded CPU implementation due to the powerful parallel computing ability of Graphics Processing Unit (GPU.
A comparative analysis of different DEM interpolation methods
Directory of Open Access Journals (Sweden)
P.V. Arun
2013-12-01
Full Text Available Visualization of geospatial entities generally entails Digital Elevation Models (DEMs that are interpolated to establish three dimensional co-ordinates for the entire terrain. The accuracy of generated terrain model depends on the interpolation mechanism adopted and hence it is needed to investigate the comparative performance of different approaches in this context. General interpolation techniques namely Inverse Distance Weighted, kriging, ANUDEM, Nearest Neighbor, and Spline approaches have been compared. Differential ground field survey has been conducted to generate reference DEM as well as specific set of test points for comparative evaluation. We have also investigated the suitability of Shuttle Radar Topographic Mapper Digital Elevation Mapper for Indian terrain by comparing it with the Survey of India (SOI Digital Elevation Model (DEM. Contours were generated at different intervals for comparative analysis and found SRTM as more suitable. The terrain sensitivity of various methods has also been analyzed with reference to the study area.
A Blossoming Development of Splines
Mann, Stephen
2006-01-01
In this lecture, we study Bezier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bezier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface. The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geom
Numerical Methods Using B-Splines
Shariff, Karim; Merriam, Marshal (Technical Monitor)
1997-01-01
The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.
Isogeometric analysis using T-splines
Bazilevs, Yuri
2010-01-01
We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize the current status of T-splines, their limitations, and future possibilities. © 2009 Elsevier B.V.
Institute of Scientific and Technical Information of China (English)
Xing-hua; WANG
2007-01-01
Explicit representations for the Hermite interpolation and their derivatives of any order are provided.Furthermore,suppose that the interpolated function f has continuous derivatives of sufficiently high order on some sufficiently small neighborhood of a given point x and any group of nodes are also given on the neighborhood.If the derivatives of any order of the Hermite interpolation polynomial of f at the point x are applied to approximating the corresponding derivatives of the function f(x),the asymptotic representations for the remainder are presented.
Next Generation Network Real-Time Kinematic Interpolation Segment to Improve the User Accuracy
Directory of Open Access Journals (Sweden)
Mohammed Ouassou
2015-01-01
Full Text Available This paper demonstrates that automatic selection of the right interpolation/smoothing method in a GNSS-based network real-time kinematic (NRTK interpolation segment can improve the accuracy of the rover position estimates and also the processing time in the NRTK processing center. The methods discussed and investigated are inverse distance weighting (IDW; bilinear and bicubic spline interpolation; kriging interpolation; thin-plate splines; and numerical approximation methods for spatial processes. The methods are implemented and tested using GNSS data from reference stations in the Norwegian network RTK service called CPOS. Data sets with an average baseline between reference stations of 60–70 km were selected. 12 prediction locations were used to analyze the performance of the interpolation methods by computing and comparing different measures of the goodness of fit such as the root mean square error (RMSE, mean square error, and mean absolute error, and also the computation time was compared. Results of the tests show that ordinary kriging with the Matérn covariance function clearly provides the best results. The thin-plate spline provides the second best results of the methods selected and with the test data used.
Diversification improves interpolation
Giesbrecht, Mark
2011-01-01
We consider the problem of interpolating an unknown multivariate polynomial with coefficients taken from a finite field or as numerical approximations of complex numbers. Building on the recent work of Garg and Schost, we improve on the best-known algorithm for interpolation over large finite fields by presenting a Las Vegas randomized algorithm that uses fewer black box evaluations. Using related techniques, we also address numerical interpolation of sparse complex polynomials, and provide the first provably stable algorithm (in the sense of relative error) for this problem, at the cost of modestly more interpolation points. A key new technique is a randomization which makes all coefficients of the unknown polynomial distinguishable, producing what we call a diverse polynomial. Another departure of our algorithms from most previous approaches is that they do not rely on root finding as a subroutine. We show how these improvements affect the practical performance with trial implementations.
Extension Of Lagrange Interpolation
Directory of Open Access Journals (Sweden)
Mousa Makey Krady
2015-01-01
Full Text Available Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
Extension Of Lagrange Interpolation
Mousa Makey Krady
2015-01-01
Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
[Comparison of spatial interpolation methods for daily meteorological elements].
Jiang, Xiao-Jian; Liu, Xiao-Jun; Huang, Fen; Jiang, Hai-Yan; Cao, Wei-Xing; Zhu, Yan
2010-03-01
A comparative study was made to evaluate the methods of inverse distance weighting (IDW), co-kriging (CK), and thin plate spline (TPS) in interpolating the average meteorological elements (including maximum air temperature, minimum air temperature, sunshine hours, and precipitation) of the 15th day per month from the 1951-2005 comprehensive observation data of 559 meteorological stations in China. The results showed that the RMSEs for the maximum and minimum air temperature in a year interpolated by TPS were the smallest (1.02 degrees C and 1.12 degrees C, respectively), and the R2 between the observed and predicted values were the highest (0.9916 and 0.9913, respectively), compared with those interpolated by IDW and CK. In four seasons, the smallest RMSEs for the maximum and minimum air temperature interpolated by TPS were observed in autumn (0.83 degrees C) and summer (0.86 degrees C), respectively, and the R2 between the observed and predicted values interpolated by TPS were higher in autumn than in other seasons. The RMSEs for the sunshine hours and precipitation in a year interpolated by TPS were the smallest (0.59 h and 1.01 mm, respectively), and the R2 between the observed and predicted values were the highest (0.9118 and 0.8135, respectively), compared with those interpolated by IDW and CK. In four seasons, the RMSE for the sunshine hours in winter interpolated by TPS was the smallest (0.49 h), and the R2 between the observed and predicted sunshine hours was the smallest (0.9293). The RMSE for the precipitation in winter interpolated by TPS was the smallest (0.33 mm), while the RMSE for the precipitation in summer interpolated by IDW was the smallest (2.01 mm). The R2 between the observed and predicted precipitation in winter interpolated by CK was the highest (0.8781). It was suggested that TPS could be the optimal spatial interpolation method in interpolating and rasterizing the daily meteorological elements in China.
Significance of initial interpolation in band-limited signal interpolation
Yegnanarayana, B.; Fathima, S. Tanveer; Nehru, B. T. K. R.; Venkataramanan, B.
1989-01-01
An improved version of the Papoulis algorithm for bandlimited signal interpolation is presented. This algorithm uses the concept of initial interpolation. The justification for initial interpolation is developed only through experimental studies. It is shown that the performance of the interpolation scheme depends on the number and distribution of the known data samples.
HILBERTIAN APPROACH FOR UNIVARIATE SPLINE WITH TENSION
Institute of Scientific and Technical Information of China (English)
A.Bouhamidi
2001-01-01
In this work,a new approach is proposed for constructing splines with tension.The basic idea is in the use of distributions theory,which allows us to define suitable Hilbert spaces in which the tension spline minimizes some energy functional.Classical orthogonal conditions and characterizations of the spline in terms of a fundamental solution of a differential operator are provided.An explicit representation of the tension spline is given.The tension spline can be computed by solving a linear system.Some numerical examples are given to illustrate this approach.
A Hybrid Spline Metamodel for Photovoltaic/Wind/Battery Energy Systems
ZAIBI, Malek; LAYADI, Toufik Madani; Champenois, Gérard; ROBOAM, xavier; Sareni, Bruno; Belhadj, Jamel
2015-01-01
This paper proposes a metamodel design for a Photovoltaic/Wind/Battery Energy System. The modeling of a hybrid PV/wind generator coupled with two kinds of storage i.e. electric (battery) and hydraulic (tanks) devices is investigated. A metamodel is carried out by hybrid spline interpolation to solve the relationships between several design variables i.e. the design parameters of different subsystems and their associate response variables i.e. system indicators performance. The developed model...
Constructing iterative non-uniform B-spline curve and surface to fit data points
Institute of Scientific and Technical Information of China (English)
LIN Hongwei; WANG Guojin; DONG Chenshi
2004-01-01
In this paper, based on the idea of profit and loss modification, we present the iterative non-uniform B-spline curve and surface to settle a key problem in computer aided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We start with a piece of initial non-uniform B-spline curve (surface) which takes the given point set as its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higher precision. In this paper, using modern matrix theory, we strictly prove that the limit curve (surface) of the iteration interpolates the given point set. The non-uniform B-spline curves (surfaces) generated with the iteration have many advantages, such as satisfying the NURBS standard, having explicit expression, gaining locality, and convexity preserving,etc.
The use of B-splines in the assessment of strain levels associated with plain dents
Energy Technology Data Exchange (ETDEWEB)
Noronha Junior, Dauro B.; Martins, Ricardo R. [PETROBRAS, Rio de Janeiro, RJ (Brazil). Centro de Pesquisas (CENPES); Jacob, Breno P.; Souza, Eduardo [Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Civil. Lab. de Metodos Computacionais e Sistemas Offshore (LAMCSO)
2005-07-01
Most international pipeline codes consider plain dents injurious if they exceed a depth of 6% of the nominal pipe diameter. ASME B31.8 - Gas Transmission and Distribution Piping Systems - 2003 Edition gives an alternative to the above mentioned limit. According to this edition of the code, plain dents of any depth are acceptable provided strain levels associated with the deformation do not exceed 6% strain. In order to use the method for estimating strain in dents proposed in Appendix R of B31.8 Code, interpolation or other mathematical technique is usually necessary to develop surface contour information from in-line inspections (ILI) tools or direct information data. This paper describes the application of a piece-wise interpolating technique that makes use of fourth-order B-spline curves to approximating the dent profile in both longitudinal and circumferential directions. The results obtained using B-splines were tested against nonlinear finite analyses of dented pipelines and a distinct methodology proposed by Rosenfeld et al. (1998). The results obtained with the use of B-splines compared well with both techniques. Furthermore, the extension of the proposed methodology to the description of the topology of dents with more general shapes using B-spline surfaces is very promising. (author)
Optimization of straight-sided spline design
DEFF Research Database (Denmark)
Pedersen, Niels Leergaard
2011-01-01
and the subject of improving the design. The present paper concentrates on the optimization of splines and the predictions of stress concentrations, which are determined by finite element analysis (FEA). Using different design modifications, that do not change the spline load carrying capacity, it is shown......Spline connection of shaft and hub is commonly applied when large torque capacity is needed together with the possibility of disassembly. The designs of these splines are generally controlled by different standards. In view of the common use of splines, it seems that few papers deal with splines...... that large reductions in the maximum stress are possible. Fatigue life of a spline can be greatly improved with up to a 25% reduction in the maximum stress level. Design modifications are given as simple analytical functions (modified super elliptical shape) with only two active design parameters...
EOS Interpolation and Thermodynamic Consistency
Energy Technology Data Exchange (ETDEWEB)
Gammel, J. Tinka [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-11-16
As discussed in LA-UR-08-05451, the current interpolator used by Grizzly, OpenSesame, EOSPAC, and similar routines is the rational function interpolator from Kerley. While the rational function interpolator is well-suited for interpolation on sparse grids with logarithmic spacing and it preserves monotonicity in 1-d, it has some known problems.
EOS Interpolation and Thermodynamic Consistency
Energy Technology Data Exchange (ETDEWEB)
Gammel, J. Tinka [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-11-16
As discussed in LA-UR-08-05451, the current interpolator used by Grizzly, OpenSesame, EOSPAC, and similar routines is the rational function interpolator from Kerley. While the rational function interpolator is well-suited for interpolation on sparse grids with logarithmic spacing and it preserves monotonicity in 1-d, it has some known problems.
Spline and spline wavelet methods with applications to signal and image processing
Averbuch, Amir Z; Zheludev, Valery A
This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images upsampling. In addition to the design of a diverse library of splines, SW, SWP a...
Error Estimates Derived from the Data for Least-Squares Spline Fitting
Energy Technology Data Exchange (ETDEWEB)
Jerome Blair
2007-06-25
The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primary contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.
[Calculation of radioimmunochemical determinations by "spline approximation" (author's transl)].
Nolte, H; Mühlen, A; Hesch, R D; Pape, J; Warnecke, U; Jüppner, H
1976-06-01
A simplified method, based on the "spline approximation", is reported for the calculation of the standard curves of radioimmunochemical determinations. It is possible to manipulate the mathematical function with a pocket calculator, thus making it available for a large number of users. It was shown that, in contrast to the usual procedures, it is possible to achieve optimal quality control in the preparation of the standard curves and in the interpolation of unknown plasma samples. The recaluculation of interpolated values from their own standard curve revealed an error of 4.9% which would normally be an error of interpolation. The new method was compared with two established methods for 8 different radioimmunochemical determinations. The measured values of the standard curve showed a weighting, and there was a resulting quality control of these values, which, according to their statistical evalution, were more accurate than those of the others models (Ekins et al., Yalow et al., (1968), in: Radioisotopes in Medicine: in vitro studies (Hayes, R. L., Goswitz, F.A. & Murphy, B. E. P., eds) USA EC, Oak Ridge) and Rodbard et al. (1971), in: Competitive protein Binding Assys(Odell, W. D. & Danghedy, W. H., eds.) Lipincott, Philadelphia and Toronto). In contrast with these other models, the described method makes no mathematical or kinetic preconditions with respect to the dose-response relationship. To achieve optimal reaction conditions, experimentally determined reaction data are preferable to model theories.
Directory of Open Access Journals (Sweden)
Neng Wan
2014-01-01
Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.
Institute of Scientific and Technical Information of China (English)
李桂清; 李华
2001-01-01
顶点位置和法向插值是参数曲面造型的重要内容．文中基于混合子分方法生成三次B样条控制网格，使得相应的三次B样条曲面插值初始网格中指定的顶点，并通过引入插值模板的概念，把法向的插值转化为对模板的旋转变换，使得曲面在不改变插值顶点的情况下插值法向，最后得到一张C2连续的插值指定顶点和法向的曲面．与传统的逐片Bézier或Coons曲面片构造方法相比，此方法更为简洁且具有更高的连续阶，而且易于推广到高阶B样条和任意拓扑情形，具有较强的实用性．%Interpolation to vertex positions and normals is one of important contents in parametric surface modeling. This paper presents an approach based on Catmull-Clark and Doo-Sabin subdivision schemes to generate the control net of bi-cubic B-spline surface interpolating the given vertices of initial net. The notion of stencils is introduced such that the normal interpolation is converted into the rotation transformation of stencils without influencing the effects of vertex interpolation, thus a C2-continuous surface interpolating given vertices and normals is obtained. Compared to traditional methods through stitching patches piece by piece, our method is more compact and has smoothness of higher degree. In addition, the method can be easily extended to high degree B-spline surfaces with arbitrary topology nets and it is also fairly useful for practical applications.
Multivariate Birkhoff interpolation
Lorentz, Rudolph A
1992-01-01
The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well a...
SUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULAR ELEMENT OF THE FINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
Qi-ding Zhu
2000-01-01
In this paper, we construct a projection interpolation for cubic triangular ele- ment by using othogonal expansion triangular method. We show two fundamental formulas of estimation on a special partion and obtain a superconvergence result of 1 -e order higher for the placement function and its tangential derivative on the third order Lobatto points and Gauss points on each edge of triangular element.
