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.
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...
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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
Shape preserving rational cubic spline for positive and convex data
Directory of Open Access Journals (Sweden)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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...
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.
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...
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.
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.
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.
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.
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).
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.
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.
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.
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.
Rational trigonometric cubic spline to conserve convexity of 2D data
Directory of Open Access Journals (Sweden)
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.
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
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
Directory of Open Access Journals (Sweden)
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.
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.
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.
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.
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.
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.
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...
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.
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.
Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface
Directory of Open Access Journals (Sweden)
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.
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.
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.
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.
G1 Continuity Conditions of B－spline Surfaces
Institute of Scientific and Technical Information of China (English)
车翔玖; 梁学章
2002-01-01
According to the B-spline theory and Boehm algorithm,this paper presents several necessary and sufficient G1 continuity conditions betwwen two adjacent B-spline surfaces,In Order to meet the need of application,a kind of sufficient conditions of G1 continuity are developed,and a kind of sufficient conditions of G1 continuity among N(N>2) patch B-shline surfaces meeting at a common corner are given at the end.
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.
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|
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.
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.
An Areal Isotropic Spline Filter for Surface Metrology.
Zhang, Hao; Tong, Mingsi; Chu, Wei
2015-01-01
This paper deals with the application of the spline filter as an areal filter for surface metrology. A profile (2D) filter is often applied in orthogonal directions to yield an areal filter for a three-dimensional (3D) measurement. Unlike the Gaussian filter, the spline filter presents an anisotropic characteristic when used as an areal filter. This disadvantage hampers the wide application of spline filters for evaluation and analysis of areal surface topography. An approximation method is proposed in this paper to overcome the problem. In this method, a profile high-order spline filter serial is constructed to approximate the filtering characteristic of the Gaussian filter. Then an areal filter with isotropic characteristic is composed by implementing the profile spline filter in the orthogonal directions. It is demonstrated that the constructed areal filter has two important features for surface metrology: an isotropic amplitude characteristic and no end effects. Some examples of applying this method on simulated and practical surfaces are analyzed.
RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES
Institute of Scientific and Technical Information of China (English)
ZHU Weidong; KE Yinglin
2007-01-01
A method to reconstruct Symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using Symmetric knot vector and Symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a Symmetric knot vector is selected in order to get Symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be Symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.
The Shape Parameter in the Shifted Surface Spline
Luh, Lin-Tian
2010-01-01
There is a constant c contained in the famous radial basis function shifted surface spline. It's called shape parameter. RBF people only know that this constant is very influential, while its optimal choice is unknown. This paper presents criteria of its optimal choice.
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.
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
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.
Adaptive Surface Reconstruction Based on Tensor Product Algebraic Splines
Institute of Scientific and Technical Information of China (English)
Xinghua Song; Falai Chen
2009-01-01
Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Jiittler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.AMS subject classifications: 65D17
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...
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
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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.
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.
Stacy, J. E.
1984-01-01
Asymmetric spline surfaces appear useful for the design of high-quality general optical systems (systems without symmetries). A spline influence function defined as the actual surface resulting from a simple perturbation in the spline definition array shows that a subarea is independent of others four or more points away. Optimization methods presented in this paper are used to vary a reflective spline surface near the focal plane of a decentered Schmidt-Cassegrain to reduce rms spot radii by a factor of 3 across the field.
A fast direct point-by-point generating algorithm for B Spline curves and surfaces
Institute of Scientific and Technical Information of China (English)
LI Zhong; HAN Dan-fu
2005-01-01
Traditional generating algorithms for B Spline curves and surfaces require approximation methods where how to increment the parameter to get the best approximation is problematic; or they take the pixel-based method needing matrix transformation from B Spline representation to Bezier form. Here, a fast, direct point-by-point generating algorithm for B Spline curves and surfaces is presented. The algorithm does not need matrix transformation, can be used for uniform or nonuniform B Spline curves and surfaces of any degree, and has high generating speed and good rendering accuracy.
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.
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.
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.
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．
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...
Symmetric alteration of four knots of B-spline and NURBS surfaces
Institute of Scientific and Technical Information of China (English)
LI Ya-juan; WANG Guo-zhao
2006-01-01
Modifying the knots ofa B-spline curve, the shape of the curve will be changed. In this paper, we present the effect of the symmetric alteration of four knots of the B-spline and the NURBS surfaces, i.e., symmetrical alteration of the knots of surface,the extended paths of points of the surface will converge to a point which should be expressed with several control points. This theory can be used in the constrained shape modification of B-spline and NURBS surfaces.
Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data
Garcia-Capulin, C. H.; F. J. Cuevas; Trejo-Caballero, G.; Rostro-Gonzalez, H.
2014-01-01
B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor pro...
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...
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.
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.
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.
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.
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.
Approximating Spline filter: New Approach for Gaussian Filtering in Surface Metrology
Directory of Open Access Journals (Sweden)
Hao Zhang
2009-10-01
Full Text Available This paper presents a new spline filter named approximating spline filter for surface metrology. The purpose is to provide a new approach of Gaussian filter and evaluate the characteristics of an engineering surface more accurately and comprehensively. First, the configuration of approximating spline filter is investigated, which describes that this filter inherits all the merits of an ordinary spline filter e.g. no phase distortion and no end distortion. Then, the approximating coefficient selection is discussed, which specifies an important property of this filter-the convergence to Gaussian filter. The maximum approximation deviation between them can be controlled below 4.36% , moreover, be decreased to less than 1% when cascaded. Since extended to 2 dimensional (2D filter, the transmission deviation yields within -0.63% : +1.48% . It is proved that the approximating spline filter not only achieves the transmission characteristic of Gaussian filter, but also alleviates the end effect on a data sequence. The whole computational procedure is illustrated and applied to a work piece to acquire mean line whereas a simulated surface to mean surface. These experimental results indicate that this filtering algorithm for 11200 profile points and 2000 × 2000 form data, only spends 8ms and 2.3s respectively.
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.
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.
Zhang, X.; Liang, S.; Wang, G.
2015-12-01
Incident solar radiation (ISR) over the Earth's surface plays an important role in determining the Earth's climate and environment. Generally, can be obtained from direct measurements, remotely sensed data, or reanalysis and general circulation models (GCMs) data. Each type of product has advantages and limitations: the surface direct measurements provide accurate but sparse spatial coverage, whereas other global products may have large uncertainties. Ground measurements have been normally used for validation and occasionally calibration, but transforming their "true values" spatially to improve the satellite products is still a new and challenging topic. In this study, an improved thin-plate smoothing spline approach is presented to locally "calibrate" the Global LAnd Surface Satellite (GLASS) ISR product using the reconstructed ISR data from surface meteorological measurements. The influences of surface elevation on ISR estimation was also considered in the proposed method. The point-based surface reconstructed ISR was used as the response variable, and the GLASS ISR product and the surface elevation data at the corresponding locations as explanatory variables to train the thin plate spline model. We evaluated the performance of the approach using the cross-validation method at both daily and monthly time scales over China. We also evaluated estimated ISR based on the thin-plate spline method using independent ground measurements at 10 sites from the Coordinated Enhanced Observation Network (CEON). These validation results indicated that the thin plate smoothing spline method can be effectively used for calibrating satellite derived ISR products using ground measurements to achieve better accuracy.
Cubic surfaces and their invariants: Some memories of Raymond Stora
Directory of Open Access Journals (Sweden)
Michel Bauer
2016-11-01
I then turn to the study of the family of cubic surfaces. They depend on 20 parameters, and the action of the 15 parameter group SL4(C splits the family in orbits depending on 5 parameters. This takes us into the realm of (geometric invariant theory. I review briefly the classical theorems on the structure of the ring of polynomial invariants and illustrate its many facets by looking at a simple example, before turning to the already involved case of cubic surfaces. The invariant ring was described in the 19th century. I show how to retrieve this description via counting/generating functions and character formulae.
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.
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.
Cubic surfaces and their invariants: Some memories of Raymond Stora
Bauer, Michel
2016-11-01
Cubic surfaces embedded in complex projective 3-space are a classical illustration of the use of old and new methods in algebraic geometry. Recently, they made their appearance in physics, and in particular aroused the interest of Raymond Stora, to the memory of whom these notes are dedicated, and to whom I'm very much indebted. Each smooth cubic surface has a rich geometric structure, which I review briefly, with emphasis on the 27 lines and the combinatorics of their intersections. Only elementary methods are used, relying on first order perturbation/deformation theory. I then turn to the study of the family of cubic surfaces. They depend on 20 parameters, and the action of the 15 parameter group SL4 (C) splits the family in orbits depending on 5 parameters. This takes us into the realm of (geometric) invariant theory. I review briefly the classical theorems on the structure of the ring of polynomial invariants and illustrate its many facets by looking at a simple example, before turning to the already involved case of cubic surfaces. The invariant ring was described in the 19th century. I show how to retrieve this description via counting/generating functions and character formulae.
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.
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.
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.
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
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.
Ship hull plate processing surface fairing with constraints based on B-spline
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The problem of ship hull plate processing surface fairing with constraints based on B-spline is solved in this paper. The algorithm for B-spline curve fairing with constraints is one of the most common methods in plane curve fairing. The algorithm can be applied to global and local curve fairing. It can constrain the perturbation range of the control points and the shape variation of the curve, and get a better fairing result in plane curves. In this paper, a new fairing algorithm with constraints for curves and surfaces in space is presented. Then this method is applied to the experiments of ship hull plate processing surface. Finally numerical results are obtained to show the efficiency of this method.
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
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.
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．
Harmening, Corinna; Neuner, Hans
2017-03-01
Freeform surfaces like B-splines have proven to be a suitable tool to model laser scanner point clouds and to form the basis for an areal data analysis, for example an areal deformation analysis. A variety of parameters determine the B-spline's appearance, the B-spline's complexity being mostly determined by the number of control points. Usually, this parameter type is chosen by intuitive trial-and-error-procedures. In [10] the problem of finding an alternative to these trial-and-error-procedures was addressed for the case of B-spline curves: The task of choosing the optimal number of control points was interpreted as a model selection problem. Two model selection criteria, the Akaike and the Bayesian Information Criterion, were used to identify the B-spline curve with the optimal number of control points from a set of candidate B-spline models. In order to overcome the drawbacks of the information criteria, an alternative approach based on statistical learning theory was developed. The criteria were evaluated by means of simulated data sets. The present paper continues these investigations. If necessary, the methods proposed in [10] are extended to areal approaches so that they can be used to determine the optimal number of B-spline surface control points. Furthermore, the methods are evaluated by means of real laser scanner data sets rather than by simulated ones. The application of those methods to B-spline surfaces reveals the datum problem of those surfaces, meaning that location and number of control points of two B-splines surfaces are only comparable if they are based on the same parameterization. First investigations to solve this problem are presented.
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.
Generalized b-spline subdivision-surface wavelets and lossless compression
Energy Technology Data Exchange (ETDEWEB)
Bertram, M; Duchaineau, M A; Hamann, B; Joy, K I
1999-11-24
We present a new construction of wavelets on arbitrary two-manifold topology for geometry compression. The constructed wavelets generalize symmetric tensor product wavelets with associated B-spline scaling functions to irregular polygonal base mesh domains. The wavelets and scaling functions are tensor products almost everywhere, except in the neighborhoods of some extraordinary points (points of valence unequal four) in the base mesh that defines the topology. The compression of arbitrary polygonal meshes representing isosurfaces of scalar-valued trivariate functions is a primary application. The main contribution of this paper is the generalization of lifted symmetric tensor product B-spline wavelets to two-manifold geometries. Surfaces composed of B-spline patches can easily be converted to this scheme. We present a lossless compression method for geometries with or without associated functions like color, texture, or normals. The new wavelet transform is highly efficient and can represent surfaces at any level of resolution with high degrees of continuity, except at a finite number of extraordinary points in the base mesh. In the neighborhoods of these points detail can be added to the surface to approximate any degree of continuity.
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.
Cubic versus spherical magnetic nanoparticles: the role of surface anisotropy.
Salazar-Alvarez, G; Qin, J; Sepelák, V; Bergmann, I; Vasilakaki, M; Trohidou, K N; Ardisson, J D; Macedo, W A A; Mikhaylova, M; Muhammed, M; Baró, M D; Nogués, J
2008-10-08
The magnetic properties of maghemite (gamma-Fe2O3) cubic and spherical nanoparticles of similar sizes have been experimentally and theoretically studied. The blocking temperature, T(B), of the nanoparticles depends on their shape, with the spherical ones exhibiting larger T(B). Other low temperature properties such as saturation magnetization, coercivity, loop shift or spin canting are rather similar. The experimental effective anisotropy and the Monte Carlo simulations indicate that the different random surface anisotropy of the two morphologies combined with the low magnetocrystalline anisotropy of gamma-Fe2O3 is the origin of these effects.
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.
3-D Design of Free-Form B-Spline Surfaces
1974-09-01
a Mathematical Representation 5 11.2 Coons and Bezier Formulations 7 Coons Patches 7 Bözler Patches U 11.3 Local Basis Formulations 15 B-splines...lt|aa|^|MM|aM^|[ia|J|||.ai|h. j : ’ ^-*^ 16 Figure 2.4 Bezier Surface and Control Point Array. mmägmgft mm ^i^i_...isoparametric curvas (rendered as collections of straight line segments) in the surface and emphasized dots to represent the control points. Figure 3.G shows
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.
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.