Quadrotor system identification using the multivariate multiplex b-spline
Visser, T.; De Visser, C.C.; Van Kampen, E.J.
2015-01-01
A novel method for aircraft system identification is presented that is based on a new multivariate spline type; the multivariate multiplex B-spline. The multivariate multiplex B-spline is a generalization of the recently introduced tensor-simplex B-spline. Multivariate multiplex splines obtain simil
Directory of Open Access Journals (Sweden)
Mingjian Sun
2015-01-01
Full Text Available Photoacoustic imaging is an innovative imaging technique to image biomedical tissues. The time reversal reconstruction algorithm in which a numerical model of the acoustic forward problem is run backwards in time is widely used. In the paper, a time reversal reconstruction algorithm based on particle swarm optimization (PSO optimized support vector machine (SVM interpolation method is proposed for photoacoustics imaging. Numerical results show that the reconstructed images of the proposed algorithm are more accurate than those of the nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation based time reversal algorithm, which can provide higher imaging quality by using significantly fewer measurement positions or scanning times.
Optimal image interpolation using local low-order surfaces
Gustafson, Steven C.; Claypoole, Roger L., Jr.; Magee, Eric P.; Loomis, John S.
2002-05-01
Desirable features of any digital image resolution- enhancement algorithm include exact interpolation (for 'distortionless' or 'lossless' processing) adjustable resolution, adjustable smoothness, and ease of computation. A given low-order polynomial surface (linear, quadratic, cubic, etc.) optimally fit by least squares to a given local neighborhood of a pixel to be interpolated can enable all of these features. For example, if the surface is cubic, if a pixel and the 5-by-5 pixel array surrounding it are selected, and if interpolation of this pixel must yield a 4- by-4 array of sub-pixels, then the 10 coefficients that define the surface may be determined by the constrained least squares solution of 25 linear equations in 10 unknowns, where each equation sets the surface value at a pixel center equal to the pixel gray value and where the constraint is that the mean of the surface values at the sub-pixel centers equals the gray value of the interpolated pixel. Note that resolution is adjustable because the interpolating surface for each pixel may be subdivided arbitrarily, that smoothness is adjustable (within each pixel) because the polynomial order and number neighboring pixels may be selected, and that the most computationally demanding operation is solving a relatively small number of simultaneous linear equations for each pixel.
基于曲线插补的多轴联动交叉耦合控制方法%Multi-axis cross-coupled control approach based on curve interpolation
Institute of Scientific and Technical Information of China (English)
赵国勇; 赵玉刚
2011-01-01
针对高精度轮廓跟踪需要,将曲线插补和交叉耦合控制器结合起来进行研究。在每个采样周期根据各轴反馈的实际刀具位置与插补缓冲区中存储的一定数量的插补点,研究了一种＂三点圆弧法＂轮廓误差计算模型,并研究了轮廓误差补偿修正量计算及分配方法。在数控试验台上跟踪一段三次非均匀有理B样条轮廓曲线,对比试验表明,所提出的基于曲线插补的轮廓误差交叉耦合控制方法能够有效减小轮廓误差,获得更高轮廓精度。%Aiming at the tracking demand of high precision contour,the cross-coupled controller integrated with curve interpolation was studied.According to the real cutter positions from each axis feedback and the interpolation dots stored in the interpolation buffer in every sampling period,a ＂three-point arc approach＂ contour error computing model was developed.Moreover,the contour error compensated correction quantity computation and distribution approach was put forward.A cubic Non-Uniform Rational B-Spline Curve（NURBS） profile curve on the numerial control experiment table was tracked.The experiment results showed that the developed contour error cross-coupled control approach based on curve interpolation could effectively reduce contour error and obtain satisfactory contour precision.
Fuzzy Interpolation and Other Interpolation Methods Used in Robot Calibrations
Directory of Open Access Journals (Sweden)
Ying Bai
2012-01-01
Full Text Available A novel interpolation algorithm, fuzzy interpolation, is presented and compared with other popular interpolation methods widely implemented in industrial robots calibrations and manufacturing applications. Different interpolation algorithms have been developed, reported, and implemented in many industrial robot calibrations and manufacturing processes in recent years. Most of them are based on looking for the optimal interpolation trajectories based on some known values on given points around a workspace. However, it is rare to build an optimal interpolation results based on some random noises, and this is one of the most popular topics in industrial testing and measurement applications. The fuzzy interpolation algorithm (FIA reported in this paper provides a convenient and simple way to solve this problem and offers more accurate interpolation results based on given position or orientation errors that are randomly distributed in real time. This method can be implemented in many industrial applications, such as manipulators measurements and calibrations, industrial automations, and semiconductor manufacturing processes.
Institute of Scientific and Technical Information of China (English)
叶留青; 杨梦龙; 陈绍春
2006-01-01
给出了C1[a,b]保形三次Spline插值函数的充要条件,采取控制导数的调节参数使角点横坐标满足一定限制条件,建立一类C1连续保形三次样条插值函数的构造方法.
Institute of Scientific and Technical Information of China (English)
邱绵浩; 刘箐; 丛华
2007-01-01
经典的经验模式分解(EMD)方法通过求解信号的上下2条三次样条包络曲线的均值曲线,实现对原始信号的分解.但是对于非平稳、非线性信号,包络平均无法代替真正的局部平均.另外,基于包络平均的分解方法还会引入极值过冲和欠冲问题.利用B样条的良好局部性质直接计算信号的局部均值插值曲线,克服了三次样条包络方法在EMD分解中的不足.通过对旋转机械故障振动信号的分解处理,表明基于B样条局部均值插值曲线的经验模式分解方法得到的固有模式函数更符合信号的真实物理意义,分解结果更好.
Institute of Scientific and Technical Information of China (English)
王秀峰; 陈心昭
2001-01-01
基于三次B样条插值的统计边界元法，对随机振动结构声辐射的计算进行了研究。以随机振动球作为算例，计算了其在表面振速功率谱密度函数分布已知情况下的随机声场，计算结果与理论解比较表明：即使在边界剖分比较粗的情况下，利用该方法计算随机振动结构声辐射问题在相当宽的振动频率范围内，也能给出良好的计算精度。
Institute of Scientific and Technical Information of China (English)
冯仁忠; 查理
2005-01-01
为了避免一般的局部插值算法生成的B样条曲线和曲面在段点处达不到理想的连续性以及出现多重内节点的问题,一种局部构造C2连续的三次B样条插值曲线和双三次插值曲面的方法被介绍.该方法借助节点插入算法逐步地迭代出样条控制顶点,其思想简单、几何直观、算法速度快,在曲线中夹直线段、尖点以及在曲面中夹棱边和平面都能比较容易实现.生成的曲线光滑度高、无重节点.文章最后还利用这种构造方法给出了一种在指定范围内按规定变形曲线的方法.
Optimal Knot Selection for Least-squares Fitting of Noisy Data with Spline Functions
Energy Technology Data Exchange (ETDEWEB)
Jerome Blair
2008-05-15
An automatic data-smoothing algorithm for data from digital oscilloscopes is described. The algorithm adjusts the bandwidth of the filtering as a function of time to provide minimum mean squared error at each time. It produces an estimate of the root-mean-square error as a function of time and does so without any statistical assumptions about the unknown signal. The algorithm is based on least-squares fitting to the data of cubic spline functions.
Conformal Solid T-spline Construction from Boundary T-spline Representations
2012-07-01
idea of isogeo- metric analysis [6, 2], one challenge is to automatically cre- ate a conformal solid NURBS /T-spline model with the given spline...solid NURBS construction method for patient-specific vas- cular geometric models was presented. In [1], a swept vol- ume parameterization was built for...representations. A general methodology for constructing a conformal solid T-spline from boundary T-spline/ NURBS representations is 2 Yongjie Zhang et al. (a
Kaiser-Bessel Basis for the Particle-Mesh Interpolation
Gao, Xingyu; Wang, Han
2016-01-01
In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the optimized Kaiser-Bessel basis with the traditional B-spline basis, we demonstrate that the former is more accurate than the latter in part of the working parameter space, saying a relatively small real space cutoff, a relatively small reciprocal space mesh and a relatively large truncation of basis. In some cases, the Kaiser-Bessel basis is found to be more than one order of magnitude more accurate. Therefore, it is worth trying the Kaiser-Bessel basis in the simulations where the computational accuracy of the electrostatic interaction is critical.
Kaiser-Bessel basis for particle-mesh interpolation
Gao, Xingyu; Fang, Jun; Wang, Han
2017-06-01
In this work, we introduce the Kaiser-Bessel interpolation basis for the particle-mesh interpolation in the fast Ewald method. A reliable a priori error estimate is developed to measure the accuracy of the force computation in correlated charge systems, and is shown to be effective in optimizing the shape parameter of the Kaiser-Bessel basis in terms of accuracy. By comparing the optimized Kaiser-Bessel basis with the traditional B -spline basis, we demonstrate that the former is more accurate than the latter in part of the working parameter space, say, a relatively small real-space cutoff, a relatively small reciprocal space mesh, and a relatively large truncation of basis. In some cases, the Kaiser-Bessel basis is found to be more than one order of magnitude more accurate.
Spline-based automatic path generation of welding robot
Institute of Scientific and Technical Information of China (English)
Niu Xuejuan; Li Liangyu
2007-01-01
This paper presents a flexible method for the representation of welded seam based on spline interpolation. In this method, the tool path of welding robot can be generated automatically from a 3D CAD model. This technique has been implemented and demonstrated in the FANUC Arc Welding Robot Workstation. According to the method, a software system is developed using VBA of SolidWorks 2006. It offers an interface between SolidWorks and ROBOGUIDE, the off-line programming software of FANUC robot. It combines the strong modeling function of the former and the simulating function of the latter. It also has the capability of communication with on-line robot. The result data have shown its high accuracy and strong reliability in experiments. This method will improve the intelligence and the flexibility of the welding robot workstation.
Fast regularized image interpolation method
Institute of Scientific and Technical Information of China (English)
Hongchen Liu; Yong Feng; Linjing Li
2007-01-01
The regularized image interpolation method is widely used based on the vector interpolation model in which down-sampling matrix has very large dimension and needs large storage consumption and higher computation complexity. In this paper, a fast algorithm for image interpolation based on the tensor product of matrices is presented, which transforms the vector interpolation model to matrix form. The proposed algorithm can extremely reduce the storage requirement and time consumption. The simulation results verify their validity.
A new method for automatically constructing convexity-preserving interpolatory splines
Institute of Scientific and Technical Information of China (English)
PAN Yongjuan; WANG Guojin
2004-01-01
Constructing a convexity-preserving interpolating curve according to the given planar data points is a problem to be solved in computer aided geometric design (CAGD). So far, almost all methods must solve a system of equations or recur to a complicated iterative process, and most of them can only generate some function-form convexity-preserving interpolating curves which are unaccommodated with the parametric curves, commonly used in CAGD systems. In order to overcome these drawbacks, this paper proposes a new method that can automatically generate some parametric convexity-preserving polynomial interpolating curves but dispensing with solving any system of equations or going at any iterative computation. The main idea is to construct a family of interpolating spline curves first with the shape parameter a as its family parameter; then, using the positive conditions of Bernstein polynomial to respectively find a range in which the shape parameter a takes its value for two cases of global convex data points and piecewise convex data points so as to make the corresponding interpolating curves convexity-preserving and C2(or G1) continuous. The method is simple and convenient, and the resulting interpolating curves possess smooth distribution of curvature. Numerical examples illustrate the correctness and the validity of theoretical reasoning.
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
航测数据处理中的空间插值方法比较%Spatial Interpolation Methods in Aerial Survey Data Processing
Institute of Scientific and Technical Information of China (English)
王颖; 祝民强; 乔康宁
2011-01-01
航测数据的航线间距与采样点间距差异很大,生成等值线时需要进行空间插值.以云南省江川地区的航测数据为实验数据源,分别采用反距离权重插值(IDW)、规则样条函数插值(Regularized Spline)、张力样条函数(Tension Spline)插值和Kriging插值等4种插值方法,对航测数据进行分析与比较,从中选出一种最优的插值方法及其参数,以提高航空放射性测量数据的预浏精度和质量.验证结果表明,4种插值方法,相对均方差(RMSE)的排列顺序为:Tension Spline < Regularized Spline < IDW < Kriging,且插值分析中Tension所绘制的铀含量等值线也为最佳分布.因此,Tension插值方法在该航测数据处理中插值效果最好,预测的精度也最高.%The route distance of aerial survey data is quite different from the sample points distance. When sample points generate contours, they need spatial interpolation. This paper took the aerial survey data of Jiangchuan of Yunnan Province as the experimental data source, and applied the Inverse Distance Weighted( IDW ), Regularized Spline, Tension Spline, Kriging four interpolation methods respectively for analyzing and comparing aerial survey data to chose one of the optimal interpolation methods and its parameters,so forth to improve the accuracy and quality of aerial radiological survey data. The validation results showed that the order of Relative Mean Square Error(RMSE) of the four kinds of interpolation methods is Tension Spline ＜ Regularized Spline ＜ IDW ＜ Kriging, and Tension interpolation methods’contour map is the most optimal distribution in the interpolation analyze. Therefore, Tension of Spline interpolation methods’effort is the most natural and the highest prediction accuracy in the aerial survey data processing.
Quantitative evaluation of convolution-based methods for medical image interpolation.
Meijering, E H; Niessen, W J; Viergever, M A
2001-06-01
Interpolation is required in a variety of medical image processing applications. Although many interpolation techniques are known from the literature, evaluations of these techniques for the specific task of applying geometrical transformations to medical images are still lacking. In this paper we present such an evaluation. We consider convolution-based interpolation methods and rigid transformations (rotations and translations). A large number of sinc-approximating kernels are evaluated, including piecewise polynomial kernels and a large number of windowed sinc kernels, with spatial supports ranging from two to ten grid intervals. In the evaluation we use images from a wide variety of medical image modalities. The results show that spline interpolation is to be preferred over all other methods, both for its accuracy and its relatively low computational cost.
A temporal interpolation approach for dynamic reconstruction in perfusion CT.
Montes, Pau; Lauritsch, Günter
2007-07-01
This article presents a dynamic CT reconstruction algorithm for objects with time dependent attenuation coefficient. Projection data acquired over several rotations are interpreted as samples of a continuous signal. Based on this idea, a temporal interpolation approach is proposed which provides the maximum temporal resolution for a given rotational speed of the CT scanner. Interpolation is performed using polynomial splines. The algorithm can be adapted to slow signals, reducing the amount of data acquired and the computational cost. A theoretical analysis of the approximations made by the algorithm is provided. In simulation studies, the temporal interpolation approach is compared with three other dynamic reconstruction algorithms based on linear regression, linear interpolation, and generalized Parker weighting. The presented algorithm exhibits the highest temporal resolution for a given sampling interval. Hence, our approach needs less input data to achieve a certain quality in the reconstruction than the other algorithms discussed or, equivalently, less x-ray exposure and computational complexity. The proposed algorithm additionally allows the possibility of using slow rotating scanners for perfusion imaging purposes.
Interpolation of Vector Measures
Institute of Scientific and Technical Information of China (English)
Ricardo del CAMPO; Antonio FERN(A)NDEZ; Fernando MAYORAL; Francisco NARANJO; Enrique A. S(A)NCHEZ-P(E)REZ
2011-01-01
Let (Ω, ∑) be a measurable space and m0: ∑→ X0 and m1: ∑ -→ X1 be positive vector measures with values in the Banach K(o)the function spaces X0 and X1. If 0 < α < 1, we define a X10-αXα1 and we analyze the space of integrable functions with respect to measure [m0, m1]α in order to prove suitable extensions of the classical Stein-Weiss formulas that hold for the complex interpolation of Lp-spaces.Since each p-convex order continuous K(o)the function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces.
Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.
Craciunescu, O I; Das, S K; Poulson, J M; Samulski, T V
2001-04-01
It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.
Spatial Sampling Strategies for the Effect of Interpolation Accuracy
Directory of Open Access Journals (Sweden)
Hairong Zhang
2015-12-01
Full Text Available Spatial interpolation methods are widely used in various fields and have been studied by several scholars with one or a few specific sampling datasets that do not reflect the complexity of the spatial characteristics and lead to conclusions that cannot be widely applied. In this paper, three factors that affect the accuracy of interpolation have been considered, i.e., sampling density, sampling mode, and sampling location. We studied the inverse distance weighted (IDW, regular spline (RS, and ordinary kriging (OK interpolation methods using 162 DEM datasets considering six sampling densities, nine terrain complexities, and three sampling modes. The experimental results show that, in selective sampling and combined sampling, the maximum absolute errors of interpolation methods rapidly increase and the estimated values are overestimated. In regular-grid sampling, the RS method has the highest interpolation accuracy, and IDW has the lowest interpolation accuracy. However, in both selective and combined sampling, the accuracy of the IDW method is significantly improved and the RS method performs worse. The OK method does not significantly change between the three sampling modes. The following conclusion can be obtained from the above analysis: the combined sampling mode is recommended for sampling, and more sampling points should be added in the ridges, valleys, and other complex terrain. The IDW method should not be used in the regular-grid sampling mode, but it has good performance in the selective sampling mode and combined sampling mode. However, the RS method shows the opposite phenomenon. The sampling dataset should be analyzed before using the OK method, which can select suitable models based on the analysis results of the sampling dataset.
Uniform trigonometric polynomial B-spline curves
Institute of Scientific and Technical Information of China (English)
吕勇刚; 汪国昭; 杨勋年
2002-01-01
This paper presents a new kind of uniform spline curve, named trigonometric polynomialB-splines, over space Ω = span{sint, cost, tk-3,tk-4,…,t,1} of which k is an arbitrary integerlarger than or equal to 3. We show that trigonometric polynomial B-spline curves have many similarV properties to traditional B-splines. Based on the explicit representation of the curve we have also presented the subdivision formulae for this new kind of curve. Since the new spline can include both polynomial curves and trigonometric curves as special cases without rational form, it can be used as an efficient new model for geometric design in the fields of CAD/CAM.
Cubic Subalgebras and Cubic Closed Ideals of B-algebras
Directory of Open Access Journals (Sweden)
Tapan Senapati
2015-06-01
Full Text Available In this paper, the concept of cubic set to subalgebras, ideals and closed ideals of B-algebras are introduced. Relations among cubic subalgebras with cubic ideals and cubic closed ideals of B-algebras investigated. The homomorphic image and inverse image of cubic subalgebras, ideals are studied and some related properties are investigated. Also, the product of cubic B-algebras are investigated.
A Quasi-Interpolation Satisfying Quadratic Polynomial Reproduction with Radial Basis Functions
Institute of Scientific and Technical Information of China (English)
Li Zha; Renzhong Feng
2007-01-01
In this paper, a new quasi-interpolation with radial basis functions which satisfies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data. A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function. In particular, for twicely differentiable function the proposed method provides better approximation and also takes care of derivatives approximation.
Evaluating Error of LIDAR Derived dem Interpolation for Vegetation Area
Ismail, Z.; Khanan, M. F. Abdul; Omar, F. Z.; Rahman, M. Z. Abdul; Mohd Salleh, M. R.
2016-09-01
Light Detection and Ranging or LiDAR data is a data source for deriving digital terrain model while Digital Elevation Model or DEM is usable within Geographical Information System or GIS. The aim of this study is to evaluate the accuracy of LiDAR derived DEM generated based on different interpolation methods and slope classes. Initially, the study area is divided into three slope classes: (a) slope class one (0° - 5°), (b) slope class two (6° - 10°) and (c) slope class three (11° - 15°). Secondly, each slope class is tested using three distinctive interpolation methods: (a) Kriging, (b) Inverse Distance Weighting (IDW) and (c) Spline. Next, accuracy assessment is done based on field survey tachymetry data. The finding reveals that the overall Root Mean Square Error or RMSE for Kriging provided the lowest value of 0.727 m for both 0.5 m and 1 m spatial resolutions of oil palm area, followed by Spline with values of 0.734 m for 0.5 m spatial resolution and 0.747 m for spatial resolution of 1 m. Concurrently, IDW provided the highest RMSE value of 0.784 m for both spatial resolutions of 0.5 and 1 m. For rubber area, Spline provided the lowest RMSE value of 0.746 m for 0.5 m spatial resolution and 0.760 m for 1 m spatial resolution. The highest value of RMSE for rubber area is IDW with the value of 1.061 m for both spatial resolutions. Finally, Kriging gave the RMSE value of 0.790m for both spatial resolutions.
EVALUATING ERROR OF LIDAR DERIVED DEM INTERPOLATION FOR VEGETATION AREA
Directory of Open Access Journals (Sweden)
Z. Ismail
2016-09-01
Full Text Available Light Detection and Ranging or LiDAR data is a data source for deriving digital terrain model while Digital Elevation Model or DEM is usable within Geographical Information System or GIS. The aim of this study is to evaluate the accuracy of LiDAR derived DEM generated based on different interpolation methods and slope classes. Initially, the study area is divided into three slope classes: (a slope class one (0° – 5°, (b slope class two (6° – 10° and (c slope class three (11° – 15°. Secondly, each slope class is tested using three distinctive interpolation methods: (a Kriging, (b Inverse Distance Weighting (IDW and (c Spline. Next, accuracy assessment is done based on field survey tachymetry data. The finding reveals that the overall Root Mean Square Error or RMSE for Kriging provided the lowest value of 0.727 m for both 0.5 m and 1 m spatial resolutions of oil palm area, followed by Spline with values of 0.734 m for 0.5 m spatial resolution and 0.747 m for spatial resolution of 1 m. Concurrently, IDW provided the highest RMSE value of 0.784 m for both spatial resolutions of 0.5 and 1 m. For rubber area, Spline provided the lowest RMSE value of 0.746 m for 0.5 m spatial resolution and 0.760 m for 1 m spatial resolution. The highest value of RMSE for rubber area is IDW with the value of 1.061 m for both spatial resolutions. Finally, Kriging gave the RMSE value of 0.790m for both spatial resolutions.
Institute of Scientific and Technical Information of China (English)
郭旺; 路游
2016-01-01
利用 Box Splines 空间中的拟插值算子对封闭曲面进行重构，大大改进了张量积型样条的曲面重构的特性和效率。此方法以 S12（Δ（2）mn ）样条空间的基为基础，然后利用拟插值算子 W mn （ f ）对定义在封闭曲面 S 上的三维数据进行拟合，并且用边界宽度重合的方法处理曲面封闭的条件。通过示例试验以及分析比较，该方法能够实现在 Box Splines 空间中曲面的封闭，而且对于封闭曲面的重构有很好的效果。%Using the quasi‐interpolation operator in Box Splines space to reconstructure the closed surfaces ,the efficien‐cy and performance of the tensor product spline surfaces reconstruction are improved greatly .This method is based on the ba‐sis function of S12 (Δ(2)mn ) spline space then uses the quasi‐interpolation operator W mn ( f ) to fit the 3D data defined on the closed surface S ,and handles the conditions of closed surfaces by the method of boundary width overlap .Through the test and anal‐ysis ,this method can be able to achieve closed surface in Box Splines space ,and it has good effect on the reconstruction of closed surface .
Spatial interpolation methods for monthly rainfalls and temperatures in Basilicata
Directory of Open Access Journals (Sweden)
Ferrara A
2008-12-01
Full Text Available Spatial interpolated climatic data on grids are important as input in forest modeling because climate spatial variability has a direct effect on productivity and forest growth. Maps of climatic variables can be obtained by different interpolation methods depending on data quality (number of station, spatial distribution, missed data etc. and topographic and climatic features of study area. In this paper four methods are compared to interpolate monthly rainfall at regional scale: 1 inverse distance weighting (IDW; 2 regularized spline with tension (RST; 3 ordinary kriging (OK; 4 universal kriging (UK. Besides, an approach to generate monthly surfaces of temperatures over regions of complex terrain and with limited number of stations is presented. Daily data were gathered from 1976 to 2006 period and then gaps in the time series were filled in order to obtain monthly mean temperatures and cumulative precipitation. Basic statistics of monthly dataset and analysis of relationship of temperature and precipitation to elevation were performed. A linear relationship was found between temperature and altitude, while no relationship was found between rainfall and elevation. Precipitations were then interpolated without taking into account elevation. Based on root mean squared error for each month the best method was ranked. Results showed that universal kriging (UK is the best method in spatial interpolation of rainfall in study area. Then cross validation was used to compare prediction performance of tree different variogram model (circular, spherical, exponential using UK algorithm in order to produce final maps of monthly precipitations. Before interpolating temperatures were referred to see level using the calculated lapse rate and a digital elevation model (DEM. The result of interpolation with RST was then set to originally elevation with an inverse procedure. To evaluate the quality of interpolated surfaces a comparison between interpolated and
B-Spline Active Contour with Handling of Topology Changes for Fast Video Segmentation
Directory of Open Access Journals (Sweden)
Frederic Precioso
2002-06-01
Full Text Available This paper deals with video segmentation for MPEG-4 and MPEG-7 applications. Region-based active contour is a powerful technique for segmentation. However most of these methods are implemented using level sets. Although level-set methods provide accurate segmentation, they suffer from large computational cost. We propose to use a regular B-spline parametric method to provide a fast and accurate segmentation. Our B-spline interpolation is based on a fixed number of points 2j depending on the level of the desired details. Through this spatial multiresolution approach, the computational cost of the segmentation is reduced. We introduce a length penalty. This results in improving both smoothness and accuracy. Then we show some experiments on real-video sequences.
Institute of Scientific and Technical Information of China (English)
Juan Chen; Chong-Jun Li; Wan-Ji Chen
2011-01-01
In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.
Approaches for Constrained Parametric Curve Interpolation
Institute of Scientific and Technical Information of China (English)
ZHANG CaiMing(张彩明); YANG XingQiang(杨兴强); WANG JiaYe(汪嘉业)
2003-01-01
The construction of a GC 1 cubic interpolating curve that lies on the same side of agiven straight line as the data points is studied. The main task is to choose appropriate approachesto modify tangent vectors at the data points for the desired curve. Three types of approaches forchanging the magnitudes of the tangent vectors are presented. The first-type approach nodifiesthe tangent vectors by applying a constraint to the curve segment. The second one does the workby optimization techniques. The third one is a modification of the existing method. Three criteriaare presented to compare the three types of approaches with the existing method. The experimentsthat test the effectiveness of the approaches are included.
Interpolation and partial differential equations
MALIGRANDA, Lech; Persson, Lars-Erik; Wyller, John
1994-01-01
One of the main motivations for developing the theory of interpolation was to apply it to the theory of partial differential equations (PDEs). Nowadays interpolation theory has been developed in an almost unbelievable way {see the bibliography of Maligranda [Interpolation of Operators and Applications (1926-1990), 2nd ed. (Luleå University, Luleå, 1993), p. 154]}. In this article some model examples are presented which display how powerful this theory is when dealing with PDEs. One main aim i...
Spatiotemporal Interpolation for Environmental Modelling
Ferry Susanto; Paulo de Souza; Jing He
2016-01-01
A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania’s South Esk Hy...
Directory of Open Access Journals (Sweden)
Ishfaq Ahmad Ganaie
2014-01-01
Full Text Available Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.
Improved Ternary Subdivision Interpolation Scheme
Institute of Scientific and Technical Information of China (English)
WANG Huawei; QIN Kaihuai
2005-01-01
An improved ternary subdivision interpolation scheme was developed for computer graphics applications that can manipulate open control polygons unlike the previous ternary scheme, with the resulting curve proved to be still C2-continuous. Parameterizations of the limit curve near the two endpoints are given with expressions for the boundary derivatives. The split joint problem is handled with the interpolating ternary subdivision scheme. The improved scheme can be used for modeling interpolation curves in computer aided geometric design systems, and provides a method for joining two limit curves of interpolating ternary subdivisions.
Twelfth degree spline with application to quadrature.
Mohammed, P O; Hamasalh, F K
2016-01-01
In this paper existence and uniqueness of twelfth degree spline is proved with application to quadrature. This formula is in the class of splines of degree 12 and continuity order [Formula: see text] that matches the derivatives up to order 6 at the knots of a uniform partition. Some mistakes in the literature are pointed out and corrected. Numerical examples are given to illustrate the applicability and efficiency of the new method.
P-Splines Using Derivative Information
Calderon, Christopher P.
2010-01-01
Time series associated with single-molecule experiments and/or simulations contain a wealth of multiscale information about complex biomolecular systems. We demonstrate how a collection of Penalized-splines (P-splines) can be useful in quantitatively summarizing such data. In this work, functions estimated using P-splines are associated with stochastic differential equations (SDEs). It is shown how quantities estimated in a single SDE summarize fast-scale phenomena, whereas variation between curves associated with different SDEs partially reflects noise induced by motion evolving on a slower time scale. P-splines assist in "semiparametrically" estimating nonlinear SDEs in situations where a time-dependent external force is applied to a single-molecule system. The P-splines introduced simultaneously use function and derivative scatterplot information to refine curve estimates. We refer to the approach as the PuDI (P-splines using Derivative Information) method. It is shown how generalized least squares ideas fit seamlessly into the PuDI method. Applications demonstrating how utilizing uncertainty information/approximations along with generalized least squares techniques improve PuDI fits are presented. Although the primary application here is in estimating nonlinear SDEs, the PuDI method is applicable to situations where both unbiased function and derivative estimates are available.
Bueno, Pablo; Cano, Pablo A.
2016-11-01
We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives with respect to one of those parameters. We use our method to construct a D -dimensional cubic theory of gravity which satisfies the following properties: (1) it shares the spectrum of Einstein gravity, i.e., it only propagates a transverse and massless graviton on a maximally symmetric background; (2) it is defined in the same way in general dimensions; (3) it is neither trivial nor topological in four dimensions. Up to cubic order in curvature, the only previously known theories satisfying the first two requirements are the Lovelock ones. We show that, up to cubic order, there exists only one additional theory satisfying requirements (1) and (2). Interestingly, this theory is, along with Einstein gravity, the only one which also satisfies (3).