均匀B样条曲线曲面的小波表示%Wavelets-Based Representation of Uniform B-Spline Curves and Surfaces
Institute of Scientific and Technical Information of China (English)
赵罡; 穆国旺; 闫光荣; 朱心雄
2001-01-01
Wavelets-based representation provides a more flexible method for expressing curves and surfaces in different resolution levels. For uniform B-spline curves and surfaces, a unified expression can be adopted after decomposition to describe the wavelets for the interior and boundaries of the domain defined, and hence the multiplication is the only operation be needed to wavelets reconstruction. This results in high efficiency for the computation. The paper describes, from the point of geometry view, the principles and methods of realizing wavelets-based multiresolution representation of uniform cubic B-spline curves and surfaces.%小波基为曲线曲面带来了更为灵活的表达方式。均匀B样条曲线曲面在经过小波分解以后所得到的小波在定义域边界与内部可以采用统一的表达式，在进行小波重构时仅需作乘法运算，计算效率高。本文试图从几何概念出发由浅入深地论述基于小波的均匀三次B样条曲线曲面多分辨表示的原理及其实现。
Generalized B-spline subdivision-surface wavelets for geometry compression.
Bertram, Martin; Duchaineau, Mark A; Hamann, Bernd; Joy, Kenneth I
2004-01-01
We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail can be expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-Spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform can be computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.
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.
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.
G1 Continuity Conditions of B-spline Surfaces%B样条曲面间的G1连续条件
Institute of Scientific and Technical Information of China (English)
车翔玖; 梁学章
2002-01-01
According to the B-spline theory and Boehm algorithm, this paper presents severalnecessary and sufficient G1 continuity conditions between two adjacent B-spline surfaces. In orderto meet the need of application, a kind of sufficient conditions of G1 continuity are developed, anda kind of sufficient conditions of G1 continuity among N(N ＞ 2) patch B-spline surfaces meetingat a common corner are given at the end.
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.
Fast simulation of x-ray projections of spline-based surfaces using an append buffer.
Maier, Andreas; Hofmann, Hannes G; Schwemmer, Chris; Hornegger, Joachim; Keil, Andreas; Fahrig, Rebecca
2012-10-07
Many scientists in the field of x-ray imaging rely on the simulation of x-ray images. As the phantom models become more and more realistic, their projection requires high computational effort. Since x-ray images are based on transmission, many standard graphics acceleration algorithms cannot be applied to this task. However, if adapted properly, the simulation speed can be increased dramatically using state-of-the-art graphics hardware. A custom graphics pipeline that simulates transmission projections for tomographic reconstruction was implemented based on moving spline surface models. All steps from tessellation of the splines, projection onto the detector and drawing are implemented in OpenCL. We introduced a special append buffer for increased performance in order to store the intersections with the scene for every ray. Intersections are then sorted and resolved to materials. Lastly, an absorption model is evaluated to yield an absorption value for each projection pixel. Projection of a moving spline structure is fast and accurate. Projections of size 640 × 480 can be generated within 254 ms. Reconstructions using the projections show errors below 1 HU with a sharp reconstruction kernel. Traditional GPU-based acceleration schemes are not suitable for our reconstruction task. Even in the absence of noise, they result in errors up to 9 HU on average, although projection images appear to be correct under visual examination. Projections generated with our new method are suitable for the validation of novel CT reconstruction algorithms. For complex simulations, such as the evaluation of motion-compensated reconstruction algorithms, this kind of x-ray simulation will reduce the computation time dramatically.
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 .
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.
Cubic Invariant Spherical Surface Harmonics in Conjunction With Diffraction Strain Pole-Figures
Brakman, C.M.
1986-01-01
Four kinds of cubic invariant spherical surface harmonics are introduced. It has been shown previously that these harmonics occur in the equations relating measured diffraction (line-shift) elastic strain and macro-stresses generating these strains for the case of textured cubic materials. As a cons
Li, Wen-long; Wang, Gang; Zhang, Gang; Pang, Chang-tao; Yin, Zhou-pin
2016-09-01
Onsite surface inspection with a touch probe or a laser scanner is a promising technique for efficiently evaluating surface profile error. The existing work of 5-axis inspection path generation bears a serious drawback, however, as there is a drastic orientation change of the inspection axis. Such a sudden change may exceed the stringent physical limit on the speed and acceleration of the rotary motions of the machine tool. In this paper, we propose a novel path generation method for onsite 5-axis surface inspection. The accessibility cones are defined and used to generate alternative interference-free inspection directions. Then, the control points are optimally calculated to obtain the dual-cubic non-Uniform rational B-splines (NURBS) curves, which respectively determine the path points and the axis vectors in an inspection path. The generated inspection path is smooth and non-interference, which deals with the ‘mutation and shake’ problems and guarantees a stable speed and acceleration of machine tool rotary motions. Its feasibility and validity is verified by the onsite inspection experiments of impeller blade.
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 .
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.
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.
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.
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.
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.
Regional magnetic anomaly fields: 3D Taylor polynomial and surface spline models
Feng, Yan; Jiang, Yong; Jiang, Yi; Li, Zheng; Jiang, Jin; Liu, Zhong-Wei; Ye, Mei-Chen; Wang, Hong-Sheng; Li, Xiu-Ming
2016-03-01
We used data from 1960.0, 1970.0, 1980.0, 1990.0, and 2000.0 to study the geomagnetic anomaly field over the Chinese mainland by using the three-dimensional Taylor polynomial (3DTP) and the surface spline (SS) models. To obtain the pure anomaly field, the main field and the induced field of the ionospheric and magnetospheric fields were removed from measured data. We also compared the SS model anomalies and the data obtained with Kriging interpolation (KI). The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0-1990.0 to 2000.0. The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity. The anomalous distributions in the X-, Y-, and Z-direction and F are mainly negative. The 3DTP model anomalies suggest that the intensity in the X-direction increases from -100 nT to 0 nT with longitude, whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative. The intensity in the Z-direction and F are very similar and in most areas it is about -50nT and higher in western Tibet. The SS model anomalies overall reflect the actual distribution of the magnetic field anomalies; however, because of the uneven distribution of measurements, it yields several big anomalies. Owing to the added altitude term, the 3DTP model offers higher precision and is consistent with KI.
Regional magnetic anomalyfi elds：3D Taylor polynomial and surface spline models
Institute of Scientific and Technical Information of China (English)
Feng Yan; Jiang Yong; Jiang Yi; Li Zheng; Jiang Jin; Liu Zhong-Wei; Ye Mei-Chen; Wang Hong-Sheng; Li Xiu-Ming
2016-01-01
We used data from 1960.0, 1970.0, 1980.0, 1990.0, and 2000.0 to study the geomagnetic anomalyfi eld over the Chinese mainland by using the three-dimensional Taylor polynomial (3DTP) and the surface spline (SS) models. To obtain the pure anomalyfi eld, the mainfi eld and the inducedfi eld of the ionospheric and magnetosphericfi elds were removed from measured data. We also compared the SS model anomalies and the data obtained with Kriging interpolation (KI). The geomagnetic anomaly distribution over the mainland was analyzed based on the SS and 3DTP models by transferring all points from 1960.0−1990.0 to 2000.0. The results suggest that the total intensity F anomalies estimated based on the SS and KI for each year are basically consistent in distribution and intensity. The anomalous distributions in the X-, Y-, and Z-direction and F are mainly negative. The 3DTP model anomalies suggest that the intensity in the X-direction increases from−100 nT to 0 nT with longitude, whereas the intensity in the Y-direction decreases from 400 nT to 20 nT with longitude and over the eastern mainland is almost negative. The intensity in the Z-direction and F are very similar and in most areas it is about−50nT and higher in western Tibet. The SS model anomalies overall refl ect the actual distribution of the magneticfi eld anomalies; however, because of the uneven distribution of measurements, it yields several big anomalies. Owing to the added altitude term, the 3DTP model offers higher precision and is consistent with KI.
Curvature properties of the slowness surface of the system of crystal acoustics for cubic crystals
LIESS, Otto
2008-01-01
In this paper we study geometric properties of the slowness surface of the system of crystal acoustics for cubic crystals. In particular we shall study curvature properties of the surface and the behaviour of the surface near singular points. The main result is that in the generic nearly isotropic case there are no planes which are tangent to the surface along entire curves. This is in contrast with what happens for the slowness surface of the system of crystal optics for...
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)
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.
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).
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.
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.
Pivotal surfaces in inverse hexagonal and cubic phases of phospholipids and glycolipids.
Marsh, Derek
2011-03-01
Data on the location and dimensions of the pivotal surfaces in inverse hexagonal (H(II)) and inverse cubic (Q(II)) phases of phospholipids and glycolipids are reviewed. This includes the H(II) phases of dioleoyl phosphatidylethanolamine, 2:1 mol/mol mixtures of saturated fatty acids with the corresponding diacyl phosphatidylcholine, and glucosyl didodecylglycerol, and also the Q(II)(230/G) gyroid inverse cubic phases of monooleoylglycerol and glucosyl didodecylglycerol. Data from the inverse cubic phases are largely compatible with those from inverse hexagonal H(II)-phases. The pivotal plane is located in the hydrophobic region, relatively close to the polar-apolar interface. The area per lipid at the pivotal plane is similar in size to lipid cross-sectional areas found in the fluid lamellar phase (L(α)) of lipid bilayers. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.
Almeida, Nuno; Friboulet, Denis; Sarvari, Sebastian Imre; Bernard, Olivier; Barbosa, Daniel; Samset, Eigil; Dhooge, Jan
2016-02-01
Segmentation of the left atrium (LA) of the heart allows quantification of LA volume dynamics which can give insight into cardiac function. However, very little attention has been given to LA segmentation from three-dimensional (3-D) ultrasound (US), most efforts being focused on the segmentation of the left ventricle (LV). The B-spline explicit active surfaces (BEAS) framework has been shown to be a very robust and efficient methodology to perform LV segmentation. In this study, we propose an extension of the BEAS framework, introducing B-splines with uncoupled scaling. This formulation improves the shape support for less regular and more variable structures, by giving independent control over smoothness and number of control points. Semiautomatic segmentation of the LA endocardium using this framework was tested in a setup requiring little user input, on 20 volumetric sequences of echocardiographic data from healthy subjects. The segmentation results were evaluated against manual reference delineations of the LA. Relevant LA morphological and functional parameters were derived from the segmented surfaces, in order to assess the performance of the proposed method on its clinical usage. The results showed that the modified BEAS framework is capable of accurate semiautomatic LA segmentation in 3-D transthoracic US, providing reliable quantification of the LA morphology and function.
The Electric Field of a Uniformly Charged Non-Conducting Cubic Surface
McCreery, Kaitlin
2016-01-01
As an integrative and insightful example for undergraduates learning about electrostatics, we discuss how to use symmetry, Coulomb's Law, superposition, Gauss's law, and visualization to understand the electric field produced by a non-conducting cubic surface that is covered with a uniform surface charge density. We first discuss how to deduce qualitatively, using only elementary physics, the surprising fact that the electric field inside the cubic surface is nonzero and has a complex structure, pointing inwards towards the cube center from the midface of each cube and pointing outwards towards each edge and corner. We then discuss how to understand the quantitative features of the electric field by plotting an analytical expression for E along symmetry lines and on symmetry surfaces. This example would be a good choice for group problem solving in a recitation or flipped classroom.
Strong phonon anomalies and Fermi surface nesting of simple cubic Polonium
Belabbes, A.; Zaoui, A.; Ferhat, M.
2010-12-01
The unknown lattice dynamics of simple cubic Polonium is calculated using first-principles density-functional perturbation theory with pseudopotentials and a plane-wave basis set. We notice several phonon anomalies, in particular along major symmetry directions namely M-R, R-Γ, Γ-M, M-X, and X-Γ. The analysis of the Fermi surface strongly suggests that the observed phonon anomalies are Kohn anomalies arising from strong Fermi surface nesting.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Vasconcelos, Geovane Vitor; Dantas, Carlos Costa, E-mail: geovitor@bol.com.b, E-mail: ccd@ufpe.b [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Dept. de Energia Nuclear. Grupo de Radioquimica; Melo, Silvio de Barros; Pires, Renan Ferraz, E-mail: sbm@cin.ufpe.b, E-mail: rfp@cin.ufpe.b [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Centro de Informatica
2009-07-01
The 3D tomography reconstruction has been a profitable alternative in the analysis of the FCC-type- riser (Fluid Catalytic Cracking), for appropriately keeping track of the sectional catalyst concentration distribution in the process of oil refining. The method of tomography reconstruction proposed by M. Azzi and colleagues (1991) uses a relatively small amount of trajectories (from 3 to 5) and projections (from 5 to 7) of gamma rays, a desirable feature in the industrial process tomography. Compared to more popular methods, such as the FBP (Filtered Back Projection), which demands a much higher amount of gamma rays projections, the method by Azzi et al. is more appropriate for the industrial process, where the physical limitations and the cost of the process require more economical arrangements. The use of few projections and trajectories facilitates the diagnosis in the flow dynamical process. This article proposes an improvement in the basis functions introduced by Azzi et al., through the use of quadratic B-splines functions. The use of B-splines functions makes possible a smoother surface reconstruction of the density distribution, since the functions are continuous and smooth. This work describes how the modeling can be done. (author)
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
LIESS, Otto; Sonobe, Tetsuya
2012-01-01
In this paper we study geometric properties of the slowness surface of the system of crystal acoustics for cubic crystals in the special case when the stiffness constants satisfy the condition $a = -2b$. The paper is a natural continuation of the paper [9] in which related properties were studied for general constants $a$ and $b$, but assuming that we were in the nearly isotropic case, in which case $a - b$ has to be small. We also take this opportunity to correct a state...