Classification based polynomial image interpolation
Lenke, Sebastian; Schröder, Hartmut
2008-02-01
Due to the fast migration of high resolution displays for home and office environments there is a strong demand for high quality picture scaling. This is caused on the one hand by large picture sizes and on the other hand due to an enhanced visibility of picture artifacts on these displays [1]. There are many proposals for an enhanced spatial interpolation adaptively matched to picture contents like e.g. edges. The drawback of these approaches is the normally integer and often limited interpolation factor. In order to achieve rational factors there exist combinations of adaptive and non adaptive linear filters, but due to the non adaptive step the overall quality is notably limited. We present in this paper a content adaptive polyphase interpolation method which uses "offline" trained filter coefficients and an "online" linear filtering depending on a simple classification of the input situation. Furthermore we present a new approach to a content adaptive interpolation polynomial, which allows arbitrary polyphase interpolation factors at runtime and further improves the overall interpolation quality. The main goal of our new approach is to optimize interpolation quality by adapting higher order polynomials directly to the image content. In addition we derive filter constraints for enhanced picture quality. Furthermore we extend the classification based filtering to the temporal dimension in order to use it for an intermediate image interpolation.
A disposition of interpolation techniques
Knotters, M.; Heuvelink, G.B.M.
2010-01-01
A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated v
A disposition of interpolation techniques
Knotters, M.; Heuvelink, G.B.M.
2010-01-01
A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated v
CUBLIC SPLINE SOLUTIONS OF AXISYMMETRICAL NONLINEAR BENDING AND BRCKLING OF CIRCULAR SANDWICH PLATES
Institute of Scientific and Technical Information of China (English)
侯朝胜; 张守恺; 林锋
2005-01-01
Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads,uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.
B-spline parameterization of spatial response in a monolithic scintillation camera
Solovov, V; Chepel, V; Domingos, V; Martins, R
2016-01-01
A framework for parameterization of the light response functions (LRFs) in a scintillation camera was developed. It is based on approximation of the measured or simulated photosensor response with weighted sums of uniform cubic B-splines or their tensor products. The LRFs represented in this way are smooth, computationally inexpensive to evaluate and require much less memory than non-parametric alternatives. The parameters are found in a straightforward way by the linear least squares method. The use of linear fit makes the fitting process stable and predictable enough to be used in non-supervised mode. Several techniques that allow to reduce the storage and processing power requirements were developed. A software library for fitting simulated and measured light response with spline functions was developed and integrated into an open source software package ANTS2 designed for simulation and data processing for Anger camera-type detectors.
Noise-induced bias for convolution-based interpolation in digital image correlation.
Su, Yong; Zhang, Qingchuan; Gao, Zeren; Xu, Xiaohai
2016-01-25
In digital image correlation (DIC), the noise-induced bias is significant if the noise level is high or the contrast of the image is low. However, existing methods for the estimation of the noise-induced bias are merely applicable to traditional interpolation methods such as linear and cubic interpolation, but are not applicable to generalized interpolation methods such as BSpline and OMOMS. Both traditional interpolation and generalized interpolation belong to convolution-based interpolation. Considering the widely use of generalized interpolation, this paper presents a theoretical analysis of noise-induced bias for convolution-based interpolation. A sinusoidal approximate formula for noise-induced bias is derived; this formula motivates an estimating strategy which is with speed, ease, and accuracy; furthermore, based on this formula, the mechanism of sophisticated interpolation methods generally reducing noise-induced bias is revealed. The validity of the theoretical analysis is established by both numerical simulations and actual subpixel translation experiment. Compared to existing methods, formulae provided by this paper are simpler, briefer, and more general. In addition, a more intuitionistic explanation of the cause of noise-induced bias is provided by quantitatively characterized the position-dependence of noise variability in the spatial domain.
Interpolating function and Stokes Phenomena
Honda, Masazumi
2015-01-01
When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such interpolating functions and discuss their physical implications. We propose that the analytic structures of the interpolating functions provide information on analytic property and Stokes phenomena of the physical quantity, which we approximate by the interpolating functions. We explicitly check our proposal for partition functions of zero-dimensional $\\varphi^4$ theory and Sine-Gordon model. In the zero dimensional Sine-Gordon model, we compare our result with a recent result from resurgence analysis. We also comment on construction of interpolating function in Borel plane.
An integral conservative gridding--algorithm using Hermitian curve interpolation.
Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K
2008-11-07
The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to
2014-10-01
cubic splines or B - splines [3]. This sparkles many studies to provide mathematically sounding alternatives to the EMD method. For examples, in [4...respectively based on cubic spline envelopes (CSE), a segment power-function based envelopes (SPFE) and monotone piecewise cubic interpolation based...by the average of upper and lower envelopes calculated by cubic splines through the extreme points. However, overshoots and undershoots are common, it
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald;
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning with co...
The structure of uniform B-spline curves with parameters
Institute of Scientific and Technical Information of China (English)
Juan Cao; Guozhao Wang
2008-01-01
The shape-adjustable curve constructed by uniform B-spline basis function with parameter is an extension of uniform B-spline curve. In this paper, we study the relation between the uniform B-spline basis functions with parameter and the B-spline basis functions. Based on the degree elevation of B-spline, we extend the uniform B-spline basis functions with parameter to ones with multiple parameters. Examples show that the proposed basis functions provide more flexibility for curve design.
[Hybrid interpolation for CT metal artifact reducing].
Yu, Xiao-e; Li, Chan-juan; Chen, Wu-fan
2009-01-01
Numerous interpolation-based methods have been described for reducing metal artifacts in CT images, but due to the limit of the interpolation methods, interpolation alone often fails to meet the clinical demands. In this paper, we describe the use of quartic polynomial interpolation in reconstruction of the images of the metal implant followed by linear interpolation to eliminate the streaks. The two interpolation methods are combined according to their given weights to achieve good results.
Applications of operational calculus: trigonometric interpolating equation for the eight-point cube
Energy Technology Data Exchange (ETDEWEB)
Silver, Gary L [Los Alamos National Laboratory
2009-01-01
A general method for obtaining a trigonometric-type interpolating equation for the eight-point cubical array is illustrated. It can often be used to reproduce a ninth datum at an arbitrary point near the center of the array by adjusting a variable exponent. The new method complements operational polynomial and exponential methods for the same design.
Optimal Alternative to the Akima's Method of Smooth Interpolation Applied in Diabetology
Directory of Open Access Journals (Sweden)
Emanuel Paul
2006-12-01
Full Text Available It is presented a new method of cubic piecewise smooth interpolation applied to experimental data obtained by glycemic profile for diabetics. This method is applied to create a soft useful in clinical diabetology. The method give an alternative to the Akima's procedure of the derivatives computation on the knots from [Akima, J. Assoc. Comput. Mach., 1970] and have an optimal property.
Interpolating Operators for Multiapproximation
Directory of Open Access Journals (Sweden)
Eman S. Bhaya
2010-01-01
Full Text Available Problem statement: There are no simple definitions of operators for best multiapproximation and best one sided multiapproximation which work for any measurable function in Lp for, p>0. This study investigated operators that are good for best multiapproximation and best one sided multiapproximation. Approach: We first introduced some direct results related to the approximation problem of continuous functions by Hermit-Fejer interpolation based on the zeros of Chebyshev polynomials of the first or second kind in terms of the usual modulus of continuity. They were then improved to spaces Lp for pn(f of measurable functions, that operator based on the zeros of Chepyshev polynomials of the first kind and prove that for any measurable function defined on Lp[-1,1 ]d the sequence Hn(f converges uniformly to f. Results: The resulting operators were defined for functions f such that f(k, k = 0,1, is of bounded variation. Then, the order of best onesided trigonometric approximation to bounded measurable functions in terms of the average modulus of smoothness was characterized. Estimates characterizing the order of best onesided approximation in terms of the k-th averaged modulus of smoothness for any function in spaces Lp, pp[-1,1]d by defining a new operator for onesided approximation and prove a direct theorem for best one sided multiapproximation in terms of the first order averaged moduli of smoothness. Conclusion: The proposed method successfully construct operators for best multi approximation and best one sided multiapproximation for any measurable function in Lp for, p>0.
Interpolation in Spaces of Functions
Directory of Open Access Journals (Sweden)
K. Mosaleheh
2006-03-01
Full Text Available In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces
COMPARISONS BETWEEN DIFFERENT INTERPOLATION TECHNIQUES
Directory of Open Access Journals (Sweden)
G. Garnero
2014-01-01
In the present study different algorithms will be analysed in order to spot an optimal interpolation methodology. The availability of the recent digital model produced by the Regione Piemonte with airborne LIDAR and the presence of sections of testing realized with higher resolutions and the presence of independent digital models on the same territory allow to set a series of analysis with consequent determination of the best methodologies of interpolation. The analysis of the residuals on the test sites allows to calculate the descriptive statistics of the computed values: all the algorithms have furnished interesting results; all the more interesting, notably for dense models, the IDW (Inverse Distance Weighing algorithm results to give best results in this study case. Moreover, a comparative analysis was carried out by interpolating data at different input point density, with the purpose of highlighting thresholds in input density that may influence the quality reduction of the final output in the interpolation phase.
Spatiotemporal Interpolation for Environmental Modelling
Directory of Open Access Journals (Sweden)
Ferry Susanto
2016-08-01
Full Text Available A variation of the reduction-based approach to spatiotemporal interpolation (STI, in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW spatial interpolation method. In this study, we utilised one year of Tasmania’s South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications.
Spatiotemporal Interpolation for Environmental Modelling.
Susanto, Ferry; de Souza, Paulo; He, Jing
2016-08-06
A variation of the reduction-based approach to spatiotemporal interpolation (STI), in which time is treated independently from the spatial dimensions, is proposed in this paper. We reviewed and compared three widely-used spatial interpolation techniques: ordinary kriging, inverse distance weighting and the triangular irregular network. We also proposed a new distribution-based distance weighting (DDW) spatial interpolation method. In this study, we utilised one year of Tasmania's South Esk Hydrology model developed by CSIRO. Root mean squared error statistical methods were performed for performance evaluations. Our results show that the proposed reduction approach is superior to the extension approach to STI. However, the proposed DDW provides little benefit compared to the conventional inverse distance weighting (IDW) method. We suggest that the improved IDW technique, with the reduction approach used for the temporal dimension, is the optimal combination for large-scale spatiotemporal interpolation within environmental modelling applications.
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald;
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type-checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive...
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald;
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, enjoys canonicity for the natural numbers type, and is conjectured to support decidable type-checking. Our new type theory, guarded cubical type theory (GCTT), provides a computational interpretation of extensionality...
Fast adaptive elliptical filtering using box splines
Chaudhury, Kunal Narayan; Unser, Michael
2009-01-01
We demonstrate that it is possible to filter an image with an elliptic window of varying size, elongation and orientation with a fixed computational cost per pixel. Our method involves the application of a suitable global pre-integrator followed by a pointwise-adaptive localization mesh. We present the basic theory for the 1D case using a B-spline formalism and then appropriately extend it to 2D using radially-uniform box splines. The size and ellipticity of these radially-uniform box splines is adaptively controlled. Moreover, they converge to Gaussians as the order increases. Finally, we present a fast and practical directional filtering algorithm that has the capability of adapting to the local image features.
Study regarding the spline interpolation accuracy of the experimentally acquired data
Oanta, Emil M.; Danisor, Alin; Tamas, Razvan
2016-12-01
Experimental data processing is an issue that must be solved in almost all the domains of science. In engineering we usually have a large amount of data and we try to extract the useful signal which is relevant for the phenomenon under investigation. The criteria used to consider some points more relevant then some others may take into consideration various conditions which may be either phenomenon dependent, or general. The paper presents some of the ideas and tests regarding the identification of the best set of criteria used to filter the initial set of points in order to extract a subset which best fits the approximated function. If the function has regions where it is either constant, or it has a slow variation, fewer discretization points may be used. This means to create a simpler solution to process the experimental data, keeping the accuracy in some fair good limits.
Schwarz and multilevel methods for quadratic spline collocation
Energy Technology Data Exchange (ETDEWEB)
Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)
1994-12-31
Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.
Curve Fitting And Interpolation Model Applied In Nonel Dosage Detection
Directory of Open Access Journals (Sweden)
Jiuling Li
2013-06-01
Full Text Available The Curve Fitting and Interpolation Model are applied in Nonel dosage detection in this paper firstly, and the gray of continuous explosive in the Nonel has been forecasted. Although the traditional infrared equipment establishes the relationship of explosive dosage and light intensity, but the forecast accuracy is very low. Therefore, gray prediction models based on curve fitting and interpolation are framed separately, and the deviations from the different models are compared. Simultaneously, combining on the sample library features, the cubic polynomial fitting curve of the higher precision is used to predict grays, and 5mg-28mg Nonel gray values are calculated by MATLAB. Through the predictive values, the dosage detection operations are simplified, and the defect missing rate of the Nonel are reduced. Finally, the quality of Nonel is improved.
Scripted Bodies and Spline Driven Animation
DEFF Research Database (Denmark)
Erleben, Kenny; Henriksen, Knud
2002-01-01
In this paper we will take a close look at the details and technicalities in applying spline driven animation to scripted bodies in the context of dynamic simulation. The main contributions presented in this paper are methods for computing velocities and accelerations in the time domain of the sp......In this paper we will take a close look at the details and technicalities in applying spline driven animation to scripted bodies in the context of dynamic simulation. The main contributions presented in this paper are methods for computing velocities and accelerations in the time domain...
Scripted Bodies and Spline Driven Animation
DEFF Research Database (Denmark)
Erleben, Kenny; Henriksen, Knud
2002-01-01
In this paper we will take a close look at the details and technicalities in applying spline driven animation to scripted bodies in the context of dynamic simulation. The main contributions presented in this paper are methods for computing velocities and accelerations in the time domain of the sp......In this paper we will take a close look at the details and technicalities in applying spline driven animation to scripted bodies in the context of dynamic simulation. The main contributions presented in this paper are methods for computing velocities and accelerations in the time domain...
Multiple products of B-splines used in CAD system
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The function upgrade of computer aided design (CAD) system requested that the multiple product of B-spline functions should be represented as a linear combination of some suitable (usually higher-degree) B-splines. In this paper, we apply the theory of spline space and discrete B-splines to deduce the representation of the coefficients of all terms of the linear combination, which can be directly applied to software coding in system development.