Büchmann, Bjarne
2000-05-01
An analysis is given for the accuracy and stability of some perturbation-based time-domain boundary element models (BEMs) with B-spline basis functions, solving hydrodynamic free-surface problems, including forward speed effects. The spatial convergence rate is found as a function of the order of the B-spline basis. It is shown that for all the models examined the mixed implicit-explicit Euler time integration scheme is correct to second order. Stability diagrams are found for models based on B-splines of orders third through to sixth for two different time integration schemes. The stability analysis can be regarded as an extension of the analysis by Vada and Nakos [Vada T, Nakos DE. Time marching schemes for ship motion simulations. In Proceedings of the 8th International Workshop on Water Waves and Floating Bodies, St. John's, Newfoundland, Canada, 1993; 155-158] to include B-splines of orders higher than three (piecewise quadratic polynomials) and to include finite water depth and a current at an oblique angle to the model grid. Copyright
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.
基于C-B样条的三角形和四边形曲面生成%Triangular and quadrilateral surface construction using C-B spline
Institute of Scientific and Technical Information of China (English)
李薇; 吴卓奇; 荻原一郎
2012-01-01
This paper provides a different solution to represent basic smooth elements like triangular and quadrilateral surface patches from mesh using C-B spline curves. C-B spline curves are developed by the basis {sin t, cos t, t, 1}, and it overcomes some shortcomings of the B-spline and non-uniform rational B-splines (NURBS) model, for example, they have to increase unnecessary control point in order to satisfy the data grid topology, their derivative and integral are complex and tedious, their degrees are too high, and it is difficult to discuss their continuous conditions. How to develop C-B spline curves into surface becomes an important problem. In this paper, the interpolation operators are constructed by using side-vertex method and a convex combination of these operators is achieved. The C-B spline curves are developed into triangular and quadrilateral surface patches which can be used in reverse engineering of CAD.%文章给出了基于C-B样条的由网格数据产生三角形和四边形曲面片的方法,C-B样条是由基底函数{sin t,cos t,t,1}导出的一种新型样条曲线,它可以克服现在正在使用的B样条和有理B样条为了满足数据网格的拓扑结构而增加多余的控制点,求导求积分复杂繁琐,阶数过高,从而讨论其连续拼接时增加了困难等缺点,如何将它推广成曲面就成为一个重要问题.作者利用边-顶点方法构造插值算子,再将这些算子进行凸性组合,将C-B样条曲线推广成三角形曲面片和四边形曲面片,它可以用于CAD的逆向工程中散乱数据的曲面重构.
2012-01-22
ICES REPORT 12-05 January 2012 An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS , Immersed...M.J. Borden, E. Rank, T.J.R. Hughes, An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS , Immersed...analysis Methodology based on Adaptive Hierarchical Refinement of NURBS , Immersed Boundary Methods, and T-spline CAD Surfaces 5a. CONTRACT NUMBER 5b
Projection of curves on B-spline surfaces using quadratic reparameterization
Yang, Yijun
2010-09-01
Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a hyperbola approximation method based on the quadratic reparameterization of Bézier surfaces, which generates reasonable low degree curves lying completely on the surfaces by using iso-parameter curves of the reparameterized surfaces. The Hausdorff distance between the projected curve and the original curve is controlled under the user-specified distance tolerance. The projected curve is T-G 1 continuous, where T is the user-specified angle tolerance. Examples are given to show the performance of our algorithm. © 2010 Elsevier Inc. All rights reserved.
Directional dependence of nonlinear surface acoustic waves in the (001) plane of cubic crystals.
Kumon, R E; Hamilton, M F
2002-05-01
Spectral evolution equations are used to perform analytical and numerical studies of nonlinear surface acoustic waves in the (001) plane of a variety of nonpiezoelectric cubic crystals. The basic theory underlying the model equations is outlined, and quasilinear solutions of the equations are presented. Expressions are also developed for a characteristic length scale for nonlinear distortion and a nonlinearity coefficient. A time-domain equation corresponding to the spectral equations is derived. Numerical calculations based on measured second- and third-order elastic constants taken from the literature are performed to predict the evolution of initially monofrequency surface waves. Nonlinearity matrix elements that indicate the coupling strength of harmonic interactions are shown to provide a useful tool for characterizing waveform distortion. The formation of compression or rarefaction shocks can be strongly dependent on the direction of propagation, and harmonic generation is suppressed or increased in certain directions.
Constructing C1 Continuous Surface on Irregular Quad Meshes
Institute of Scientific and Technical Information of China (English)
HE Jun; GUO Qiang
2013-01-01
A new method is proposed for surface construction on irregular quad meshes as extensions to uniform B-spline surfaces. Given a number of control points, which form a regular or irregular quad mesh, a weight function is constructed for each control point. The weight function is defined on a local domain and is C1 continuous. Then the whole surface is constructed by the weighted combination of all the control points. The property of the new method is that the surface is defined by piecewise C1 bi-cubic rational parametric polynomial with each quad face. It is an extension to uniform B-spline surfaces in the sense that its definition is an analogy of the B-spline surface, and it produces a uniform bi-cubic B-spline surface if the control mesh is a regular quad mesh. Examples produced by the new method are also included.
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
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
Soukiassian, Patrick G.; Enriquez, Hanna B.
2004-05-01
The atomic scale ordering and properties of cubic silicon carbide (bgr-SiC) surfaces and nanostructures are investigated by atom-resolved room and high-temperature scanning tunnelling microscopy (STM) and spectroscopy (STS), synchrotron radiation-based valence band and core level photoelectron spectroscopy (VB-PES, CL-PES) and grazing incidence x-ray diffraction (GIXRD). In this paper, we review the latest results on the atomic scale understanding of (i) the structure of bgr-SiC(100) surface reconstructions, (ii) temperature-induced metallic surface phase transition, (iii) one dimensional Si(C) self-organized nanostructures having unprecedented characteristics, and on (iv) nanochemistry at SiC surfaces with hydrogen. The organization of these surface reconstructions as well as the 1D nanostructures' self-organization are primarily driven by surface stress. In this paper, we address such important issues as (i) the structure of the Si-rich 3 × 2, the Si-terminated c (4 × 2), the C-terminated c (2 × 2) reconstructions of the bgr-SiC(100) surface, (ii) the temperature-induced reversible {\\mathrm {c}}(4\\times 2) \\Leftrightarrow 2\\times 1 metallic phase transition, (iii) the formation of highly stable (up to 900 °C) Si atomic and vacancy lines, (iv) the temperature-induced sp to sp3 diamond like surface transformation, and (v) the first example of H-induced semiconductor surface metallization on the bgr-SiC (100) 3 × 2 surface. The results are discussed and compared to other experimental and theoretical investigations.
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
Clifford groups of quantum gates, BN-pairs and smooth cubic surfaces
Energy Technology Data Exchange (ETDEWEB)
Planat, Michel [Institut FEMTO-ST, CNRS, 32 Avenue de l' Observatoire, F-25044 Besancon (France); Sole, Patrick [CNRS I3S, Les Algorithmes, Euclide B, 2000 route des Lucioles, BP 121, 06903 Sophia Antipolis (France)
2009-01-30
The recent proposal (Planat and Kibler 2008 arXiv:0807.3650 [quant-ph]) of representing Clifford quantum gates in terms of unitary reflections is revisited. In this communication, the geometry of a Clifford group G is expressed as a BN-pair, i.e. a pair of subgroups B and N that generate G, is such that intersection H = B intersection N is normal in G, the group W = N/H is a Coxeter group and two extra axioms are satisfied by the double cosets acting on B. The BN-pair used in this decomposition relies on the swap and match gates already introduced for classically simulating quantum circuits (Jozsa and Miyake 2008 arXiv:0804.4050 [quant-ph]). The two- and three-qubit cases are related to the configuration with 27 lines on a smooth cubic surface. (fast track communication)
Adaptive Hierarchical B-spline Surface Representation of Large-Scale Scattered Data
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The representation of large scale scattered data is a difficult problem, especially when various features of the representation, such as C2-continuity, are required. This paper describes a fast algorithm for large scale scattered data approximation and interpolation. The interpolation algorithm uses a coarse-to-fine hierarchical control lattice to fit the scattered data. The refinement process is only used in the regions where the error between the scattered data and the result in a surface is greater than a specified tolerance. A method to ensure C2-continuity is introduced to calculate the control lattice under constrained conditions. Experimental results show that this method can quickly represent large scale scattered data set.
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.
Surface relaxation and surface energy of face –centered Cubic ...
African Journals Online (AJOL)
DR. MIKE HORSFALL
were based on perturbation theory or non-perturbative variational methods. ... knowledge for Rh, Ir, Pb, Ca, Sr and Th metal surfaces. ... represented in the ECT by the inclusion of the three – ... the ECT method to an fcc (100) metallic surface,.
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 .
Functional Spline Curves and Surfaces with Different Degrees of Smoothness%异度隐函数样条曲线曲面
Institute of Scientific and Technical Information of China (English)
朱春钢; 李彩云; 王仁宏
2009-01-01
Implicit curves and surfaces are extensively used in interpolation, approximation and blending. By adding auxiliary curves and surfaces, the functional spline curves and surfaces with different degrees of smoothness are presented. In addition, convexity, regularity and convexity are also discussed. The examples show that the functional spline curves and surfaces provide the lower degree, simple, and flexible interpolation and blending means of curves and surfaces.%隐式曲线曲面被广泛应用于曲线曲面插值、逼近与拼接. 通过添加辅助曲线曲面,提出异度隐函数样条曲线曲面方法,并对其插值性、凸性与正则性进行分析. 具体实例表明,异度隐函数样条提供了次数低、构造简单、灵活性好的曲线曲面插值与拼接方法.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Hasenbusch, M.; Hasenbusch, Martin; Pinn, Klaus
1992-01-01
We compute properties of the interface of the 3-dimensional Ising model for a wide range of temperatures and for interface extensions up to 64 by 64. The interface tension sigma is obtained by integrating the surface energy density over the inverse temperature beta. The surface stiffness coefficient kappa is determined. We also study universal quantities like xi^2 sigma and xi^2 kappa. The behavior of the interfacial width on lattices up to 512 times 512 times 27 is also investigated.
Higher-Order Level-Set Method and Its Application in Biomolecular Surfaces Construction
Institute of Scientific and Technical Information of China (English)
Chandrajit L. Bajaj; Guo-Liang Xu; Qin Zhang
2008-01-01
We present a general framework for a higher-order spline level-set (HLS) method and apply this to biomolecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formulation of geometric partial differential equation, and provide an efficient approach to solving this partial differential equation using a C2 spline basis. We also present a fast cubic spline interpolation algorithm based on convolution and the Z-transform, which exploits the local relationship of interpolatory cubic spline coefficients with respect to given function data values. One example of our HLS method is demonstrated, which is the construction of biomolecule surfaces (an implicit salvation interface) with their individual atomic coordinates and solvated radii as prerequisites.
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.
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.
Shape Designing of Engineering Images Using Rational Spline Interpolation
Directory of Open Access Journals (Sweden)
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.
Structural and electronic properties of cubic KNbO{sub 3} (0 0 1) surfaces: A first-principles study
Energy Technology Data Exchange (ETDEWEB)
Luo, Bingcheng [State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China); Wang, Xiaohui, E-mail: wxh@mail.tsinghua.edu.cn [State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China); Tian, Enke [School of Science, China University of Geosciences, Beijing 100083 (China); Li, Guowu [Crystal Structure Laboratory, National Laboratory of Mineral Materials, China University of Geosciences, Beijing 100083 (China); Li, Longtu [State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China)
2015-10-01
Highlights: • To the best of our knowledge, the (0 0 1) surfaces of SrTiO{sub 3}, BaTiO{sub 3}, CaTiO{sub 3} and PbTiO{sub 3} have been extensively investigated, but few ab initio calculations of structural and electronic properties of cubic KNbO{sub 3} (0 0 1) surface are reported. • The surface energy for the KO terminated was 1.21 eV, higher than the calculated surface energy of 0.75 eV for NbO{sub 2} termination, revealing that it take much less energy to cleave on the NbO{sub 2} plane than on the KO plane. • Mulliken population showed a strong increase in the K−O chemical bonding on the top surface of the KO-terminated slab, while the Nb−O chemical bonding on the top surface of the NbO{sub 2}-terminated slab decreased by 50 me. • The bond populations for K−O were much smaller than that for Nb−O, indicating significant covalency for Nb−O bonding. - Abstract: We present the calculations of the cubic perovskite KNbO{sub 3} (0 0 1) surface with NbO{sub 2} and KO terminations within the first-principles density functional theory. The electronic structure, surface energy, and charge distribution for both termination are calculated. For the case of NbO{sub 2}-terminated surfaces, the largest atomic relaxation is in the first-layer atoms, while for KO terminations in the second-layer atoms. The surface energy for the KO terminated was 1.21 eV, higher than the calculated surface energy of 0.75 eV for NbO{sub 2} termination, revealing that it takes much less energy to cleave on NbO{sub 2} plane than on a KO plane. The band gaps for KO-terminated and NbO{sub 2}-terminated surface are 1.70 and 1.30 eV, respectively. Mulliken population analysis shows the strong increase in the K−O chemical bonding on the top surface of the KO-terminated slab and significant covalency for Nb−O bonding.
Convolution Surface Modeling for Cubic B-Spline Skeletons%三次B样条曲线骨架卷积曲面造型
Institute of Scientific and Technical Information of China (English)
张海林; 金小刚; 冯结青
2006-01-01
提出一种基于B样条曲线降阶的三次B样条曲线骨架卷积曲面造型方法.首先通过顶点扰动降阶方法把三次B样条曲线骨架(C1连续)降阶为C1连续的二次B样条,然后应用二次B样条曲线骨架的卷积曲面势函数计算方法得到三次B样条曲线骨架的势函数.
Surface-induced ordering and disordering in face-centered-cubic alloys: A Monte Carlo study
Schweika, W.; Landau, D. P.; Binder, K.
1996-04-01
Using extensive Monte Carlo simulations we have studied phase transitions in a fcc model with antiferromagnetic nearest-neighbor couplings J in the presence of different free surfaces which lead either to surface-induced order or to surface-induced disorder. Our model is a prototype for CuAu-type ordering alloys and shows a strong first-order bulk transition at a temperature kTcb/||J||=1.738 005(50). For free (100) surfaces, we find a continuous surface transition at a temperature Tcs>~Tcb exhibiting critical exponents of the two-dimensional Ising model. Surface-induced ordering occurs as the temperature approaches Tcb and the surface excess order and surface excess energy diverges logarithmically. For a free (111) surface, the surface order vanishes continuously at Tcb accompanied by surface-induced disorder (SID). In addition to a logarithmic divergence of the excess quantities of order and energy, we find further critical exponents which confirm the actual theory of SID and critical wetting and which can be understood in terms of rough interfaces. For both cases of free surfaces, the asymptotic behavior of the squared interfacial width shows the expected logarithmic divergence.
CONSTRUCTION OF G2 CONTINUOUS CURVES ON SURFACE WITH PLANAR CUBIC B(E)ZIER CURVES
Institute of Scientific and Technical Information of China (English)
Wang Xiaoping; Zhang Weizhong; Zhang Liyan; Zhou Rurong
2005-01-01
The problem of constructing curve on parametric surface (or surface that can be parameterized) such that it interpolates a sequence of points with prescribed tangent direction and curvature vector (or geodesic curvature) at every point and the issue of curve blending on this kind of surface are researched. The mapping and tangent mapping from the surface to its parametric plane are introduced and thus several conclusions with differential geometry are deduced. Based on those conclusions, the problem of interpolating (or blending) curve on a parametric surface is converted to a similar one on its parametric plane. The final solution curve of either interpolation or blending issue is explicit and can still be expressed by parametric form. And so, unlike existing methods, the presented method needs not to use any surface/surface intersection algorithms, usually a troublesome process, for displaying such interpolation curve. Experiment results show the presented methods are feasible and applicable to CAD/CAM and computer graphics.
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.
DFT Study of the Electronic Structure of Cubic-SiC Nanopores with a C-Terminated Surface
Directory of Open Access Journals (Sweden)
M. Calvino
2014-01-01
Full Text Available A study of the dependence of the electronic structure and energetic stability on the chemical surface passivation of cubic porous silicon carbide (pSiC was performed using density functional theory (DFT and the supercell technique. The pores were modeled by removing atoms in the [001] direction to produce a surface chemistry composed of only carbon atoms (C-phase. Changes in the electronic states of the porous structures were studied by using different passivation schemes: one with hydrogen (H atoms and the others gradually replacing pairs of H atoms with oxygen (O atoms, fluorine (F atoms, and hydroxide (OH radicals. The results indicate that the band gap behavior of the C-phase pSiC depends on the number of passivation agents (other than H per supercell. The band gap decreased with an increasing number of F, O, or OH radical groups. Furthermore, the influence of the passivation of the pSiC on its surface relaxation and the differences in such parameters as bond lengths, bond angles, and cell volume are compared between all surfaces. The results indicate the possibility of nanostructure band gap engineering based on SiC via surface passivation agents.
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.
The formation energy for steps and kinks on cubic transition metal surfaces
DEFF Research Database (Denmark)
Vitos, Levente; Skriver, Hans Lomholt; Kollàr, Janos
1999-01-01
We have used our first-principles database of surface energies for metals in conjunction with the concept of vicinal surfaces to derive the energies of formation of monoatomic steps and corresponding kinks on close-packed surface facets of bcc and fee transition metals. The entries in the database...... allow for a direct calculation of the energies of a number of important steps. For the remaining steps and for all the kinks the energies of formation have been estimated from pair potential expansions of the entries in the database. (C) 1999 Elsevier Science B.V. All rights reserved....
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.
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...
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...
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.
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
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.
Yang, Kun; He, Yanqing; Cheng, Yi; Che, Li; Yao, Li
2017-03-01
First-principles density functional theory (DFT) calculations have been used to investigate the structural and electronic properties of the cubic KCaF3 and NaCaF3 (001) surfaces with MF (M = K or Na) and CaF2 terminations. For both KCaF3 and NaCaF3 (001) surfaces, the MF termination has stronger surface rumpling than the CaF2 termination. All the computed band gaps for the KCaF3 and NaCaF3 (001) surfaces are smaller than those of the bulks. Furthermore, separated bands that originate from surface layer F p states are introduced at the top of the valance band of MF-terminated surfaces, indicating the emergence of the surface states. The calculated surface energies show that the MF-terminated surface is energetically more favorable than the CaF2-terminated surface.
First-principles study of the (001) surface of cubic PbHfO3 and BaHfO3
Institute of Scientific and Technical Information of China (English)
Ni Guang-Xin; Wang Yuan-Xu
2009-01-01
Using first-principles techniques, we investigate the (001) surfaces of cubic PbHfO3 (PHO) and BaHfO3 (BHO) terminated with both AO (A=Pb and Ba) and HfO2- Surface structure, partial density of states, band structure, and surface energy are obtained. The BaO surface is found to be similar to its counterpart in BHO. For the HfO2-terminated surface of cubic PHO, the largest relaxation appears on the second-layer atoms but not on the first-layer ones. The analysis of the structure relaxation parameters reveals that the rumpling of the (001) surface for PHO is stronger than that for BHO. The surface thermodynamic stability is explored, and it is found that both the PbO- and the BaO-terminated surfaces are more stable than the HfO2-terminated surfaces for PHO and BHO, respectively. The surface energy calculations show that the (001) surface of PHO is more easily constructed than that of BHO.
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.”.
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.
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...
A free-form deformation method based on B-splines surface control%一种基于B-样条曲面控制的自由变形方法
Institute of Scientific and Technical Information of China (English)
林金花; 李万龙; 王璐; 李鑫
2011-01-01
With Doo-Sabin subdivision mode,a control grid for the interpolation vertex position and the bi-quadratic B-spline surface is constructed to obtain the parametric representation of the interpolation surface.The model points are attached to the interpolation surface to get the local coordinates which keep constant during the transformation.As the subdivision can deal with random topology grid,the multi-resolution deformation of the 3D model is realized by editing the B-spline control grid.%利用Doo-Sabin细分模式构造插值顶点位置和法向双二次B样条曲面控制网格,得到插值曲面的参数表示,再将模型上的点参数化到插值曲面上,得到该点的局部坐标。由于局部坐标在变形过程中保持不变,并且细分方法具有处理任意拓扑网格的能力,从而通过编辑模型的B-样条曲面控制网格,实现了三维模型的多分辨率变形。
Jørgensen, Mads R V; Skovsen, Iben; Clausen, Henrik F; Mi, Jian-Li; Christensen, Mogens; Nishibori, Eiji; Spackman, Mark A; Iversen, Bo B
2012-02-06
The Mn atom in the cubic polymorph of CeMnNi(4) appears to be located in an oversized cage-like structure, and anomalously large atomic displacement parameters (ADPs) for the Mn atom indicate that it is a potential "rattler" atom. Here, multitemperature synchrotron powder X-ray diffraction data measured between 110 and 900 K are used to estimate ADPs for the Mn "guest" atom and the "host" structure atoms in cubic CeMnNi(4). The ADPs are subsequently fitted with Debye and Einstein models, giving Θ(D) = 301(2) K for the "host" structure and Θ(E) = 165(2) K for the Mn atom. This is higher than typical Einstein temperatures for rattlers in thermoelectric skutterudites and clathrates (Θ(E) = 50-80 K), indicating that the Mn atom in cubic CeMnNi(4) is more strongly bonded. In order to probe the chemical interactions of the potential Mn rattler atom, atomic Hirshfeld surface (AHS) analysis is carried out and compared with AHS analysis of well-established guest atom rattlers in archetypical skutterudites, MCoSb(3). Surprisingly, the skutterudite rattlers have more deformed AHSs than the Mn atom in cubic CeMnNi(4). This is related to the highly ionic nature of the skutterudite rattlers, which is not taken into account in the neutral spherical atom approach of the AHS. Additionally, visualization of void spaces in the two materials using the procrystal electron density shows that while the Mn atom is tightly fitting in the CeMnNi(4) structure then the La atom in the skutterudite is truly situated in an oversized cage of the host structure. Overall, we conclude that the Mn atom in cubic CeMnNi(4) cannot be coined a rattler.
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.
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
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.
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.
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.
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.
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...
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
Bao, Luyao; Hu, Haibao; Wen, Jun; Sepri, Paavo; Luo, Kai
2016-07-19
A liquid in the vicinity of a solid-liquid interface (SLI) may exhibit complex structures. In this study, we used molecular dynamics simulations demonstrating for the first time that the liquid adjacent to the SLI can have a two-level structure in some cases: a major structure and a minor structure. Through a time-averaging process of molecular motions, we identified the type of the liquid structure by calculating positions of the maximum liquid density in three spatial dimensions, and these positions were found to distribute in many dispersed zones (called high-density zones (HDZs)). The major structure appears throughout the SLI, while the minor structure only occurs significantly within the third layer. Instead of the previously reported body-centered cubic (BCC) or face-centered-cubic (FCC) types, the major structure was found to show a body-centered tetragonal (BCT) type. The adjacent HDZs are connected by specific junctions, demonstrating that atoms diffuse along some particular high probability paths from one HDZ to another. By considering the three-dimensional liquid density distribution from the continuum point of view, more complete details of the structure and diffusive behavior of liquids in the SLI are also possible to be revealed.
Bao, Luyao; Hu, Haibao; Wen, Jun; Sepri, Paavo; Luo, Kai
2016-07-01
A liquid in the vicinity of a solid-liquid interface (SLI) may exhibit complex structures. In this study, we used molecular dynamics simulations demonstrating for the first time that the liquid adjacent to the SLI can have a two-level structure in some cases: a major structure and a minor structure. Through a time-averaging process of molecular motions, we identified the type of the liquid structure by calculating positions of the maximum liquid density in three spatial dimensions, and these positions were found to distribute in many dispersed zones (called high-density zones (HDZs)). The major structure appears throughout the SLI, while the minor structure only occurs significantly within the third layer. Instead of the previously reported body-centered cubic (BCC) or face-centered-cubic (FCC) types, the major structure was found to show a body-centered tetragonal (BCT) type. The adjacent HDZs are connected by specific junctions, demonstrating that atoms diffuse along some particular high probability paths from one HDZ to another. By considering the three-dimensional liquid density distribution from the continuum point of view, more complete details of the structure and diffusive behavior of liquids in the SLI are also possible to be revealed.
NUAH T-splines of Odd Bi-degree%双奇次NUAH T样条
Institute of Scientific and Technical Information of China (English)
段小娟; 汪国昭
2015-01-01
针对 T 样条无法精确表示双曲超越曲面的问题，构造了一种样条曲面——双奇次代数双曲 T 样条曲面(NUAH T样条)，探讨了其细分算法和调配函数的线性无关性。通过将非均匀代数双曲B样条曲面(NUAH B样条曲面)定义在T网上，给出了双奇次NUAH T样条的定义；基于NUAH B样条的节点插入公式，提出NUAH T样条的一种局部细分算法；并证明了NUAH T样条的调配函数线性无关的充要条件，即由NUAH T样条转化为NUAH B样条曲面的过渡矩阵是满秩矩阵。最后，通过实例验证了曲面构建和细分算法的有效性。%Since T-splines cannot represent hyperbolic spline surfaces exactly, this paper presents a kind of spline surfaces, called non-uniform algebraic hyperbolic T-spline surfaces (NUAH T-splines for short) of odd bi-degree. The NUAH T-splines are defined by applying the T-spline framework to the non-uniform al-gebraic hyperbolic B-spline surfaces (NUAH B-spline surfaces). Based on the knot insertion of NUAH B-splines, a local refinement algorithm for NUAH T-splines of odd bi-degree is shown. This paper proves that, for any NUAH T-spline of odd bi-degree, the linear independence of its blending functions can be de-termined by computing the rank of the NUAH T-spline-to-NUAH B-spline transformation matrix. Finally, the examples verify the effectiveness of the local refinement algorithm of NUAH T-splines.
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)
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.
On Knot Modifications of B-Spline or NURBS Surface%改变B样条曲面与NURBS曲面的节点
Institute of Scientific and Technical Information of China (English)
李亚娟; 汪国昭
2005-01-01
通过改变k×h阶B样条曲面和NURBS(Non-Uniform Rational B-spline)曲面的若干节点,分别产生一个B样条曲面族和NURBS曲面族,并指出:曲面族的包络是用相同控制顶点定义的(k-α)×(h-b)阶B样条曲面和NURBS曲面,其中α,b分别是两个方向上所改变的节点的重数.对于B样条曲面来说,曲面族与其包络的任意阶相同偏微分之间只相差一个因子,文中所得结果可以作为计算机辅助设计系统中曲面造型和形状修改的理论参考.
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.