On the Nesting Behavior of T-splines
2011-05-01
splines were originally introduced as a superior alternative to NURBS [1] and have emerged as an important technology across several disciplines...watertight geometry and can be locally re- fined [2, 3]. These basic properties make it possible to merge multiple NURBS patches into a single T...spline [4, 1] and any trimmed NURBS model can be represented as a watertight T-spline [5]. T-splines are an ideal discretization technology for
Alvarez, Otto; Guo, Qinghua; Klinger, Robert C.; Li, Wenkai; Doherty, Paul
2013-01-01
Climate models may be limited in their inferential use if they cannot be locally validated or do not account for spatial uncertainty. Much of the focus has gone into determining which interpolation method is best suited for creating gridded climate surfaces, which often a covariate such as elevation (Digital Elevation Model, DEM) is used to improve the interpolation accuracy. One key area where little research has addressed is in determining which covariate best improves the accuracy in the interpolation. In this study, a comprehensive evaluation was carried out in determining which covariates were most suitable for interpolating climatic variables (e.g. precipitation, mean temperature, minimum temperature, and maximum temperature). We compiled data for each climate variable from 1950 to 1999 from approximately 500 weather stations across the Western United States (32° to 49° latitude and −124.7° to −112.9° longitude). In addition, we examined the uncertainty of the interpolated climate surface. Specifically, Thin Plate Spline (TPS) was used as the interpolation method since it is one of the most popular interpolation techniques to generate climate surfaces. We considered several covariates, including DEM, slope, distance to coast (Euclidean distance), aspect, solar potential, radar, and two Normalized Difference Vegetation Index (NDVI) products derived from Advanced Very High Resolution Radiometer (AVHRR) and Moderate Resolution Imaging Spectroradiometer (MODIS). A tenfold cross-validation was applied to determine the uncertainty of the interpolation based on each covariate. In general, the leading covariate for precipitation was radar, while DEM was the leading covariate for maximum, mean, and minimum temperatures. A comparison to other products such as PRISM and WorldClim showed strong agreement across large geographic areas but climate surfaces generated in this study (ClimSurf) had greater variability at high elevation regions, such as in the Sierra
Institute of Scientific and Technical Information of China (English)
Joong-Hyun Rhim; Doo-Yeoun Cho; Kyu-Yeul Lee; Tae-Wan Kim
2006-01-01
We propose a method that automatically generates discrete bicubic G1 continuous B-spline surfaces that interpolate the curve network of a ship hullform. First, the curves in the network are classified into two types: boundary curves and "reference curves". The boundary curves correspond to a set of rectangular (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. Next, in the interior of the patches,surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing "virtual" isoparametric curves. Finally, a discrete G1 continuous B-spline surface is generated by a surface fitting algorithm. Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.
Diabat Interpolation for Polymorph Free-Energy Differences.
Kamat, Kartik; Peters, Baron
2017-02-02
Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.
Matuschek, Hannes; Kliegl, Reinhold; Holschneider, Matthias
2015-01-01
The Smoothing Spline ANOVA (SS-ANOVA) requires a specialized construction of basis and penalty terms in order to incorporate prior knowledge about the data to be fitted. Typically, one resorts to the most general approach using tensor product splines. This implies severe constraints on the correlation structure, i.e. the assumption of isotropy of smoothness can not be incorporated in general. This may increase the variance of the spline fit, especially if only a relatively small set of observations are given. In this article, we propose an alternative method that allows to incorporate prior knowledge without the need to construct specialized bases and penalties, allowing the researcher to choose the spline basis and penalty according to the prior knowledge of the observations rather than choosing them according to the analysis to be done. The two approaches are compared with an artificial example and with analyses of fixation durations during reading.
A multiresolution analysis for tensor-product splines using weighted spline wavelets
Kapl, Mario; Jüttler, Bert
2009-09-01
We construct biorthogonal spline wavelets for periodic splines which extend the notion of "lazy" wavelets for linear functions (where the wavelets are simply a subset of the scaling functions) to splines of higher degree. We then use the lifting scheme in order to improve the approximation properties with respect to a norm induced by a weighted inner product with a piecewise constant weight function. Using the lifted wavelets we define a multiresolution analysis of tensor-product spline functions and apply it to image compression of black-and-white images. By performing-as a model problem-image compression with black-and-white images, we demonstrate that the use of a weight function allows to adapt the norm to the specific problem.
Rogers, David
1991-01-01
G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.
A Spline Regression Model for Latent Variables
Harring, Jeffrey R.
2014-01-01
Spline (or piecewise) regression models have been used in the past to account for patterns in observed data that exhibit distinct phases. The changepoint or knot marking the shift from one phase to the other, in many applications, is an unknown parameter to be estimated. As an extension of this framework, this research considers modeling the…
FORMATION OF SHAFT SPLINES USING ROLLING METHOD
Directory of Open Access Journals (Sweden)
M. Sidorenko
2012-01-01
Full Text Available The paper describes design of rolling heads used for cold rolling of straight-sided splines on shafts and presents theoretical principles of this process. These principles make it possible to calculate an effort which is required for pushing billet through rolling-on rolls with due account of metal hardening during deformation.
Single authentication: exposing weighted splining artifacts
Ciptasari, Rimba W.
2016-05-01
A common form of manipulation is to combine parts of the image fragment into another different image either to remove or blend the objects. Inspired by this situation, we propose a single authentication technique for detecting traces of weighted average splining technique. In this paper, we assume that image composite could be created by joining two images so that the edge between them is imperceptible. The weighted average technique is constructed from overlapped images so that it is possible to compute the gray level value of points within a transition zone. This approach works on the assumption that although splining process leaves the transition zone smoothly. They may, nevertheless, alter the underlying statistics of an image. In other words, it introduces specific correlation into the image. The proposed idea dealing with identifying these correlations is to generate an original model of both weighting function, left and right functions, as references to their synthetic models. The overall process of the authentication is divided into two main stages, which are pixel predictive coding and weighting function estimation. In the former stage, the set of intensity pairs {Il,Ir} is computed by exploiting pixel extrapolation technique. The least-squares estimation method is then employed to yield the weighted coefficients. We show the efficacy of the proposed scheme on revealing the splining artifacts. We believe that this is the first work that exposes the image splining artifact as evidence of digital tampering.
REAL ROOT ISOLATION OF SPLINE FUNCTIONS
Institute of Scientific and Technical Information of China (English)
Renhong Wang; Jinming Wu
2008-01-01
In this paper,we propose an algorithm for isolating real roots of a given univariate spline function,which is based on the use of Descartes' rule of signs and de Casteljau algorithm.Numerical examples illustrate the flexibility and effectiveness of the algorithm.
Spline smoothing of histograms by linear programming
Bennett, J. O.
1972-01-01
An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.
NURBS 插补快速求值算法%An Efficient Evaluation Algorithm for NURBS Interpolation
Institute of Scientific and Technical Information of China (English)
孔祥洪; 李迪; 焦青松
2016-01-01
In the high-density interpolation of non-uniform rational B-spline ( NURBS) curves, using the piecewise power function method to evaluate the B-spline basis function consumes much less computing time than the tradi-tional de-Boor algorithm.Therefore, on the basis of the characteristic of the NURBS interpolation, an efficient eva-luation algorithm for the NURBS interpolation is proposed by drawing on the recursive calculation laws of the de-Boor algorithm.First, the proposed algorithm is used to deduce the explicit equations of the B-spline basis function in each spline parameter knot interval.Then, NURBS interpolation points are evaluated by using explicit equa-tions, and a corresponding NURBS curve interpolator is designed.The results of the milling experiment with com-plex NURBS curves show that the proposed algorithm can effectively reduce the computing time of the NURBS curve interpolation and can improve the real-time performance of NURBS interpolators.%当对非均匀有理B样条（ NURBS）曲线进行高密度插值时，运用分段幂函数方法对基函数进行求值的效率远高于传统的de－Boor算法。为此，文中从NURBS插补计算的特点出发，结合de－Boor递推计算规律，设计了NURBS插补快速求值算法。首先采用该算法计算NURBS在各节点区间的基函数显式方程，再运用显式方程进行NURBS插补点求值，并设计相应的NURBS曲线插补器。复杂NURBS曲线的铣削加工实验结果表明，该算法能够有效地缩减NURBS曲线插补求值的计算耗时，提高插补计算的实时性。
A modification of HASM for interpolating precipitation in China
Zhao, Na; Yue, Tianxiang
2014-04-01
Based on the spatial distribution of precipitation in China, this study gives a modification of High Accuracy Surface Modeling (HASM) method for improving interpolation of precipitation. To assess the feasibility of this modified model, namely, HASM-PRE, we use precipitation data measured at 712 stations for the period 1951-2010, using 605 stations for function development and reserving 107 for validation tests. The performance of HASM-PRE is compared with those of HASM and other classical methods: kriging, inverse distance weighted (IDW) method and spline. Results show that HASM-PRE has less root mean square error (RMSE) and mean absolute error (MAE) than the other techniques tested in this study. The precipitation map obtained from HASM-PRE is better than that obtained using other methods. Therefore, HASM-PRE can be seen as an alternative to the popular interpolation techniques, particularly if we focus on simulation accuracy. In addition, the effective way to combine the strengths of both human expert and differential geometry in this study can be applied for calculating precipitation for other areas in other temporal scales. For better improvement, HASM-PRE can be combined with ancillary variables and implemented in parallel environments.
A Geometric Approach for Multi-Degree Spline
Institute of Scientific and Technical Information of China (English)
Xin Li; Zhang-Jin Huang; Zhao Liu
2012-01-01
Multi-degree spline (MD-spline for short) is a generalization of B-spline which comprises of polynomial segments of various degrees.The present paper provides a new definition for MD-spline curves in a geometric intuitive way based on an efficient and simple evaluation algorithm.MD-spline curves maintain various desirable properties of B-spline curves,such as convex hull,local support and variation diminishing properties.They can also be refined exactly with knot insertion.The continuity between two adjacent segments with different degrees is at least C1 and that between two adjacent segments of same degrees d is Cd-1.Benefited by the exact refinement algorithm,we also provide several operators for MD-spline curves,such as converting each curve segment into Bézier form,an efficient merging algorithm and a new curve subdivision scheme which allows different degrees for each segment.
Adaptive Parametrization of Multivariate B-splines for Image Registration
DEFF Research Database (Denmark)
Hansen, Michael Sass; Glocker, Benjamin; Navab, Nassir;
2008-01-01
cost function. In the current work we introduce multivariate B-splines as a novel alternative to the widely used tensor B-splines enabling us to make efficient use of the derived measure.The multivariate B-splines of order n are Cn- 1 smooth and are based on Delaunay configurations of arbitrary 2D or 3......D control point sets. Efficient algorithms for finding the configurations are presented, and B-splines are through their flexibility shown to feature several advantages over the tensor B-splines. In spite of efforts to make the tensor product B-splines more flexible, the knots are still bound...... to reside on a regular grid. In contrast, by efficient non- constrained placement of the knots, the multivariate B- splines are shown to give a good representation of inho- mogeneous objects in natural settings. The wide applicability of the method is illustrated through its application on medical data...
Spline Based Shape Prediction and Analysis of Uniformly Rotating Sessile and Pendant Droplets.
Jakhar, Karan; Chattopadhyay, Ashesh; Thakur, Atul; Raj, Rishi
2017-06-06
Prediction and analysis of the shapes of liquid-vapor interface of droplets under the influence of external forces is critical for various applications. In this regard, a geometric model that can capture the macroscopic shape of the liquid-vapor interface in tandem with the subtleties near the contact line, particularly in the regime where the droplet shape deviates significantly from the idealized spherical cap geometry, is desirable. Such deviations may occur when external forces such as gravity or centrifugal dominate over the surface tension force. Here we use vector parametrized cubic spline representation for axisymmetric fluid-fluid interfaces along with a novel thermodynamic free energy minimization based heuristic to determine the shape of liquid-vapor interface of droplets. We show that the current scheme can easily predict the shapes of sessile and pendant droplets under the action of centrifugal force over a broad range of surface contact angle values and droplet sizes encountered in practical applications. Finally, we show that the cubic spline based modeling approach makes it convenient to perform the inverse analysis as well, i.e., predict interfacial properties from the shape of a droplet under the action of various types of external forces including gravity and centrifugal. We believe that this versatile modeling approach can be extended to model droplet shapes under various other external forces including electric and acoustic. In addition, the simple shape analysis approach is also promising for the development of inexpensive interfacial analysis tools such as surface tensiometers.
Image Interpolation Through Surface Reconstruction
Institute of Scientific and Technical Information of China (English)
ZHANG Ling; LI Xue-mei
2013-01-01
Reconstructing an HR (high-resolution) image which preserves the image intrinsic structures from its LR ( low-resolution) counterpart is highly challenging. This paper proposes a new surface reconstruction algorithm applied to image interpolation. The interpolation surface for the whole image is generated by putting all the quadratic polynomial patches together. In order to eliminate the jaggies of the edge, a new weight function containing edge information is incorporated into the patch reconstruction procedure as a constraint. Extensive experimental results demonstrate that our method produces better results across a wide range of scenes in terms of both quantitative evaluation and subjective visual quality.
The Nonlinear Analysis of Thick Composite Plates Using a Cubic Spline Function.
1984-09-01
nature. These traits when exploited by the designer provide the means for constructing weight efficient, strong structures which respond to loads in...Me,chanics Divisi on \\SCE, 98, EHM , (1972). 3 . Bathe, K-J, Finite Element Procedures in Eng.n ering \
Describing the soil physical characteristics of soil samples with cubical splines
Wesseling, J.G.; Ritsema, C.J.; Stolte, J.; Oostindie, K.; Dekker, K.
2008-01-01
The Mualem-Van Genuchten equations have become very popular in recent decades. Problems were encountered fitting the equations¿ parameters through sets of data measured in the laboratory: parameters were found which yielded results that were not monotonic increasing or decreasing. Due to the interac
青藏高原地区气温空间插值分析%Analysis on Spatial Interpolation of Temperature in Qinghai-Tibet Plateau Area
Institute of Scientific and Technical Information of China (English)
王文娇; 陈珂; 刘德坤
2013-01-01
The spatial interpolation of temperature on the Tibetan Plateau was carried out by using Kriging interpolation ,the inverse distance weighting method(IDW),and Spline interpolation method. Ten actual site data and three interpolation data of the Tibetan Plateau were involved to com-plete the simulation,and the simulation results were evaluated by IA(consistency index). The statistical analysis of three kinds of temperature interpol-ation results and measured values were as follows,IA were-0.81,-1.05,-1.73 respectively,Kriging method showed the best accuracy,while the Spline method worked worst.%使用Kriging插值、采用反距离权重法（IDW）、Spline插值方法对青藏高原气温进行空间插值比较研究，利用青藏高原10个实测站点数据与3种插值数据进行模拟，同时采用IA（一致性指数）来评价模拟的结果，3种气温插值结果与实测值之间的统计分析如下，IA分别为-0.81、-1.05、-1.73；插值精度效果最好的是Kriging，最差的是Spline。
Xiao, Yong; Gu, Xiaomin; Yin, Shiyang; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Niu, Yong
2016-01-01
Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R(2)) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial-proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001-2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.
Anisotropic cubic curvature couplings
Bailey, Quentin G
2016-01-01
To complement recent work on tests of spacetime symmetry in gravity, cubic curvature couplings are studied using an effective field theory description of spacetime-symmetry breaking. The associated mass dimension 8 coefficients for Lorentz violation studied do not result in any linearized gravity modifications and instead are revealed in the first nonlinear terms in an expansion of spacetime around a flat background. We consider effects on gravitational radiation through the energy loss of a binary system and we study two-body orbital perturbations using the post-Newtonian metric. Some effects depend on the internal structure of the source and test bodies, thereby breaking the Weak Equivalence Principle for self-gravitating bodies. These coefficients can be measured in solar-system tests, while binary-pulsar systems and short-range gravity tests are particularly sensitive.
Some extremal properties of multivariate polynomial splines in the metric Lp (Rd )
Institute of Scientific and Technical Information of China (English)
LlU; Yongping(
2001-01-01
［1］Li Chun, Infinite dimensional widths of function classes, J. Approx. Theory, 1992, 69(1): 15-34.［2］Luo Junbo, Liu Yongping, Average width and optimal recovery of some anisotropic classes of smooth functions defined on the Euclidean space Bd, Northeast Math. J. , 1999, 15(4): 423-432.［3］Schoenberg, I. J., Cardinal interpolation and spline functions Ⅱ. Interpolation of data of power growth, J. Approx. Theory, 1972, 6(4): 404-420.［4］Fang Gensun, Liu Yongping, Average width and optimal interpolation of the Sobolev-Wiener class Wpd (B) in the metric Lq(Y), J. Approx Theory, 1993, 74(3): 335-352.［5］Pinkus, A., N-widths in Approximation Theory, New York: Springer-Verlag, 1985.［6］Foumier, J. J. F., Stewart, J., Amalgams of Lp and lq, Bull. Amer. Math. Soc., 1985, 13(1): 1-12.
COMPACT SUPPORT THIN PLATE SPLINE ALGORITHM
Institute of Scientific and Technical Information of China (English)
Li Jing; Yang Xuan; Yu Jianping
2007-01-01
Common tools based on landmarks in medical image elastic registration are Thin Plate Spline (TPS) and Compact Support Radial Basis Function (CSRBF). TPS forces the corresponding landmarks to exactly match each other and minimizes the bending energy of the whole image. However,in real application, such scheme would deform the image globally when deformation is only local.CSRBF needs manually determine the support size, although its deformation is limited local. Therefore,to limit the effect of the deformation, new Compact Support Thin Plate Spline algorithm (CSTPS) is approached, analyzed and applied. Such new approach gains optimal mutual information, which shows its registration result satisfactory. The experiments also show it can apply in both local and global elastic registration.
Higher-order numerical methods derived from three-point polynomial interpolation
Rubin, S. G.; Khosla, P. K.
1976-01-01
Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.
Radial Basis Function Based Implicit Surface Reconstruction Interpolating Arbitrary Triangular Mesh
Institute of Scientific and Technical Information of China (English)
PANG Mingyong
2006-01-01
In this paper, we present an approach for smooth surface reconstructions interpolating triangular meshes with arbitrary topology and geometry. The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces. Our algorithm first defines a pair of offset points for each vertex of a given mesh to enhance the controllability of local geometry and to assure stability of the construction. A linear system is then solved by LU decomposition and the implicit governing equation of interpolating surface is obtained. The constructed surfaces finally are visualized by a Marching Cubes based polygonizer. The approach provides a robust and efficient solution for smooth surface reconstruction from various 3D meshes.
Measurement and tricubic interpolation of the magnetic field for the OLYMPUS experiment
Bernauer, J C; Elbakian, G; Gavrilov, G; Goerrissen, N; Hasel, D K; Henderson, B S; Holler, Y; Karyan, G; Ludwig, J; Marukyan, H; Naryshkin, Y; O'Connor, C; Russell, R L; Schmidt, A; Schneekloth, U; Suvorov, K; Veretennikov, D
2016-01-01
The OLYMPUS experiment used a 0.3 T toroidal magnetic spectrometer to measure the momenta of outgoing charged particles. In order to accurately determine particle trajectories, knowledge of the magnetic field was needed throughout the spectrometer volume. For that purpose, the magnetic field was measured at over 36,000 positions using a three-dimensional Hall probe actuated by a system of translation tables. We used these field data to fit a numerical magnetic field model, which could be employed to calculate the magnetic field at any point in the spectrometer volume. Calculations with this model were computationally intensive; for analysis applications where speed was crucial, we pre-computed the magnetic field and its derivatives on an evenly spaced grid so that the field could be interpolated between grid points. We developed a spline-based interpolation scheme suitable for SIMD implementations, with a memory layout chosen to minimize space and optimize the cache behavior to quickly calculate field values....
Marginal longitudinal semiparametric regression via penalized splines
Al Kadiri, M.
2010-08-01
We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.
Marginal longitudinal semiparametric regression via penalized splines.
Kadiri, M Al; Carroll, R J; Wand, M P
2010-08-01
We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.
Multinode rational operators for univariate interpolation
Dell'Accio, Francesco; Di Tommaso, Filomena; Hormann, Kai
2016-10-01
Birkhoff (or lacunary) interpolation is an extension of polynomial interpolation that appears when observation gives irregular information about function and its derivatives. A Birkhoff interpolation problem is not always solvable even in the appropriate polynomial or rational space. In this talk we split up the initial problem in subproblems having a unique polynomial solution and use multinode rational basis functions in order to obtain a global interpolant.
General Structures of Block Based Interpolational Function
Institute of Scientific and Technical Information of China (English)
ZOU LE; TANG SHUO; Ma Fu-ming
2012-01-01
We construct general structures of one and two variable interpolation function,without depending on the existence of divided difference or inverse differences,and we also discuss the block based osculatory interpolation in one variable case.Clearly,our method offers many flexible interpolation schemes for choices.Error terms for the interpolation are determined and numerical examples are given to show the effectiveness of the results.
Inverse Distance Weighted Interpolation Involving Position Shading
Li, Zhengquan; WU Yaoxiang
2015-01-01
Considering the shortcomings of inverse distance weighted (IDW) interpolation in practical applications, this study improved the IDW algorithm and put forward a new spatial interpolation method that named as adjusted inverse distance weighted (AIDW). In interpolating process, the AIDW is capable of taking into account the comprehensive influence of distance and position of sample point to interpolation point, by adding a coefficient (K) into the normal IDW formula. The coefficient (K) is used...
BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON RECTANGULAR DOMAINS
Institute of Scientific and Technical Information of China (English)
Xiao-yuan Qian
2002-01-01
Non-tensor product bivariate fractal interpolation functions defined on gridded rectangular domains are constructed. Linear spaces consisting of these functions are introduced.The relevant Lagrange interpolation problem is discussed. A negative result about the existence of affine fractal interpolation functions defined on such domains is obtained.
Average of Distribution and Remarks on Box-Splines
Institute of Scientific and Technical Information of China (English)
LI Yue-sheng
2001-01-01
A class of generalized moving average operators is introduced, and the integral representations of an average function are provided. It has been shown that the average of Dirac δ-distribution is just the well known box-spline. Some remarks on box-splines, such as their smoothness and the corresponding partition of unity, are made. The factorization of average operators is derived. Then, the subdivision algorithm for efficient computing of box-splines and their linear combinations follows.
Temporal interpolation in Meteosat images
DEFF Research Database (Denmark)
Larsen, Rasmus; Hansen, Johan Dore; Ersbøll, Bjarne Kjær;
a threshold between clouds and land/water. The temperature maps are estimated using observations from the image sequence itself at cloud free pixels and ground temperature measurements from a series of meteor ological observation stations in Europe. The temporal interpolation of the images is bas ed on a path...... in such animated films are perceived as being jerky due to t he low temporal sampling rate in general and missing images in particular. In order to perform a satisfactory temporal interpolation we estimate and use the optical flow corresponding to every image in the sequenc e. The estimation of the optical flow...... is based on images sequences where the clouds are segmented from the land/water that might a lso be visible in the images. Because the pixel values measured correspond directly to temperature and because clouds (normally) are colder than land/water we use an estimated lan d temperature map to perform...
Yield statistics of interpolated superoscillations
Katzav, Eytan; Perlsman, Ehud; Schwartz, Moshe
2017-01-01
Yield optimized interpolated superoscillations have been recently introduced as a means for possibly making the use of the phenomenon of superoscillation practical. In this paper we study how good is a superoscillation that is not optimal. Namely, by how much is the yield decreased when the signal departs from the optimal one. We consider two situations. One is the case where the signal strictly obeys the interpolation requirement and the other is when that requirement is relaxed. In the latter case the yield can be increased at the expense of deterioration of signal quality. An important conclusion is that optimizing superoscillations may be challenging in terms of the precision needed, however, storing and using them is not at all that sensitive. This is of great importance in any physical system where noise and error are inevitable.
Segment adaptive gradient angle interpolation.
Zwart, Christine M; Frakes, David H
2013-08-01
We introduce a new edge-directed interpolator based on locally defined, straight line approximations of image isophotes. Spatial derivatives of image intensity are used to describe the principal behavior of pixel-intersecting isophotes in terms of their slopes. The slopes are determined by inverting a tridiagonal matrix and are forced to vary linearly from pixel-to-pixel within segments. Image resizing is performed by interpolating along the approximated isophotes. The proposed method can accommodate arbitrary scaling factors, provides state-of-the-art results in terms of PSNR as well as other quantitative visual quality metrics, and has the advantage of reduced computational complexity that is directly proportional to the number of pixels.
Interpolation and Polynomial Curve Fitting
Yang, Yajun; Gordon, Sheldon P.
2014-01-01
Two points determine a line. Three noncollinear points determine a quadratic function. Four points that do not lie on a lower-degree polynomial curve determine a cubic function. In general, n + 1 points uniquely determine a polynomial of degree n, presuming that they do not fall onto a polynomial of lower degree. The process of finding such a…
Application of spline wavelet transform in differential of electroanalytical signal
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Investigating characteristics of spline wavelet, we found that if the two-order spline function, the derivative function of the three-order B spline function, is used as the wavelet base function, the spline wavelet transform has both the property of denoising and that of differential. As a result, the relation between the spline wavelet transform and the differential was studied in theory. Experimental results show that the spline wavelet transform can well be applied to the differential of the electroanalytical signal. Compared with other kinds of wavelet transform, the spline wavelet trans-form has a characteristic of differential. Compared with the digital differential and simulative differential with electronic circuit, the spline wavelet transform not only can carry out denoising and differential for a signal, but also has the ad-vantages of simple operation and small quantity of calcula-tion, because step length, RC constant and other kinds of parameters need not be selected. Compared with Alexander Kai-man Leung's differential method, the differential method with spline wavelet transform has the characteristic that the differential order is not dependent on the number of data points in the original signal.
The Analysis of Curved Beam Using B-Spline Wavelet on Interval Finite Element Method
Directory of Open Access Journals (Sweden)
Zhibo Yang
2014-01-01
Full Text Available A B-spline wavelet on interval (BSWI finite element is developed for curved beams, and the static and free vibration behaviors of curved beam (arch are investigated in this paper. Instead of the traditional polynomial interpolation, scaling functions at a certain scale have been adopted to form the shape functions and construct wavelet-based elements. Different from the process of the direct wavelet addition in the other wavelet numerical methods, the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space by aid of the corresponding transformation matrix. Furthermore, compared with the commonly used Daubechies wavelet, BSWI has explicit expressions and excellent approximation properties, which guarantee satisfactory results. Numerical examples are performed to demonstrate the accuracy and efficiency with respect to previously published formulations for curved beams.
Rapid Satellite-to-Site Visibility Determination Based on Self-Adaptive Interpolation Technique
Han, Chao; Sun, Xiucong
2016-01-01
Rapid satellite-to-site visibility determination is of great significance to coverage analysis of satellite constellations as well as onboard mission planning of autonomous spacecraft. This paper presents a novel self-adaptive Hermite interpolation technique for rapid satellite-to-site visibility determination. Piecewise cubic curves are utilized to approximate the waveform of the visibility function versus time. The fourth-order derivative is used to control the approximation error and to optimize the time step for interpolation. The rise and set times are analytically obtained from the roots of cubic polynomials. To further increase the computational speed, an interval shrinking strategy is adopted via investigating the geometric relationship between the ground viewing cone and the orbit trajectory. Simulation results show a 98% decrease in computation time over the brute force method. The method is suitable for all orbital types and analytical orbit propagators.
On piecewise interpolation techniques for estimating solar radiation missing values in Kedah
Energy Technology Data Exchange (ETDEWEB)
Saaban, Azizan; Zainudin, Lutfi [School of Science Quantitative, UUMCAS, Universiti Utara Malaysia, 06010 Sintok, Kedah (Malaysia); Bakar, Mohd Nazari Abu [Faculty of Applied Science, Universiti Teknologi MARA, 02600 Arau, Perlis (Malaysia)
2014-12-04
This paper discusses the use of piecewise interpolation method based on cubic Ball and Bézier curves representation to estimate the missing value of solar radiation in Kedah. An hourly solar radiation dataset is collected at Alor Setar Meteorology Station that is taken from Malaysian Meteorology Deparment. The piecewise cubic Ball and Bézier functions that interpolate the data points are defined on each hourly intervals of solar radiation measurement and is obtained by prescribing first order derivatives at the starts and ends of the intervals. We compare the performance of our proposed method with existing methods using Root Mean Squared Error (RMSE) and Coefficient of Detemination (CoD) which is based on missing values simulation datasets. The results show that our method is outperformed the other previous methods.
Seta, Ryo; Okubo, Kan; Tagawa, Norio
2009-01-01
Image interpolation can be performed by a convolution operation using the neighboring image values. To achieve accurate image interpolation, some of the conventional methods use basis function with large support, and therefore their implementation may have a large computational cost. Interpolation by the Hermite interpolating polynomials can be performed using image values and their derivatives. This makes it possible to realize the high-order interpolation with small support. In this study, ...
Välimäki, Vesa; Pekonen, Jussi; Nam, Juhan
2012-01-01
Digital subtractive synthesis is a popular music synthesis method, which requires oscillators that are aliasing-free in a perceptual sense. It is a research challenge to find computationally efficient waveform generation algorithms that produce similar-sounding signals to analog music synthesizers but which are free from audible aliasing. A technique for approximately bandlimited waveform generation is considered that is based on a polynomial correction function, which is defined as the difference of a non-bandlimited step function and a polynomial approximation of the ideal bandlimited step function. It is shown that the ideal bandlimited step function is equivalent to the sine integral, and that integrated polynomial interpolation methods can successfully approximate it. Integrated Lagrange interpolation and B-spline basis functions are considered for polynomial approximation. The polynomial correction function can be added onto samples around each discontinuity in a non-bandlimited waveform to suppress aliasing. Comparison against previously known methods shows that the proposed technique yields the best tradeoff between computational cost and sound quality. The superior method amongst those considered in this study is the integrated third-order B-spline correction function, which offers perceptually aliasing-free sawtooth emulation up to the fundamental frequency of 7.8 kHz at the sample rate of 44.1 kHz.