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
Tang, T-Y Dora; Seddon, Annela M; Jeworrek, Christoph; Winter, Roland; Ces, Oscar; Seddon, John M; Templer, Richard H
2014-05-07
We have studied the effect of pressure and temperature on the location of the pivotal surface in a lipid inverse bicontinuous gyroid cubic phase (Q(G)(II)), described by the area at the pivotal surface (An), the volume between the pivotal surface and the bilayer midplane (Vn), and the molecular volume of the lipid (V). Small angle X-ray scattering (SAXS) was used to measure the swelling behaviour of the lipid, monolinolein, as a function of pressure and temperature, and the data were fitted to two different geometric models: the parallel interface model (PIM), and the constant mean curvature model (CMCM). The results show that an increase in temperature leads to a shift in the location of the pivotal surface towards the bilayer midplane, whilst an increase in pressure causes the pivotal surface to move towards the interfacial region. In addition, we describe the relevance of An, Vn and V for modeling the energetics of curved mesophases with specific reference to the mean curvature at the pivotal surface and discuss the significance of this parameter for modelling the energetics of curved mesophases.
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.
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.
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...
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...
Anisotropic surface melting in lyotropic cubic crystals. Part 1: Pn3m/L1 interface, poor faceting.
Grenier, J; Plötzing, T; Rohe, D; Pieranski, P
2006-02-01
From experiments with ice or metal crystals, in the vicinity of their crystal/liquid/vapor triple points, it is known that melting of crystals starts on their surfaces and is anisotropic. It is shown here by direct observations under an optical microscope that this anisotropic surface melting phenomenon occurs also in lyotropic systems. In the case of C12EO2/water mixture, it takes place in the vicinity of the peritectic Pn3m/L3/L1 triple point. Above the peritectic triple point, where the Pn3m and L1 phases coexist in the bulk, the surface of a Pn3m-in-L1 crystal is composed of (111)-type facets surrounded by rough surfaces. The angular junction suggests that rough surfaces are wet by a L3-like layer while facets stay "dry". This is analogous to the pre-melting at rough surfaces in solid crystals. Upon cooling below the peritectic triple point, where L3 and L1 phases coexist in the bulk, a thick layer of the L3 phase grows from the pre-melted, rough Pn3m/L1 interface. Simultaneously, facets stay dry and their radius decreases. In this tri-phasic configuration, stable in a narrow temperature range, the L3/L1 and L3/Pn3m interfaces have shapes of constant mean curvature surfaces having common borders: edges of facets.
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.
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.
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.
Posada-Pérez, Sergio; Viñes, Francesc; Valero, Rosendo; Rodriguez, José A.; Illas, Francesc
2017-02-01
Molybdenum carbides are increasingly used in heterogeneously catalyzed hydrogenation reactions, which imply the adsorption and dissociation of molecular hydrogen. Here a systematic density functional theory based study, including or excluding dispersion terms, concerning the interaction and stability of H2 with cubic δ-MoC(001) and orthorhombic β-Mo2C(001) surfaces, is presented. In the latter case the two possible C or Mo terminations are considered. In addition, different situations for the H covered surfaces are examined. Computational results including dispersive forces predict an essentially spontaneous dissociation of H2 on β-Mo2C(001) independently of the surface termination, whereas on δ-MoC(001) molecular hydrogen dissociation implies a small but noticeable energy barrier. Furthermore, the ab initio thermodynamics formalism has been used to compare the stability of different H coverages. Finally, core level binding energies and vibrational frequencies are presented with the aim to assist the interpretation of yet unavailable data from X-ray photoelectron and infrared spectroscopies.
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
双五次B-样条曲面的G2连续条件%G2 CONTINUOS CONDITIONS OF BIQUINTIC B-SPLINE SURFACES
Institute of Scientific and Technical Information of China (English)
赵岩; 施锡泉
2004-01-01
Some practical problems in designing the outline of hidden airplane require to construct high-order surfaces with at least second order continuity. The high-order smooth surfaces'construction has been always a difficuit problem in CAGD. In this paper, G2 smoothness between two biquintic surface patches is discussed, and the intrinsic conditions of the control vectors of the common boundary curve are presented.
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.
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.
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
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.
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.
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.
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.
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.
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.
MECHANICS ANALYSIS ON PRECISE FORMING PROCESS OF EXTERNAL SPLINE COLD ROLLING
Institute of Scientific and Technical Information of China (English)
ZHANG Dawei; LI Yongtang; FU Jianhua; ZHENG Quangang
2007-01-01
According to the suitable assumption, the deformation process of external spline cold rolling is analyzed. By the graphing method, the slip-line field of plastically deforming area in process of external spline cold rolling is set up. Different friction-conditions are used in different contact areas in order to realistically reflect the actual situation. The unit average pressure on contact surface of the rolling process is solved according to the stress filed theory of slip-line. And the formulae of the rolling-force and rolling-moment are established. The theoretical result is well consistent with the finite element analysis. A theoretical basis is provided for the precise forming process of spline cold rolling and the production of external splined shafts.
A B-spline method used to calculate added resistance in waves
Zangeneh, Razieh; Ghiasi, Mahmood
2017-01-01
Making an exact computation of added resistance in sea waves is of high interest due to the economic effects relating to ship design and operation. In this paper, a B-spline based method is developed for computation of added resistance. Based on the potential flow assumption, the velocity potential is computed using Green's formula. The Kochin function is applied to compute added resistance using Maruo's far-field method, the body surface is described by a B-spline curve and potentials and normal derivation of potentials are also described by B-spline basis functions and B-spline derivations. A collocation approach is applied for numerical computation, and integral equations are then evaluated by applying Gauss-Legendre quadrature. Computations are performed for a spheroid and different hull forms; results are validated by a comparison with experimental results. All results obtained with the present method show good agreement with experimental results.
Ng-Thow-Hing, Victor; Agur, Anne; Ball, Kevin A.; Fiume, Eugene; McKee, Nancy
1998-05-01
We introduce a mathematical primitive called the B-spline solid that can be used to create deformable models of muscle shape. B-spline solids can be used to model skeletal muscle for the purpose of building a data library of reusable, deformable muscles that are reconstructed from actual muscle data. Algorithms are provided for minimizing shape distortions that may be caused when fitting discrete sampled data to a continuous B-spline solid model. Visible Human image data provides a good indication of the perimeter of a muscle, but is not suitable for providing internal muscle fiber bundle arrangements which are important for physical simulation of muscle function. To obtain these fiber bundle orientations, we obtain 3-D muscle fiber bundle coordinates by triangulating optical images taken from three different camera views of serially dissected human soleus specimens. B-spline solids are represented as mathematical three-dimensional vector functions which can parameterize an enclosed volume as well as its boundary surface. They are based on B-spline basis functions, allowing local deformations via adjustable control points and smooth continuity of shape. After the B-spline solid muscle model is fitted with its external surface and internal volume arrangements, we can subsequently deform its shape to allow simulation of animated muscle tissue.
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.
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.
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.
Removal of Baseline Wander Noise from Electrocardiogram (ECG using Fifth-order Spline Interpolation
Directory of Open Access Journals (Sweden)
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.
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.
Cubic III-nitrides: potential photonic materials
Onabe, K.; Sanorpim, S.; Kato, H.; Kakuda, M.; Nakamura, T.; Nakamura, K.; Kuboya, S.; Katayama, R.
2011-01-01
The growth and characterization of some cubic III-nitride films on suitable cubic substrates have been done, namely, c- GaN on GaAs by MOVPE, c-GaN and c-AlGaN on MgO by RF-MBE, and c-InN and c-InGaN (In-rich) on YSZ by RFMBE. This series of study has been much focused on the cubic-phase purity as dependent on the respective growth conditions and resulting electrical and optical properties. For c-GaN and c-InN films, a cubic-phase purity higher than 95% is attained in spite of the metastable nature of the cubic III-nitrides. However, for c-AlGaN and c-InGaN films, the cubic-phase purity is rapidly degraded with significant incorporation of the hexagonal phase through stacking faults on cubic {111} faces which may be exposed on the roughened growing or substrate surface. It has been shown that the electron mobilities in c-GaN and c-AlGaN films are much related to phase purity.
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).
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
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.
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.
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.
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.
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.
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.
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
Institute of Scientific and Technical Information of China (English)
K.Iqbal; A.Basit
2011-01-01
@@ The presence of oxygen in the subsurface in monomer-dimer reactions(CO-O2 and NO-CO)is observed experimentally.The effect of subsurface oxygen on a CO-O2 catalytic reaction on a face-centered cubic(FCC)lattice is studied using Monte Carlo simulation.The effect of adding subsurface neighbours on the phase diagram is also extensively explored.It is observed that the subsurface oxygen totally eliminates the typical second order phase transition.It is also shown that the introduction of the diffusion of O atoms and the subsurface of the FCC lattice shifts the single transition point towards the stoichiometric ratio.%The presence of oxygen in the subsurface in monomer-dimer reactions (CO-O2 and NO-CO) is observed experimentally. The effect of subsurface oxygen on a CO-O2 catalytic reaction on a face-centered cubic (FCC) lattice is studied using Monte Carlo simulation. The effect of adding subsurface neighbours on the phase diagram is also extensively explored. It is observed that the subsurface oxygen totally eliminates the typical second order phase transition. It is also shown that the introduction of the diffusion of O atoms and the subsurface of the FCC lattice shifts the single transition point towards the stoichiometric ratio.
Low pressure growth of cubic boron nitride films
Ong, Tiong P. (Inventor); Shing, Yuh-Han (Inventor)
1997-01-01
A method for forming thin films of cubic boron nitride on substrates at low pressures and temperatures. A substrate is first coated with polycrystalline diamond to provide a uniform surface upon which cubic boron nitride can be deposited by chemical vapor deposition. The cubic boron nitride film is useful as a substitute for diamond coatings for a variety of applications in which diamond is not suitable. any tetragonal or hexagonal boron nitride. The cubic boron nitride produced in accordance with the preceding example is particularly well-suited for use as a coating for ultra hard tool bits and abrasives, especially those intended to use in cutting or otherwise fabricating iron.
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.
Institute of Scientific and Technical Information of China (English)
毛林繁; 刘彦佩
2001-01-01
Since Tutte disproved that every simple 3-polytope is hamiltonian in 1946,various techniques have been presented for constructing 3-connected non-hamiltonian cubic planar maps.However,none can be used for finding one on surfaces with genus ≥ 1.In this paper,a new approach is established,which can be used for constructing infinite 3-connected non-hamiltonian cubic maps on every surface.%Tutte在1946年构造性证明了并非每个简单的3-凸胞腔都是Hamiltonian的后,人们又陆续提出了多种构造三次3-连通非Hamiltonian平面图的方法,但无一能用于在一般曲面上寻找三次3-连通非Hamiltonian地图.本文提出了一种新的构造方法,可在任一个曲面上构造出三次3-连通非Hamiltonian地图.
基于小波的B样条曲线多分辨表示及编辑%Wavelets-Based Multiresolution Representation and Edit of B-Spline Curves
Institute of Scientific and Technical Information of China (English)
赵罡; 朱心雄
2001-01-01
Multiresolution representation provides a more flexible approach to edit curves and surfaces in different resolution levels. The paper describes, from the viewpoint of geometry, the principles and methods of realizing wavelets-based multiresolution representation of quasi-uniform cubic B-spline curves. An example is given to illustrate the editing of B-spline curves in multiresolution level.%多分辨表示方法为曲线提供了更为灵活的表达方式，使得我们可以在不同分辨率下对曲线进行编辑.小波技术是实现曲线多分辨表示的一种新颖方法，已有许多论文从理论上论述了这项技术.文中从几何概念出发,由浅入深地论述了基于小波的准均匀三次B样条曲线多分辨表示的原理及其实现，并通过实例描述了B样条曲线的多分辨编辑.
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...
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 \
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
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
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.
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.
A Fast Variational Method for the Construction of Resolution Adaptive C-Smooth Molecular Surfaces.
Bajaj, Chandrajit L; Xu, Guoliang; Zhang, Qin
2009-05-01
We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleic-acid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic-acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo- atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C(2) interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C(2) smooth and resolution adaptive molecular surfaces.
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.
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)
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.
Multivariate Adaptive Regression Splines (Preprint)
1990-08-01
characteristics of olive oils as a function of production year by multivariate methods. La Revista Italiana delle Sostanze Grasse, 60, Oct. . Friedman, J...Projection pursuit 76, 817-823. Friedman, J. H. and Wright, M. J. (1981). A nested partitioni: integration. ACM Trans. Math. Software, March. simonious...data. Proc. 1964 ACM Nat. Conf., 517-524. Shumaker, L. L. (1976). Fitting surfaces to scattered data. In Approximation Theory III, G. G. Lorentz, C
Face-Centered-Cubic Nanostructured Polymer Foams
Cui, C.; Baughman, R. H.; Liu, L. M.; Zakhidov, A. A.; Khayrullin, I. I.
1998-03-01
Beautifully iridescent polymer foams having Fm-3m cubic symmetry and periodicities on the scale of the wavelength of light have been synthesized by the templating of porous synthetic opals. These fabrication processes involve the filling of porous SiO2 opals (with typical cubic lattice parameters of 250 nm) with either polymers or polymer precursors, polymerization of the precursors if necessary, and removal of the fcc array of SiO2 balls to provide an all-polymer structure. The structures of these foams are similar to periodic minimal surfaces, although the Gaussian curvature can have both positive and negative values. Depending upon whether the internal surfaces of the opal are polymer filled or polymer coated, the polymer replica has either one or two sets of independent channels. We fill these channels with semiconductors, metals, or superconductors to provide electronic and optical materials with novel properties dependent on the nanoscale periodicity.
Harmening, Corinna; Neuner, Hans
2016-09-01
Due to the establishment of terrestrial laser scanner, the analysis strategies in engineering geodesy change from pointwise approaches to areal ones. These areal analysis strategies are commonly built on the modelling of the acquired point clouds. Freeform curves and surfaces like B-spline curves/surfaces are one possible approach to obtain space continuous information. A variety of parameters determines the B-spline's appearance; the B-spline's complexity is mostly determined by the number of control points. Usually, this number of control points is chosen quite arbitrarily by intuitive trial-and-error-procedures. In this paper, the Akaike Information Criterion and the Bayesian Information Criterion are investigated with regard to a justified and reproducible choice of the optimal number of control points of B-spline curves. Additionally, we develop a method which is based on the structural risk minimization of the statistical learning theory. Unlike the Akaike and the Bayesian Information Criteria this method doesn't use the number of parameters as complexity measure of the approximating functions but their Vapnik-Chervonenkis-dimension. Furthermore, it is also valid for non-linear models. Thus, the three methods differ in their target function to be minimized and consequently in their definition of optimality. The present paper will be continued by a second paper dealing with the choice of the optimal number of control points of B-spline surfaces.
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.
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.
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.
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
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.
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.
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.
Institute of Scientific and Technical Information of China (English)
秦开怀; 范刚; 等
1994-01-01
The new algorithms for finding B-Spline or Bezier curves and surfaces intersections using recursive subdivision techniques are presented,which use extrapolating acceleration technique,and have convergent precision of order 2.Matrix method is used to subdivide the curves or surfaces which makes the subdivision more concise and intuitive.Dividing depths of Bezier curves and surfaces are used to subdivide the curves or surfaces adaptively.Therefore the convergent precision and the computing efficiency of finding the intersections of curves and surfaces have been improved by the methods proposed in the paper.
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...
Aref'eva, L. P.; Shebzukhova, I. G.
2016-07-01
A technique for the evaluation of the electron work function of metallic single crystals and the electron work function anisotropy has been developed in the framework of the electron-statistical method. The surface energy and the electron work function have been calculated for crystal faces of allotropic modifications of 4 d- and 5 d-metals. A change in the electron work function due to the allotropic transformations has been estimated, and the periodic dependence of the electron work function has been determined. It has been shown that the results obtained using the proposed technique correlate with the available experimental data for polycrystals.
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.
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.
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...
Geometry Modeling of Ship Hull Based on Non-uniform B-spline
Institute of Scientific and Technical Information of China (English)
WANG Hu; ZOU Zao-jian
2008-01-01
In order to generate the three-dimensional (3-D) hull surface accurately and smoothly, a mixed method which is made up of non-uniform B-spline together with an iterative procedure was developed. By using the iterative method the data points on each section curve are calculated and the generalized waterlines and transverse section curves are determined. Then using the non-uniform B-spline expression, the control vertex net of the hull is calculated based on the generalized waterlines and section curves. A ship with tunnel stern was taken as test case. The numerical results prove that the proposed approach for geometry modeling of 3-D ship hull surface is accurate and effective.
Institute of Scientific and Technical Information of China (English)
丁撼; 阿达依·谢尔亚孜旦
2015-01-01
Distinguished from the approximate spherical involute tooth profile has been in a dominant position in the research field of spiral bevel gear, and whose design and processing were based on the local conjugate theory, discussing some research outcomes on recent relevant spherical involute, a theory of forming the spherical involute tooth surface was improved, and key part namely the generating line and its equation were detailed by derived. In addition, fast and accurate solutions of the boundary curves and the tooth profile curve families were done by taking advantage of forming principle of spherical involute tooth surface, and based on advantages of modeling techniques of the cubic NURBS curve and surface in CAD/CAM, spherical involute tooth surface precision fitting was completed. At last, related optimization program associated with constructed NURBS tooth surface in the use of the Skinning method was proposed, and the parameterization of tooth surface data and precise fitting surfaces were accomplished, so as to further improve the accuracy of the tooth surface and provide tooth contact analysis for the data of the tooth surfaces and the basic model.%区别于螺旋锥齿轮研究领域一直占据主导地位的局部共轭原理及其所设计和加工出来的近似球面渐开线齿形，基于近些年相关球面渐开线的研究成果的探讨，改进球面渐开线齿面形成理论，并对关键的产形线方程做推导。另外，利用球面渐开线齿面形成理论快速精确地求解边界曲线和齿廓曲线族，并结合三次NURBS曲线曲面造型技术的在CAD/CAM中的优势完成球面渐开线齿面的精确拟合。最后，在利用蒙皮法构造的NURBS齿面基础上提出相关优化方案，完成齿面数据的参数化和曲面的精确拟合，以进一步提高齿面精度，并为齿面接触分析提供齿面数据和基础模型。
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.
Quantitative surface evaluation by matching experimental and simulated ronchigram images
Kantún Montiel, Juana Rosaura; Cordero Dávila, Alberto; González García, Jorge
2011-09-01
To estimate qualitatively the surface errors with Ronchi test, the experimental and simulated ronchigrams are compared. Recently surface errors have been obtained quantitatively matching the intersection point coordinates of ronchigrama fringes with x-axis . In this case, gaussian fit must be done for each fringe, and interference orders are used in Malacara algorithm for the simulations. In order to evaluate surface errors, we added an error function in simulations, described with cubic splines, to the sagitta function of the ideal surface. We used the vectorial transversal aberration formula and a ruling with cosinusoidal transmittance, because these rulings reproduce better experimental ronchigram fringe profiles. Several error functions are tried until the whole experimental ronchigrama image is reproduced. The optimization process was done using genetic algorithms.
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.
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.
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.
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.
Converting an Unstructured Quadrilateral/Hexahedral Mesh to a Rational T-spline
2011-08-01
For the sake of integration of engineering design and analy- sis, isogeometric analysis was proposed [4, 1] which utilizes NURBS (Non-Uniform Rational B...results, and Section 7 draws conclusions. 2 Rational T-spline T-splines [13] are generalized from NURBS [8], the prevail- ing industrial standard for...and v= [v0,v1, · · · ,vn+d ,vn+d+1], the NURBS surface is defined as SN(u,v) = m ∑ i=0 n ∑ j=0 Ci jwi jNi,d(u)N j,d(v) m ∑ i=0 n ∑ j=0 wi jNi,d(u)N j,d
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
Study on signal processing in Eddy current testing for defects in spline gear
Energy Technology Data Exchange (ETDEWEB)
Lee, Jae Ho; Park, Tae Sug; Park, Ik Keun [Seoul National University of Science and Technology, Seou (Korea, Republic of)
2016-06-15
Eddy current testing (ECT) is commonly applied for the inspection of automated production lines of metallic products, because it has a high inspection speed and a reasonable price. When ECT is applied for the inspection of a metallic object having an uneven target surface, such as the spline gear of a spline shaft, it is difficult to distinguish between the original signal obtained from the sensor and the signal generated by a defect because of the relatively large surface signals having similar frequency distributions. To facilitate the detection of defect signals from the spline gear, implementation of high-order filters is essential, so that the fault signals can be distinguished from the surrounding noise signals, and simultaneously, the pass-band of the filter can be adjusted according to the status of each production line and the object to be inspected. We will examine the infinite impulse filters (IIR filters) available for implementing an advanced filter for ECT, and attempt to detect the flaw signals through optimization of system design parameters for detecting the signals at the system level.
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.
Cubication of Conservative Nonlinear Oscillators
Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…
Cryptographic Analysis in Cubic Time
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Seidl, H.
2004-01-01
The spi-calculus is a variant of the polyadic pi-calculus that admits symmetric cryptography and that admits expressing communication protocols in a precise though still abstract way. This paper shows that context-independent control flow analysis can be calculated in cubic time despite the fact ...
The diagonalization of cubic matrices
Cocolicchio, D.; Viggiano, M.
2000-08-01
This paper is devoted to analysing the problem of the diagonalization of cubic matrices. We extend the familiar algebraic approach which is based on the Cardano formulae. We rewrite the complex roots of the associated resolvent secular equation in terms of transcendental functions and we derive the diagonalizing matrix.
CAD-DIRECTED INSPECTION PLANNING FOR FREEFORM SURFACE USING CONTACT PROBES
Institute of Scientific and Technical Information of China (English)
Chen Manyi; Li Bin; Duan Zhengcheng
2005-01-01
A methodology for CAD-directed measurement of freeform surface using a coordinate measuring machine equipped with a touch-trigger probe is presented, mainly including adaptive sampling of measurement points and registration of freeform surface. The proposed sampling method follows four steps:Freeform surface is fitted by bi-cubic B-spline; Curvedness measure of the surface is computed; Given a number of sampling points, an iterative algorithm is constructed for selecting a set of measurement points by employing the curvedness information; The measurement points is regularized for tradeoffbetween maximizing the measurement accuracy and minimizing the sampling time and cost. The aforesaid algorithm is demonstrated in term of a marine propeller blade. An offset surface registration method is presented to improve alignment accuracy of freeform objects, and Monte Carlo simulation is conducted to verify the effectiveness of the method.
THE STRUCTURAL CHARACTERIZATION AND LOCALLY SUPPORTED BASES FOR BIVARIATE SUPER SPLINES
Institute of Scientific and Technical Information of China (English)
Zhi-qiang Xu; Ren-hong Wang
2004-01-01
Super splines are bivariate splines defined on triangulations, where the smoothness enforced at the vertices is larger than the smoothness enforced across the edges. In this paper, the smoothness conditions and conformality conditions for super splines are presented.Three locally supported super splines on type-1 triangulation are presented. Moreover, the criteria to select local bases is also given. By using local supported super spline function, avariation-diminishing operator is built. The approximation properties of the operator are also presented.
Spatially variant convolution with scaled B-splines.
Muñoz-Barrutia, Arrate; Artaechevarria, Xabier; Ortiz-de-Solorzano, Carlos
2010-01-01
We present an efficient algorithm to compute multidimensional spatially variant convolutions--or inner products--between N-dimensional signals and B-splines--or their derivatives--of any order and arbitrary sizes. The multidimensional B-splines are computed as tensor products of 1-D B-splines, and the input signal is expressed in a B-spline basis. The convolution is then computed by using an adequate combination of integration and scaled finite differences as to have, for moderate and large scale values, a computational complexity that does not depend on the scaling factor. To show in practice the benefit of using our spatially variant convolution approach, we present an adaptive noise filter that adjusts the kernel size to the local image characteristics and a high sensitivity local ridge detector.
Many-knot spline technique for approximation of data
Institute of Scientific and Technical Information of China (English)
齐东旭; 李华山
1999-01-01
A class of new fundamental functions with compact support called many-knot spline is introduced. The two-scale relation for the fundamental functions is investigated, and the higher order accuracy spline approximation scheme is constructed by using the available degrees of freedom which come from additional knots. The technique has been efficiently applied to the problems such as time-frequency analysis, computer aided geometric design, and digital signal processing.
Spline-based high-accuracy piecewise-polynomial phase-to-sinusoid amplitude converters.
Petrinović, Davor; Brezović, Marko
2011-04-01
We propose a method for direct digital frequency synthesis (DDS) using a cubic spline piecewise-polynomial model for a phase-to-sinusoid amplitude converter (PSAC). This method offers maximum smoothness of the output signal. Closed-form expressions for the cubic polynomial coefficients are derived in the spectral domain and the performance analysis of the model is given in the time and frequency domains. We derive the closed-form performance bounds of such DDS using conventional metrics: rms and maximum absolute errors (MAE) and maximum spurious free dynamic range (SFDR) measured in the discrete time domain. The main advantages of the proposed PSAC are its simplicity, analytical tractability, and inherent numerical stability for high table resolutions. Detailed guidelines for a fixed-point implementation are given, based on the algebraic analysis of all quantization effects. The results are verified on 81 PSAC configurations with the output resolutions from 5 to 41 bits by using a bit-exact simulation. The VHDL implementation of a high-accuracy DDS based on the proposed PSAC with 28-bit input phase word and 32-bit output value achieves SFDR of its digital output signal between 180 and 207 dB, with a signal-to-noise ratio of 192 dB. Its implementation requires only one 18 kB block RAM and three 18-bit embedded multipliers in a typical field-programmable gate array (FPGA) device.
Motion characteristic between die and workpiece in spline rolling process with round dies
Directory of Open Access Journals (Sweden)
Da-Wei Zhang
2016-06-01
Full Text Available In the spline rolling process with round dies, additional kinematic compensation is an essential mechanism for improving the division of teeth and pitch accuracy as well as surface quality. The motion characteristic between the die and workpiece under varied center distance in the spline rolling process was investigated. Mathematical models of the instantaneous center of rotation, transmission ratio, and centrodes in the rolling process were established. The models were used to analyze the rolling process of the involute spline with circular dedendum, and the results indicated that (1 with the reduction in the center distance, the instantaneous center moves toward workpiece, and the transmission ratio increases at first and then decreases; (2 the variations in the instantaneous center and transmission ratio are discontinuous, presenting an interruption when the involute flank begins to be formed; (3 the change in transmission ratio at the forming stage of the workpiece with the involute flank can be negligible; and (4 the centrode of the workpiece is an Archimedes line whose polar radius reduces, and the centrode of the rolling die is similar to Archimedes line when the workpiece is with the involute flank.
Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method
Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.
1997-01-01
A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.
Cubication of conservative nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Alvarez, Mariela L [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, Elena; Pascual, Inmaculada [Departamento de Optica, FarmacologIa y Anatomia, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2009-09-15
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Cubic Matrix, Nambu Mechanics and Beyond
Kawamura, Y
2002-01-01
We propose a generalization of cubic matrix mechanics by introducing a canonical triplet and study its relation to Nambu mechanics. The generalized cubic matrix mechanics we consider can be interpreted as a “quantum” generalization of Nambu mechanics.