On Recovering Missing Ground Penetrating Radar Traces by Statistical Interpolation Methods
Directory of Open Access Journals (Sweden)
Gonzalo Safont
2014-08-01
Full Text Available Missing traces in ground penetrating radar (GPR B-scans (radargrams may appear because of limited scanning resolution, failures during the acquisition process or the lack of accessibility to some areas under test. Four statistical interpolation methods for recovering these missing traces are compared in this paper: Kriging, Wiener structures, Splines and the expectation assuming an independent component analyzers mixture model (E-ICAMM. Kriging is an adaptation to the spatial context of the linear least mean squared error estimator. Wiener structures improve the linear estimator by including a nonlinear scalar function. Splines are a commonly used method to interpolate GPR traces. This consists of piecewise-defined polynomial curves that are smooth at the connections (or knots between pieces. E-ICAMM is a new method proposed in this paper. E-ICAMM consists of computing the optimum nonlinear estimator (the conditional mean assuming a non-Gaussian mixture model for the joint probability density in the observation space. The proposed methods were tested on a set of simulated data and a set of real data, and four performance indicators were computed. Real data were obtained by GPR inspection of two replicas of historical walls. Results show the superiority of E-ICAMM in comparison with the other three methods in the application of reconstructing incomplete B-scans.
Resistor mesh model of a spherical head: part 1: applications to scalp potential interpolation.
Chauveau, N; Morucci, J P; Franceries, X; Celsis, P; Rigaud, B
2005-11-01
A resistor mesh model (RMM) has been implemented to describe the electrical properties of the head and the configuration of the intracerebral current sources by simulation of forward and inverse problems in electroencephalogram/event related potential (EEG/ERP) studies. For this study, the RMM representing the three basic tissues of the human head (brain, skull and scalp) was superimposed on a spherical volume mimicking the head volume: it included 43 102 resistances and 14 123 nodes. The validation was performed with reference to the analytical model by consideration of a set of four dipoles close to the cortex. Using the RMM and the chosen dipoles, four distinct families of interpolation technique (nearest neighbour, polynomial, splines and lead fields) were tested and compared so that the scalp potentials could be recovered from the electrode potentials. The 3D spline interpolation and the inverse forward technique (IFT) gave the best results. The IFT is very easy to use when the lead-field matrix between scalp electrodes and cortex nodes has been calculated. By simple application of the Moore-Penrose pseudo inverse matrix to the electrode cap potentials, a set of current sources on the cortex is obtained. Then, the forward problem using these cortex sources renders all the scalp potentials.
NURBS Interpolation Technology in CNC System Based on STEP-NC%基于STEP-NC的CNC系统中NURBS插补技术研究
Institute of Scientific and Technical Information of China (English)
杜娟; 田锡天; 张振明; 朱名铨; 李建克
2007-01-01
STEP-NC is a new interface standard for data exchanging and sharing between CAD/CAM and CNC, and the CNC based on STEP-NC will be the next generation of CNC controller, which not only holds linear and circular interpolation but also possesses the capability of spline interpolation. A universal NURBS ( non-uniform rational B-spline) based interpolator was designed and the interpolation technique based on constant arc increment and interpolation algorithm were inverstigated arc increment. The validity and reliability of algorithm was tested by an instance simulation and machining.%STEP-NC是一个用来实现CAD/CAM与CNC系统间数据交换的接口标准,基于STEP-NC的CNC系统是未来数控技术发展方向之一,该系统不但具有直线和圆弧插补功能,而且还具有样条曲线插补功能.为此设计了一个统一的基于NURBS样条曲线插补的通用插补器,并开发了一种基于等弧长的插补技术和插补算法.最后通过仿真和实例加工验证了该算法的有效性和可靠性.
BLOCK BASED NEWTON-LIKE BLENDING INTERPOLATION
Institute of Scientific and Technical Information of China (English)
Qian-jin Zhao; Jie-qing Tan
2006-01-01
Newton's polynomial interpolation may be the favourite linear interpolation in the sense that it is built up by means of the divided differences which can be calculated recursively and produce useful intermediate results. However Newton interpolation is in fact point based interpolation since a new interpolating polynomial with one more degree is obtained by adding a new support point into the current set of support points once at a time. In this paper we extend the point based interpolation to the block based interpolation. Inspired by the idea of the modern architectural design, we first divide the original set of support points into some subsets (blocks), then construct each block by using whatever interpolation means, linear or rational and finally assemble these blocks by Newton's method to shape the whole interpolation scheme. Clearly our method offers many flexible interpolation schemes for choices which include the classical Newton's polynomial interpolation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of our method.
Inverse Distance Weighted Interpolation Involving Position Shading
Directory of Open Access Journals (Sweden)
LI Zhengquan
2015-01-01
Full Text Available Considering the shortcomings of inverse distance weighted (IDW interpolation in practical applications, this study improved the IDW algorithm and put forward a new spatial interpolation method that named as adjusted inverse distance weighted (AIDW. In interpolating process, the AIDW is capable of taking into account the comprehensive influence of distance and position of sample point to interpolation point, by adding a coefficient (K into the normal IDW formula. The coefficient (K is used to adjust interpolation weight of the sample point according to its position in sample points. Theoretical analysis and practical application indicates that the AIDW algorithm could diminish or eliminate the IDW interpolation defect of non-uniform distribution of sample points. Consequently the AIDW interpolating is more reasonable, compared with the IDW interpolating. On the other hand, the contour plotting of the AIDW interpolation could effectively avoid the implausible isolated and concentric circles that originated from the defect of the IDW interpolation, with the result that the contour derived from the AIDW interpolated surface is more similar to the professional manual identification.
Shah, Mazlina Muzafar; Wahab, Abdul Fatah
2017-08-01
Epilepsy disease occurs because of there is a temporary electrical disturbance in a group of brain cells (nurons). The recording of electrical signals come from the human brain which can be collected from the scalp of the head is called Electroencephalography (EEG). EEG then considered in digital format and in fuzzy form makes it a fuzzy digital space data form. The purpose of research is to identify the area (curve and surface) in fuzzy digital space affected by inside epilepsy seizure in epileptic patient's brain. The main focus for this research is to generalize fuzzy topological digital space, definition and basic operation also the properties by using digital fuzzy set and the operations. By using fuzzy digital space, the theory of digital fuzzy spline can be introduced to replace grid data that has been use previously to get better result. As a result, the flat of EEG can be fuzzy topological digital space and this type of data can be use to interpolate the digital fuzzy spline.
Ruelland, D.; Ardoin-Bardin, S.; Billen, G.; Servat, E.
2008-10-01
SummaryThis paper examines the sensitivity of a hydrological model to several methods of spatial interpolation of rainfall data. The question is investigated in a context of scarcity of data over a large West African catchment (100,000 km 2) subject to a drastic trend of rain deficit since the 1970s. Thirteen widely scattered rainfall stations and their daily time series were used to interpolate gridded rainfall surfaces over the 1950-1992 period via various methods: Thiessen polygons, inverse distance weighted (IDW) method, thin smooth plate splines (spline), and ordinary kriging. The accuracy of these interpolated datasets was evaluated using two complementary approaches. First, a point-by-point assessment was conducted, involving comparison of the interpolated values by reference to observed point data. Second, a conceptual rainfall-runoff model (Hydrostrahler) was used in order to assess whether and to what extent the alternative sets of interpolated rainfall impacted on the hydrological simulations. A lumped modelling exercise over a long period (1952-1992) and a semi-distributed exercise over a short period (1971-1976) were performed, using calibrations aimed at optimizing a Nash-Sutcliffe criterion. The results were evaluated for each interpolated forcing dataset using statistical analysis and visual inspection of the simulated and observed hydrographs and the parameters obtained from calibration. Assessment of the interpolation methods by reference to point data indicates that interpolations using the IDW and kriging methods are more efficient than the simple Thiessen technique, and, to a lesser extent, than spline. The use of these data in a daily lumped modelling application shows a different ranking of the various interpolation methods with regard to various hydrological assessments. The model is particularly sensitive to the differences in the rainfall input volume produced by each interpolation method: the IDW dataset yields the highest hydrological
Institute of Scientific and Technical Information of China (English)
刘鹏; 刘红军; 林坤; 秦荣
2016-01-01
基于 Bernoulli-Euler 梁理论，采用样条有限点法建立考虑截面高宽度沿轴线性变化的变截面 Euler 梁振动分析的计算模型，通过沿梁轴线设置一定数量的样条节点对变截面梁样条离散化，采用三次 B 样条函数对梁的位移场进行插值，基于 Hamilton 原理导出变截面 Euler 梁的振动方程，推导考虑截面尺寸变化效应的总刚度和总质量矩阵的表达式，并编制计算程序，算例分析表明，模型的变截面梁的横向自振频率解答与文献解答吻合良好，计算精度和计算效率高，且模型边界处理简单，取样条离散节点数为15时，模型可以取得较高精度且解答趋于稳定。模型可适用于不同边界、不同截面变化率和不同截面类型的变截面 Euler 梁的自由振动分析。%Based on Bernoulli-Euler beam theory,a new model was presented here to study free transverse vibration problems of tapered Euler beams by using the spline finite point method (SFPM)considering both width and height of beams'cross section linearly varying along the axial direction.With the proposed method,a beam was discretized by a set of uniformly scattered spline nodes along the axis direction instead of meshes,and the cubic-B spline interpolation functions were utilized to approximate the displacement filed of the beam.The free vibration equation of the beam was derived base on Hamilton Principle,and the global stiffness and mass matrices for the tapered beam were deduced in detail.The results of examples showed that the solutions to natural frequencies of tapered beams based on the proposed method are good in agreement with those reported in literatures;the proposed method has a higher accuracy,a lower computational cost and an easier way for boundary treatment;the solutions with a higher accuracy can be achieved by selecting the spline node number of no less than 15;the presented model is suitable for the free transverse vibration of
Directory of Open Access Journals (Sweden)
MILIVOJEVIC, Z. N.
2010-02-01
Full Text Available In this paper the fundamental frequency estimation results of the MP3 modeled speech signal are analyzed. The estimation of the fundamental frequency was performed by the Picking-Peaks algorithm with the implemented Parametric Cubic Convolution (PCC interpolation. The efficiency of PCC was tested for Catmull-Rom, Greville and Greville two-parametric kernel. Depending on MSE, a window that gives optimal results was chosen.
BLOCK BASED NEWTON-LIKE BLENDING OSCULATORY RATIONAL INTERPOLATION
Institute of Scientific and Technical Information of China (English)
Shuo Tang; Le Zou; Chensheng Li
2010-01-01
With Newton's interpolating formula,we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton's polynomial interpolation as its special case.A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.
National Research Council Canada - National Science Library
Goodwin, Adrian N
2009-01-01
A flexible tree taper model based on a cubic polynomial is described. It is algebraically invertible and integrable, and can be constrained by one or two diameters, neither of which need be diameter at breast height (DBH...
Institute of Scientific and Technical Information of China (English)
Xiang Jiawei; He Zhengjia; Chen Xuefeng
2006-01-01
Based on B-spline wavelet on the interval (BSWI), two classes of truncated conical shell elements were constructed to solve axisymmetric problems, i.e. BSWI thin truncated conical shell element and BSWI moderately thick truncated conical shell element with independent slopedeformation interpolation. In the construction of wavelet-based element, instead of traditional polynomial interpolation, the scaling functions of BSWI were employed to form the shape functions through the constructed elemental transformation matrix, and then construct BSWI element via the variational principle. Unlike the process of direct wavelets adding in the wavelet Galerkin method, the elemental displacement field represented by the coefficients of wavelets expansion was transformed into edges and internal modes via the constructed transformation matrix. BSWI element combines the accuracy of B-spline function approximation and various wavelet-based lements for structural analysis. Some static and dynamic numerical examples of conical shells were studied to demonstrate the present element with higher efficiency and precision than the traditional element.
Nonlinear and fault-tolerant flight control using multivariate splines
Tol, H.J.; De Visser, C.C.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
This paper presents a study on fault tolerant flight control of a high performance aircraft using multivariate splines. The controller is implemented by making use of spline model based adaptive nonlinear dynamic inversion (NDI). This method, indicated as SANDI, combines NDI control with nonlinear
Nonlinear and fault-tolerant flight control using multivariate splines
Tol, H.J.; De Visser, C.C.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
This paper presents a study on fault tolerant flight control of a high performance aircraft using multivariate splines. The controller is implemented by making use of spline model based adaptive nonlinear dynamic inversion (NDI). This method, indicated as SANDI, combines NDI control with nonlinear c
Trigonometric polynomial B-spline with shape parameter
Institute of Scientific and Technical Information of China (English)
WANG Wentao; WANG Guozhao
2004-01-01
The basis function of n order trigonometric polynomial B-spline with shape parameter is constructed by an integral approach. The shape of the constructed curve can be adjusted by changing the shape parameter and it has most of the properties of B-spline. The ellipse and circle can be accurately represented by this basis function.
Understanding recurrence relations for Chebyshevian B-splines via blossoms
Mazure, Marie-Laurence
2008-10-01
The purpose of this article is to show how naturally recurrence relations for most general Chebyshevian B-splines emerge from blossoms. In particular, this work gives a new insight into previous results by Lyche [A recurrence relation for Chebyshevian B-splines, Constr. Approx. 1 (1985) 155-178], the importance of which it underlines.
Exponential B-splines and the partition of unity property
DEFF Research Database (Denmark)
Christensen, Ole; Massopust, Peter
2012-01-01
We provide an explicit formula for a large class of exponential B-splines. Also, we characterize the cases where the integer-translates of an exponential B-spline form a partition of unity up to a multiplicative constant. As an application of this result we construct explicitly given pairs of dual...
Fast Harmonic Splines and Parameter Choice Methods
Gutting, Martin
2017-04-01
Solutions to boundary value problems in geoscience where the boundary is the Earth's surface are constructed in terms of harmonic splines. These are localizing trial functions that allow regional modeling or the improvement of a global model in a part of the Earth's surface. Some cases of the occurring kernels can be equipped with a fast matrix-vector multiplication using the fast multipole method (FMM). The main idea of the fast multipole algorithm consists of a hierarchical decomposition of the computational domain into cubes and a kernel approximation for the more distant points. The numerical effort of the matrix-vector multiplication becomes linear in reference to the number of points for a prescribed accuracy of the kernel approximation. This fast spline approximation which also allows the treatment of noisy data requires the choice of a smoothing parameter. We investigate several methods to (ideally automatically) choose this parameter with and without prior knowledge of the noise level. However, in order to keep a fast solution algorithm we do no longer have access to the whole matrix or e.g. its singular values whose computation requires a much larger numerical effort. This must be reflected by the parameter choice methods. Therefore, in some cases a further approximation is necessary. The performance of these methods is considered for different types of noise in a large simulation study with applications to gravitational field modeling as well as to boundary value problems.
DESIGN OF A NEW INTERPOLATED CONTROLLER FOR STABILIZATION OF A SET OF INTERPOLATED PLANTS
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Stabilization of a plant with variable operating conditions was considered. The plant is assumed to lie in a set of interpolated models composed of all interpolations generated between certain sets of proper stable coprime factorizations of transfer functions of two representative models that are defined at two representative operating points. An interpolated controller that is linear interpolation of coprime factorizations of two stabilizing controllers for the two representative models is designed to stabilize this set of interpolated models. Design of such an interpolated controller was converted to a feasibility problem constrained by several LMIs and a BMI, and a two-step iteration algorithm was employed to solve it.