Cubical sets and the topological topos
DEFF Research Database (Denmark)
Spitters, Bas
2016-01-01
Coquand's cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. This paper contributes to the understanding of this model. We make three contributions...... show that it can also be a target for cubical realization by showing that Coquand's cubical sets classify the geometric theory of flat distributive lattices. As a side result, we obtain a simplicial realization of a cubical set. 2. Using the internal `interval' in the topos of cubical sets, we...... construct a Moore path model of identity types. 3. We construct a premodel structure internally in the cubical type theory and hence on the fibrant objects in cubical sets....
Numbers for reducible cubic scrolls
Directory of Open Access Journals (Sweden)
Israel Vainsencher
2004-12-01
Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.
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).
Growth curve analysis for plasma profiles using smoothing splines
Energy Technology Data Exchange (ETDEWEB)
Imre, K.
1993-05-01
We are developing a profile analysis code for the statistical estimation of the parametric dependencies of the temperature and density profiles in tokamaks. Our code uses advanced statistical techniques to determine the optimal fit, i.e. the fit which minimized the predictive error. For a forty TFTR Ohmic profile dataset, our preliminary results indicate that the profile shape depends almost exclusively on q[sub a][prime] but that the shape dependencies are not Gaussian. We are now comparing various shape models on the TFTR data. In the first six months, we have completed the core modules of the code, including a B-spline package for variable knot locations, a data-based method to determine the optimal smoothing parameters, self-consistent estimation of the bias errors, and adaptive fitting near the plasma edge. Visualization graphics already include three dimensional surface plots, and discharge by discharge plots of the predicted curves with error bars together with the actual measurements values, and plots of the basis functions with errors.
A Novel Digital Predistortion Algorithm Based on Quadratic Spline%基于二次样条函数的功放数字预失真算法
Institute of Scientific and Technical Information of China (English)
刘学
2015-01-01
功放的非线性特性极易产生频谱扩展,这种扩展会对临近信道产生干扰.现在基于样条的预失真算法几乎都使用的三次样条,也就是样条的多项式函数阶数最多只有三次.文章提出了一种新的基于二次样条的功放数字预失真算法.二次样条函数的平滑特性可以很好地逼近功放的非线性模型,有效克服功放非线性效应对频谱产生的影响.仿真和实现的结果表明,这种新的算法性能既优于传统的基于最小均方的数字预失真算法,也优于现在一般的三次样条预失真算法.%The nonlinear effect of power amplifier creates spectral growth (broadening) beyond the signal bandwidth, which interferes with adjacent channels. Most of current spline based predistortion algorithms use cubic spline. A predistortion al-gorithm based on quadratic spline is presented, which can well approximate the nonlinear character of power amplifier and effectively remove the nonlinear effect. The simulation result verifies that the performance of the method introduced in this paper is not only better than that of the traditional algorithm based on Least Mean Square but also better than that based on the cubic spline.
2013-04-01
surfaces consisting of Bezier curves and Nonuniform Rational B-spline Surfaces ( NURBS ). There are many times however, when both modeling approaches...have allowed the integration of free-form objects in CSG systems. This presentation will discuss the development and integration of NURBS into the...Ballistics Research Laboratory CSG modeling system. 15. SUBJECT TERMS NURBS , BSpline, raytracing, CSG, BRL-CAD 16. SECURITY CLASSIFICATION OF: 17
Cubic colloids : Synthesis, functionalization and applications
Castillo, S.I.R.
2015-01-01
This thesis is a study on cubic colloids: micron-sized cubic particles with rounded corners (cubic superballs). Owing to their shape, particle packing for cubes is more efficient than for spheres and results in fascinating phase and packing behavior. For our cubes, the particle volume fraction when
Cubic colloids : Synthesis, functionalization and applications
Castillo, S.I.R.
2015-01-01
This thesis is a study on cubic colloids: micron-sized cubic particles with rounded corners (cubic superballs). Owing to their shape, particle packing for cubes is more efficient than for spheres and results in fascinating phase and packing behavior. For our cubes, the particle volume fraction when
Solving Cubic Equations by Polynomial Decomposition
Kulkarni, Raghavendra G.
2011-01-01
Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…
Cubic Icosahedra? A Problem in Assigning Symmetry
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
He, Shixuan; Xie, Wanyi; Zhang, Wei; Zhang, Liqun; Wang, Yunxia; Liu, Xiaoling; Liu, Yulong; Du, Chunlei
2015-02-25
A novel strategy which combines iteratively cubic spline fitting baseline correction method with discriminant partial least squares qualitative analysis is employed to analyze the surface enhanced Raman scattering (SERS) spectroscopy of banned food additives, such as Sudan I dye and Rhodamine B in food, Malachite green residues in aquaculture fish. Multivariate qualitative analysis methods, using the combination of spectra preprocessing iteratively cubic spline fitting (ICSF) baseline correction with principal component analysis (PCA) and discriminant partial least squares (DPLS) classification respectively, are applied to investigate the effectiveness of SERS spectroscopy for predicting the class assignments of unknown banned food additives. PCA cannot be used to predict the class assignments of unknown samples. However, the DPLS classification can discriminate the class assignment of unknown banned additives using the information of differences in relative intensities. The results demonstrate that SERS spectroscopy combined with ICSF baseline correction method and exploratory analysis methodology DPLS classification can be potentially used for distinguishing the banned food additives in field of food safety.
He, Shixuan; Xie, Wanyi; Zhang, Wei; Zhang, Liqun; Wang, Yunxia; Liu, Xiaoling; Liu, Yulong; Du, Chunlei
2015-02-01
A novel strategy which combines iteratively cubic spline fitting baseline correction method with discriminant partial least squares qualitative analysis is employed to analyze the surface enhanced Raman scattering (SERS) spectroscopy of banned food additives, such as Sudan I dye and Rhodamine B in food, Malachite green residues in aquaculture fish. Multivariate qualitative analysis methods, using the combination of spectra preprocessing iteratively cubic spline fitting (ICSF) baseline correction with principal component analysis (PCA) and discriminant partial least squares (DPLS) classification respectively, are applied to investigate the effectiveness of SERS spectroscopy for predicting the class assignments of unknown banned food additives. PCA cannot be used to predict the class assignments of unknown samples. However, the DPLS classification can discriminate the class assignment of unknown banned additives using the information of differences in relative intensities. The results demonstrate that SERS spectroscopy combined with ICSF baseline correction method and exploratory analysis methodology DPLS classification can be potentially used for distinguishing the banned food additives in field of food safety.
Cubic metaplectic forms and theta functions
Proskurin, Nikolai
1998-01-01
The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.
Defining window-boundaries for genomic analyses using smoothing spline techniques.
Beissinger, Timothy M; Rosa, Guilherme J M; Kaeppler, Shawn M; Gianola, Daniel; de Leon, Natalia
2015-04-17
High-density genomic data is often analyzed by combining information over windows of adjacent markers. Interpretation of data grouped in windows versus at individual locations may increase statistical power, simplify computation, reduce sampling noise, and reduce the total number of tests performed. However, use of adjacent marker information can result in over- or under-smoothing, undesirable window boundary specifications, or highly correlated test statistics. We introduce a method for defining windows based on statistically guided breakpoints in the data, as a foundation for the analysis of multiple adjacent data points. This method involves first fitting a cubic smoothing spline to the data and then identifying the inflection points of the fitted spline, which serve as the boundaries of adjacent windows. This technique does not require prior knowledge of linkage disequilibrium, and therefore can be applied to data collected from individual or pooled sequencing experiments. Moreover, in contrast to existing methods, an arbitrary choice of window size is not necessary, since these are determined empirically and allowed to vary along the genome. Simulations applying this method were performed to identify selection signatures from pooled sequencing FST data, for which allele frequencies were estimated from a pool of individuals. The relative ratio of true to false positives was twice that generated by existing techniques. A comparison of the approach to a previous study that involved pooled sequencing FST data from maize suggested that outlying windows were more clearly separated from their neighbors than when using a standard sliding window approach. We have developed a novel technique to identify window boundaries for subsequent analysis protocols. When applied to selection studies based on F ST data, this method provides a high discovery rate and minimizes false positives. The method is implemented in the R package GenWin, which is publicly available from CRAN.
Cubic meter volume optical coherence tomography
WANG, ZHAO; POTSAID, BENJAMIN; CHEN, LONG; DOERR, CHRIS; LEE, HSIANG-CHIEH; NIELSON, TORBEN; JAYARAMAN, VIJAYSEKHAR; CABLE, ALEX E.; SWANSON, ERIC; FUJIMOTO, JAMES G.
2017-01-01
Optical coherence tomography (OCT) is a powerful three-dimensional (3D) imaging modality with micrometer-scale axial resolution and up to multi-GigaVoxel/s imaging speed. However, the imaging range of high-speed OCT has been limited. Here, we report 3D OCT over cubic meter volumes using a long coherence length, 1310 nm vertical-cavity surface-emitting laser and silicon photonic integrated circuit dual-quadrature receiver technology combined with enhanced signal processing. We achieved 15 µm depth resolution for tomographic imaging at a 100 kHz axial scan rate over a 1.5 m range. We show 3D macroscopic imaging examples of a human mannequin, bicycle, machine shop gauge blocks, and a human skull/brain model. High-bandwidth, meter-range OCT demonstrates new capabilities that promise to enable a wide range of biomedical, scientific, industrial, and research applications. PMID:28239628
Free-Form Deformation with Rational DMS-Spline Volumes
Institute of Scientific and Technical Information of China (English)
Gang Xu; Guo-Zhao Wang; Xiao-Diao Chen
2008-01-01
In this paper, we propose a novel free-form deformation (FFD) technique, RDMS-FFD (Rational DMS-FFD),based on rational DMS-spline volumes. RDMS-FFD inherits some good properties of rational DMS-spline volumes and combines more deformation techniques than previous FFD methods in a consistent framework, such as local deformation,control lattice of arbitrary topology, smooth deformation, multiresolution deformation and direct manipulation of deforma-tion. We first introduce the rational DMS-spline volume by directly generalizing the previous results related to DMS-splies.How to generate a tetrahedral domain that approximates the shape of the object to be deformed is also introduced in this paper. Unlike the traditional FFD techniques, we manipulate the vertices of the tetrahedral domain to achieve deformation results. Our system demonstrates that RDMS-FFD is powerful and intuitive in geometric modeling.
Fast space-variant elliptical filtering using box splines
Chaudhury, Kunal Narayan; Unser, Michael
2010-01-01
The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based on a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using pre-integration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by ...
Fingerprint Representation Methods Based on B-Spline Functions
Institute of Scientific and Technical Information of China (English)
Ruan Ke; Xia De-lin; Yan Pu-liu
2004-01-01
The global characteristics of a fingerprint image such as the ridge shape and ridge topology are often ignored in most automatic fingerprint verification system. In this paper, a new representative method based on B-Spline curve is proposed to address this problem. The resultant B-Spline curves can represent the global characteristics completely and the curves are analyzable and precise. An algorithm is also proposed to extract the curves from the fingerprint image. In addition to preserve the most information of the fingerprint image, the knot-points number of the B-Spline curve is reduced to minimum in this algorithm. At the same time, the influence of the fingerprint image noise is discussed. In the end, an example is given to demonstrate the effectiveness of the representation method.
Transparent polycrystalline cubic silicon nitride
Nishiyama, Norimasa; Ishikawa, Ryo; Ohfuji, Hiroaki; Marquardt, Hauke; Kurnosov, Alexander; Taniguchi, Takashi; Kim, Byung-Nam; Yoshida, Hidehiro; Masuno, Atsunobu; Bednarcik, Jozef; Kulik, Eleonora; Ikuhara, Yuichi; Wakai, Fumihiro; Irifune, Tetsuo
2017-01-01
Glasses and single crystals have traditionally been used as optical windows. Recently, there has been a high demand for harder and tougher optical windows that are able to endure severe conditions. Transparent polycrystalline ceramics can fulfill this demand because of their superior mechanical properties. It is known that polycrystalline ceramics with a spinel structure in compositions of MgAl2O4 and aluminum oxynitride (γ-AlON) show high optical transparency. Here we report the synthesis of the hardest transparent spinel ceramic, i.e. polycrystalline cubic silicon nitride (c-Si3N4). This material shows an intrinsic optical transparency over a wide range of wavelengths below its band-gap energy (258 nm) and is categorized as one of the third hardest materials next to diamond and cubic boron nitride (cBN). Since the high temperature metastability of c-Si3N4 in air is superior to those of diamond and cBN, the transparent c-Si3N4 ceramic can potentially be used as a window under extremely severe conditions. PMID:28303948
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we study the local asymptotic behavior of the regression spline estimator in the framework of marginal semiparametric model. Similarly to Zhu, Fung and He (2008), we give explicit expression for the asymptotic bias of regression spline estimator for nonparametric function f. Our results also show that the asymptotic bias of the regression spline estimator does not depend on the working covariance matrix, which distinguishes the regression splines from the smoothing splines and the seemingly unrelated kernel. To understand the local bias result of the regression spline estimator, we show that the regression spline estimator can be obtained iteratively by applying the standard weighted least squares regression spline estimator to pseudo-observations. At each iteration, the bias of the estimator is unchanged and only the variance is updated.