LOCALLY REFINED SPLINES REPRESENTATION FOR GEOSPATIAL BIG DATA
Directory of Open Access Journals (Sweden)
T. Dokken
2015-08-01
Full Text Available When viewed from distance, large parts of the topography of landmasses and the bathymetry of the sea and ocean floor can be regarded as a smooth background with local features. Consequently a digital elevation model combining a compact smooth representation of the background with locally added features has the potential of providing a compact and accurate representation for topography and bathymetry. The recent introduction of Locally Refined B-Splines (LR B-splines allows the granularity of spline representations to be locally adapted to the complexity of the smooth shape approximated. This allows few degrees of freedom to be used in areas with little variation, while adding extra degrees of freedom in areas in need of more modelling flexibility. In the EU fp7 Integrating Project IQmulus we exploit LR B-splines for approximating large point clouds representing bathymetry of the smooth sea and ocean floor. A drastic reduction is demonstrated in the bulk of the data representation compared to the size of input point clouds. The representation is very well suited for exploiting the power of GPUs for visualization as the spline format is transferred to the GPU and the triangulation needed for the visualization is generated on the GPU according to the viewing parameters. The LR B-splines are interoperable with other elevation model representations such as LIDAR data, raster representations and triangulated irregular networks as these can be used as input to the LR B-spline approximation algorithms. Output to these formats can be generated from the LR B-spline applications according to the resolution criteria required. The spline models are well suited for change detection as new sensor data can efficiently be compared to the compact LR B-spline representation.
Analysis of moderately thin-walled beam cross-sections by cubic isoparametric elements
DEFF Research Database (Denmark)
Høgsberg, Jan Becker; Krenk, Steen
2014-01-01
numerically by introducing a cubic-linear two-dimensional isoparametric element. The cubic interpolation of this element accurately represents quadratic shear stress variations along cross-section walls, and thus moderately thin-walled cross-sections are effectively discretized by these elements. The ability......In technical beam theory the six equilibrium states associated with homogeneous tension, bending, shear and torsion are treated as individual load cases. This enables the formulation of weak form equations governing the warping from shear and torsion. These weak form equations are solved...... of this element to represent curved geometries, and to accurately determine cross-section parameters and shear stress distributions is demonstrated....
History matching by spline approximation and regularization in single-phase areal reservoirs
Lee, T. Y.; Kravaris, C.; Seinfeld, J.
1986-01-01
An automatic history matching algorithm is developed based on bi-cubic spline approximations of permeability and porosity distributions and on the theory of regularization to estimate permeability or porosity in a single-phase, two-dimensional real reservoir from well pressure data. The regularization feature of the algorithm is used to convert the ill-posed history matching problem into a well-posed problem. The algorithm employs the conjugate gradient method as its core minimization method. A number of numerical experiments are carried out to evaluate the performance of the algorithm. Comparisons with conventional (non-regularized) automatic history matching algorithms indicate the superiority of the new algorithm with respect to the parameter estimates obtained. A quasioptimal regularization parameter is determined without requiring a priori information on the statistical properties of the observations.
Interpolation of rational matrix functions
Ball, Joseph A; Rodman, Leiba
1990-01-01
This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an indepe...
Kriging Interpolating Cosmic Velocity Field
Yu, Yu; Jing, Yipeng; Zhang, Pengjie
2015-01-01
[abridge] Volume-weighted statistics of large scale peculiar velocity is preferred by peculiar velocity cosmology, since it is free of uncertainties of galaxy density bias entangled in mass-weighted statistics. However, measuring the volume-weighted velocity statistics from galaxy (halo/simulation particle) velocity data is challenging. For the first time, we apply the Kriging interpolation to obtain the volume-weighted velocity field. Kriging is a minimum variance estimator. It predicts the most likely velocity for each place based on the velocity at other places. We test the performance of Kriging quantified by the E-mode velocity power spectrum from simulations. Dependences on the variogram prior used in Kriging, the number $n_k$ of the nearby particles to interpolate and the density $n_P$ of the observed sample are investigated. (1) We find that Kriging induces $1\\%$ and $3\\%$ systematics at $k\\sim 0.1h{\\rm Mpc}^{-1}$ when $n_P\\sim 6\\times 10^{-2} ({\\rm Mpc}/h)^{-3}$ and $n_P\\sim 6\\times 10^{-3} ({\\rm Mpc...
Evaluation of various interpolants available in DICE
Energy Technology Data Exchange (ETDEWEB)
Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Reu, Phillip L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Crozier, Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-02-01
This report evaluates several interpolants implemented in the Digital Image Correlation Engine (DICe), an image correlation software package developed by Sandia. By interpolants we refer to the basis functions used to represent discrete pixel intensity data as a continuous signal. Interpolation is used to determine intensity values in an image at non - pixel locations. It is also used, in some cases, to evaluate the x and y gradients of the image intensities. Intensity gradients subsequently guide the optimization process. The goal of this report is to inform analysts as to the characteristics of each interpolant and provide guidance towards the best interpolant for a given dataset. This work also serves as an initial verification of each of the interpolants implemented.
A new interpolation method for Antarctic surface temperature
Institute of Scientific and Technical Information of China (English)
Yetang Wang; Shugui Hou
2009-01-01
We propose a new methodology for the spatial interpolation of annual mean temperature into a regular grid with a geographic resolution of 0.01° for Antarctica by applying a recent compilation of the Antarctic temperature data.A multiple linear regression model of the dependence of temperature on some geographic parameters (i.e.,latitude,longitude,and elevation) is proposed empirically,and the kriging method is used to determine the spatial distribution of regional and local deviations from the temperature calculated from the multiple linear regression model.The modeled value and residual grids are combined to derive a high-resolution map of surface air temperature.The performance of our new methodology is superior to a variety of benchmark methods (e.g.,inverse distance weighting,kriging,and spline methods) via cross-validation techniques.Our simulation resembles well with those distinct spatial features of surface temperature,such as the decrease in annual mean surface temperature with increasing latitude and the distance away from the coast line;and it also reveals the complex topographic effects on the spatial distribution of surface temperature.
Ninyerola, M.; Pons, X.; Roure, J. M.
2007-07-01
In this study, spatial interpolation techniques have been applied to develop an objective climatic cartography of precipitation in the Iberian Peninsula (583,551 km2). The resulting maps have a 200 m spatial resolution and a monthly temporal resolution. Multiple regression, combined with a residual correction method, has been used to interpolate the observed data collected from the meteorological stations. This method is attractive as it takes into account geographic information (independent variables) to interpolate the climatic data (dependent variable). Several models have been developed using different independent variables, applying several interpolation techniques and grouping the observed data into different subsets (drainage basin models) or into a single set (global model). Each map is provided with its associated accuracy, which is obtained through a simple regression between independent observed data and predicted values. This validation has shown that the most accurate results are obtained when using the global model with multiple regression mixed with the splines interpolation of the residuals. In this optimum case, the average R 2 (mean of all the months) is 0.85. The entire process has been implemented in a GIS (Geographic Information System) which has greatly facilitated the filtering, querying, mapping and distributing of the final cartography.
On Double Interpolation in Polar Coordinates
Directory of Open Access Journals (Sweden)
Antoniu Nicula
2009-10-01
Full Text Available Interpolation is an important tool in numerical modeling of real-life systems. The Lagrange interpolation is frequently used, due to particular advantages in implementation. The bi-dimensional version may be implemented with Cartesian or with polar coordinate system. Choice of the coordinate system is important in order to obtain accurate results. The polar case has particular properties that can be exploited to minimize some of the common disadvantages of polynomial interpolation.
Nohara, Yoshiro; Andersen, O. K.
2016-08-01
A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals. Periodicity is not required. The interpolation functions are localized structure-adapted linear combinations of spherical waves, the so-called unitary spherical waves (USWs), ψR L(" close=")ɛn)">ɛ ,r , centered at the spheres R , where they have cubic-harmonic character L . Input to the interpolation are the coefficients in the cubic-harmonic expansions of the target function at and slightly outside the spheres; specifically, the values and the three first radial derivatives labeled by d =0 (value) and 1-3 (derivatives). To fit this, we use USWs with four negative energies, ɛ =ɛ1,ɛ2,ɛ3 , and ɛ4. Each interpolation function, ϱd R L(r ), is actually a linear combination of these four sets of USWs with the following properties. (1) It is centered at a specific sphere where it has a specific cubic-harmonic character and radial derivative. (2) Its value and the first three radial derivatives vanish at all other spheres and for all other cubic-harmonic characters, and is therefore highly localized, essentially inside its Voronoi cell. Value-and-derivative (v&d) functions were originally introduced and used by Methfessel [Phys. Rev. B 38, 1537 (1988), 10.1103/PhysRevB.38.1537], but only for the first radial derivative. Explicit expressions are given for the v&d functions and their Coulomb potentials in terms of the USWs at the four energies, plus ɛ0≡0 for the potentials. The coefficients, as well as integrals over the interstitial such as the electrostatic energy, are given entirely in terms of the structure matrix, SR L ,R'L', describing the slopes of the USWs at the five energies and their expansions in Hankel functions. For open structures, additional constraints are installed to pinpoint the interpolated function deep
High degree interpolation polynomial in Newton form
Tal-Ezer, Hillel
1988-01-01
Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.
COMPUTATION OF VECTOR VALUED BLENDING RATIONAL INTERPOLANTS
Institute of Scientific and Technical Information of China (English)
檀结庆
2003-01-01
As we know, Newton's interpolation polynomial is based on divided differ-ences which can be calculated recursively by the divided-difference scheme while Thiele'sinterpolating continued fractions are geared towards determining a rational functionwhich can also be calculated recursively by so-called inverse differences. In this paper,both Newton's interpolation polynomial and Thiele's interpolating continued fractionsare incorporated to yield a kind of bivariate vector valued blending rational interpolantsby means of the Samelson inverse. Blending differences are introduced to calculate theblending rational interpolants recursively, algorithm and matrix-valued case are dis-cussed and a numerical example is given to illustrate the efficiency of the algorithm.
Directory of Open Access Journals (Sweden)
Saad Bakkali
2010-04-01
Full Text Available This paper focuses on presenting a method which is able to filter out noise and suppress outliers of sampled real functions under fairly general conditions. The automatic optimal spline-smoothing approach automatically determi-nes how a cubic spline should be adjusted in a least-squares optimal sense from an a priori selection of the number of points defining an adjusting spline, but not their location on that curve. The method is fast and easily allowed for selecting several knots, thereby adding desirable flexibility to the procedure. As an illustration, we apply the AOSSA method to Moroccan resistivity data phosphate deposit “disturbances” map. The AOSSA smoothing method is an e-fficient tool in interpreting geophysical potential field data which is particularly suitable in denoising, filtering and a-nalysing resistivity data singularities. The AOSSA smoothing and filtering approach was found to be consistently use-ful when applied to modeling surface phosphate “disturbances.”.
Efficient computation of smoothing splines via adaptive basis sampling
Ma, Ping
2015-06-24
© 2015 Biometrika Trust. Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is applicable, a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is generally O(n^{3}). We achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions, obtained by an adaptive sampling scheme that uses values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as full basis smoothing splines. Using simulation studies and a large-scale deep earth core-mantle boundary imaging study, we show that the proposed method outperforms a sampling method that does not use the values of response variables.
Universal Reconfiguration of (Hyper-)cubic Robots
Abel, Zachary; Kominers, Scott D.
2008-01-01
We study a simple reconfigurable robot model which has not been previously examined: cubic robots comprised of three-dimensional cubic modules which can slide across each other and rotate about each others' edges. We demonstrate that the cubic robot model is universal, i.e., that an n-module cubic robot can reconfigure itself into any specified n-module configuration. Additionally, we provide an algorithm that efficiently plans and executes cubic robot motion. Our results directly extend to a...
Testing for additivity with B-splines
Institute of Scientific and Technical Information of China (English)
Heng-jian CUI; Xu-ming HE; Li LIU
2007-01-01
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernelbased tests. The score test is found to have a good overall performance.
Testing for additivity with B-splines
Institute of Scientific and Technical Information of China (English)
2007-01-01
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey’s one degree of freedom test and a nonparametric version of Rao’s score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.
Automatic Image Interpolation Using Homography
Directory of Open Access Journals (Sweden)
Chi-Tsung Liu
2010-01-01
Full Text Available While taking photographs, we often face the problem that unwanted foreground objects (e.g., vehicles, signs, and pedestrians occlude the main subject(s. We propose to apply image interpolation (also known as inpainting techniques to remove unwanted objects in the photographs and to automatically patch the vacancy after the unwanted objects are removed. When given only a single image, if the information loss after the unwanted objects in images being removed is too great, the patching results are usually unsatisfactory. The proposed inpainting techniques employ the homographic constraints in geometry to incorporate multiple images taken from different viewpoints. Our experiment results showed that the proposed techniques could effectively reduce process in searching for potential patches from multiple input images and decide the best patches for the missing regions.
Use of B-Spline in the Finite Element Analysis: Comparison with ANCF Geometry
2011-02-04
formulations developed in this paper. 15. SUBJECT TERMS Geometric discontinuities; Finite element; Multibody systems; B-spline; NURBS 16. SECURITY...Keywords: Geometric discontinuities; Finite element; Multibody systems; B-spline; NURBS . UNCLAS: Dist A. Approved for public release 3 1...developed by computational geometry methods such as B- spline and NURBS (Non-Uniform Rational B-Splines) representations. This fact has motivated
Numerical simulation of involutes spline shaft in cold rolling forming
Institute of Scientific and Technical Information of China (English)
王志奎; 张庆
2008-01-01
Design of forming dies and whole process of simulation of cold rolling involutes spline can be realized by using of CAD software of PRO-E and CAE software of DEFORM-3D. Software DEFORM-3D provides an automatic and optimized remeshing function, especially for the large deformation. In order to use this function sufficiently, simulation of cold rolling involutes spline can be implemented indirectly. The relationship between die and workpiece, forming force and characteristic of deformation in the forming process of cold rolling involutes spline are analyzed and researched. Meanwhile, reliable proofs for the design of dies and deforming equipment are provided.
A Simple and Fast Spline Filtering Algorithm for Surface Metrology.
Zhang, Hao; Ott, Daniel; Song, John; Tong, Mingsi; Chu, Wei
2015-01-01
Spline filters and their corresponding robust filters are commonly used filters recommended in ISO (the International Organization for Standardization) standards for surface evaluation. Generally, these linear and non-linear spline filters, composed of symmetric, positive-definite matrices, are solved in an iterative fashion based on a Cholesky decomposition. They have been demonstrated to be relatively efficient, but complicated and inconvenient to implement. A new spline-filter algorithm is proposed by means of the discrete cosine transform or the discrete Fourier transform. The algorithm is conceptually simple and very convenient to implement.