AnL1 smoothing spline algorithm with cross validation
Bosworth, Ken W.; Lall, Upmanu
1993-08-01
We propose an algorithm for the computation ofL1 (LAD) smoothing splines in the spacesWM(D), with . We assume one is given data of the formyiD(f(ti) +ɛi, iD1,...,N with {itti}iD1N ⊂D, theɛi are errors withE(ɛi)D0, andf is assumed to be inWM. The LAD smoothing spline, for fixed smoothing parameterλ?;0, is defined as the solution,sλ, of the optimization problem (1/N)∑iD1N yi-g(ti +λJM(g), whereJM(g) is the seminorm consisting of the sum of the squaredL2 norms of theMth partial derivatives ofg. Such an LAD smoothing spline,sλ, would be expected to give robust smoothed estimates off in situations where theɛi are from a distribution with heavy tails. The solution to such a problem is a "thin plate spline" of known form. An algorithm for computingsλ is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The "data driven" selection of the smoothing parameter is achieved by minimizing aCV(λ) score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in λ↘0 taken on the above SQPs parametrized inλ, with the optimal smoothing parameter taken to be that value ofλ at which theCV(λ) score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.
APPLICATIONS OF SURFACE SPLINEFUNCTIONS TO STRUCTURAL ANALYSIS IN COAL GEOLOGY
Institute of Scientific and Technical Information of China (English)
HanJinyan; YuZhiwei
1996-01-01
A surface spline function is used to fit a coal seam surface in structural analysis in coal geology. From the surface spline function, the first and second partial derivatives can also be derived and used to structural analysis, especially for recognition of the concealed structures. The detection of structures related to faulting is emphasized.
Well-posedness and stability for abstract spline problems
Miglierina, E.; Molho, E.
2007-09-01
In this work well-posedness and stability properties of the abstract spline problem are studied in the framework of reflexive spaces. Tykhonov well-posedness is proved without restrictive assumptions. In the context of Hilbert spaces, also the stronger notion of Levitin-Polyak well-posedness is established. A sequence of parametric problems converging to the given abstract spline problem is considered in order to study stability. Under natural assumptions, convergence results for sequences of solutions of the perturbed problems are obtained.
Construction of generalized magnetic coordinates by B-spline expansion
Energy Technology Data Exchange (ETDEWEB)
Kurata, Michinari [Dept. of Energy Engineering and Science, Graduate School of Engineering, Nagoya Univ., Nagoya, Aichi (Japan); Todoroki, Jiro [National Inst. for Fusion Science, Toki, Gifu (Japan)
2000-06-01
Generalized Magnetic Coordinates (GMC) are curvilinear coordinates ({xi},{eta},{zeta}) in which the magnetic field is expressed in the form B={nabla}{psi}({xi},{eta},{zeta}) x {nabla}{zeta} + H{sup {zeta}}({xi},{eta}){nabla}{xi} x {nabla}{eta}. The coordinates are expanded in Fourier series in the toroidal direction and the B-spline function in other two dimensions to treat the aperiodic model magnetic field. The coordinates are well constructed, but are influenced by the boundary condition in the B-spline expansion. (author)
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.
Bending Angle Prediction Model Based on BPNN-Spline in Air Bending Springback Process
Zhefeng Guo; Wencheng Tang
2017-01-01
In order to rapidly and accurately predict the springback bending angle in V-die air bending process, a springback bending angle prediction model on the combination of error back propagation neural network and spline function (BPNN-Spline) is presented in this study. An orthogonal experimental sample set for training BPNN-Spline is obtained by finite element simulation. Through the analysis of network structure, the BPNN-Spline black box function of bending angle prediction is established, an...
C-B样条曲线的分割和拼接%Arbitrary Subdivision Algorithm and Joining of C-B-Spline
Institute of Scientific and Technical Information of China (English)
宋丽平
2011-01-01
曲线曲面造型中设计复杂的自由曲线时,单段曲线已不能满足外形设计的要求,因而在实际造型中,经常采用曲线的分割和拼接.C-B样条理论是曲线曲面造型的一项重要内容.在对C-B样条基函数及曲线端点特性分析的基础上,提出了C-B样条曲线的任意分割算法,并对C-B样条曲线间进行了G1拼接.给出了 B样条曲线和C-B样条曲线G1和G2光滑拼接的几何条件.采用分割和拼接技术会增加C-B样条曲线的灵活性,所得结论具有明确的几何意义,并可以进一步推广到C-B样条曲面造型中.%The single curve already can' t satisfy the requirements of shape design when designing complex free curve in curve/surface modeling. Thus in the actual modeling, C-B-spline theory is an important content of curve/surface modeling. Propose the algorithm of arbitrarily divided when analysing C-B-spline basis functions,then splicing between two C-B-spline. In addition,give geometry conditions about B-spline curves and C-B-spline curves. The results are benefit for the shape modification, and they can also be extended to surface modeling with C-B-spline.
Samuels, Marina A; Reed, Matthew P; Arbogast, Kristy B; Seacrist, Thomas
2016-01-01
Designing motor vehicle safety systems requires knowledge of whole body kinematics during dynamic loading for occupants of varying size and age, often obtained from sled tests with postmortem human subjects and human volunteers. Recently, we reported pediatric and adult responses in low-speed (<4 g) automotive-like impacts, noting reductions in maximum excursion with increasing age. Since the time-based trajectory shape is also relevant for restraint design, this study quantified the time-series trajectories using basis splines and developed a statistical model for predicting trajectories as a function of body dimension or age. Previously collected trajectories of the head, spine, and pelvis were modeled using cubic basis splines with eight control points. A principal component analysis was conducted on the control points and related to erect seated height using a linear regression model. The resulting statistical model quantified how trajectories became shorter and flatter with increasing body size, corresponding to the validation data-set. Trajectories were then predicted for erect seated heights corresponding to pediatric and adult anthropomorphic test devices (ATDs), thus generating performance criteria for the ATDs based on human response. This statistical model can be used to predict trajectories for a subject of specified anthropometry and utilized in subject-specific computational models of occupant response.
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.
Tame Kernels of Pure Cubic Fields
Institute of Scientific and Technical Information of China (English)
Xiao Yun CHENG
2012-01-01
In this paper,we study the p-rank of the tame kernels of pure cubic fields.In particular,we prove that for a fixed positive integer m,there exist infinitely many pure cubic fields whose 3-rank of the tame kernel equal to m.As an application,we determine the 3-rank of their tame kernels for some special pure cubic fields.
Soldea, Octavian; Elber, Gershon; Rivlin, Ehud
2006-02-01
This paper presents a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. This scheme derives a new differential scalar field for a given volumetric scalar field, which could easily be adapted to other differential properties. Moreover, this scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.
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.
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.
Differential constraints for bounded recursive identification with multivariate splines
De Visser, C.C.; Chu, Q.P.; Mulder, J.A.
2011-01-01
The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model-based control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able
Kriging and thin plate splines for mapping climate variables
Boer, E.P.J.; Beurs, de K.M.; Hartkamp, A.D.
2001-01-01
Four forms of kriging and three forms of thin plate splines are discussed in this paper to predict monthly maximum temperature and monthly mean precipitation in Jalisco State of Mexico. Results show that techniques using elevation as additional information improve the prediction results considerably
Multivariate Epi-splines and Evolving Function Identification Problems
2015-04-15
and their limits: The Polya distribution functions. Bulletin of the American Mathematical Society, 53:1114, 1947. [9] H.B. Curry and I.J. Schoenberg...On Polya frequency functions IV: The fundamental spline func- tions and their limits. Journal d’Analyse Mathématique, 17:71–107, 1966. [10] W. Dahmen
Comparative Analysis for Robust Penalized Spline Smoothing Methods
Directory of Open Access Journals (Sweden)
Bin Wang
2014-01-01
Full Text Available Smoothing noisy data is commonly encountered in engineering domain, and currently robust penalized regression spline models are perceived to be the most promising methods for coping with this issue, due to their flexibilities in capturing the nonlinear trends in the data and effectively alleviating the disturbance from the outliers. Against such a background, this paper conducts a thoroughly comparative analysis of two popular robust smoothing techniques, the M-type estimator and S-estimation for penalized regression splines, both of which are reelaborated starting from their origins, with their derivation process reformulated and the corresponding algorithms reorganized under a unified framework. Performances of these two estimators are thoroughly evaluated from the aspects of fitting accuracy, robustness, and execution time upon the MATLAB platform. Elaborately comparative experiments demonstrate that robust penalized spline smoothing methods possess the capability of resistance to the noise effect compared with the nonrobust penalized LS spline regression method. Furthermore, the M-estimator exerts stable performance only for the observations with moderate perturbation error, whereas the S-estimator behaves fairly well even for heavily contaminated observations, but consuming more execution time. These findings can be served as guidance to the selection of appropriate approach for smoothing the noisy data.
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.
Cubical local partial orders on cubically subdivided spaces - Existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
2006-01-01
The geometric models of higher dimensional automata (HDA) and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes...
Cubical local partial orders on cubically subdivided spaces - existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
The geometric models of Higher Dimensional Automata and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes...
Malmir, Hessam; Sahimi, Muhammad; Tabar, M Reza Rahimi
2016-12-01
Packing of cubic particles arises in a variety of problems, ranging from biological materials to colloids and the fabrication of new types of porous materials with controlled morphology. The properties of such packings may also be relevant to problems involving suspensions of cubic zeolites, precipitation of salt crystals during CO_{2} sequestration in rock, and intrusion of fresh water in aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We present a detailed simulation and microstructural characterization of packings of nonoverlapping monodisperse cubic particles, following up on our preliminary results [H. Malmir et al., Sci. Rep. 6, 35024 (2016)2045-232210.1038/srep35024]. A modification of the random sequential addition (RSA) algorithm has been developed to generate such packings, and a variety of microstructural descriptors, including the radial distribution function, the face-normal correlation function, two-point probability and cluster functions, the lineal-path function, the pore-size distribution function, and surface-surface and surface-void correlation functions, have been computed, along with the specific surface and mean chord length of the packings. The results indicate the existence of both spatial and orientational long-range order as the the packing density increases. The maximum packing fraction achievable with the RSA method is about 0.57, which represents the limit for a structure similar to liquid crystals.
Malmir, Hessam; Sahimi, Muhammad; Tabar, M. Reza Rahimi
2016-12-01
Packing of cubic particles arises in a variety of problems, ranging from biological materials to colloids and the fabrication of new types of porous materials with controlled morphology. The properties of such packings may also be relevant to problems involving suspensions of cubic zeolites, precipitation of salt crystals during CO2 sequestration in rock, and intrusion of fresh water in aquifers by saline water. Not much is known, however, about the structure and statistical descriptors of such packings. We present a detailed simulation and microstructural characterization of packings of nonoverlapping monodisperse cubic particles, following up on our preliminary results [H. Malmir et al., Sci. Rep. 6, 35024 (2016), 10.1038/srep35024]. A modification of the random sequential addition (RSA) algorithm has been developed to generate such packings, and a variety of microstructural descriptors, including the radial distribution function, the face-normal correlation function, two-point probability and cluster functions, the lineal-path function, the pore-size distribution function, and surface-surface and surface-void correlation functions, have been computed, along with the specific surface and mean chord length of the packings. The results indicate the existence of both spatial and orientational long-range order as the the packing density increases. The maximum packing fraction achievable with the RSA method is about 0.57, which represents the limit for a structure similar to liquid crystals.
CLASSIFICATION OF CUBIC PARAMETERIZED HOMOGENEOUS VECTOR FIELDS
Institute of Scientific and Technical Information of China (English)
Karnal H.Yasir; TANG Yun
2002-01-01
In this paper the cubic homogeneous parameterized vector fields are studied.The classification of the phase portrait near the critical point is presented. This classification is an extension of the result given by Takens to the cubic homogeneous parameterized vector fields with six parameters.
CLASSIFICATION OF CUBIC PARAMETERIZED HOMOGENEOUS VECTOR FIELDS
Institute of Scientific and Technical Information of China (English)
KamalH.Yasir; TNAGYun
2002-01-01
In this paper the cubic homogeneous parameterized vector fields are studied.The classification of the phase portrait near the critical point is presented.This classification is an extension of the result given by takens to the cubic homogeneous parameterized vector fields with six parameters.
A matrix method for degree-raising of B-spline curves
Institute of Scientific and Technical Information of China (English)
秦开怀
1997-01-01
A new identity is proved that represents the kth order B-splines as linear combinations of the (k + 1) th order B-splines A new method for degree-raising of B-spline curves is presented based on the identity. The new method can be used for all kinds of B-spline curves, that is, both uniform and arbitrarily nonuniform B-spline curves. When used for degree-raising of a segment of a uniform B-spline curve of degree k - 1, it can help obtain a segment of curve of degree k that is still a uniform B-spline curve without raising the multiplicity of any knot. The method for degree-raising of Bezier curves can be regarded as the special case of the new method presented. Moreover, the conventional theory for degree-raising, whose shortcoming has been found, is discussed.
Rheology of cubic particles suspended in a Newtonian fluid.
Cwalina, Colin D; Harrison, Kelsey J; Wagner, Norman J
2016-05-18
Many real-world industrial processes involve non-spherical particles suspended in a fluid medium. Knowledge of the flow behavior of these suspensions is essential for optimizing their transport properties and designing processing equipment. In the present work, we explore and report on the rheology of concentrated suspensions of cubic-shaped colloidal particles under steady and dynamic shear flow. These suspensions exhibit a rich non-Newtonian rheology that includes shear thickening and normal stress differences at high shear stresses. Scalings are proposed to connect the material properties of these suspensions of cubic particle to those measured for suspensions of spherical particles. Negative first normal stress differences indicate that lubrication hydrodynamic forces dominate the stress in the shear-thickened state. Accounting for the increased lubrication hydrodynamic interactions between the flat surfaces of the cubic particles allows for a quantitative comparison of the deviatoric stress in the shear-thickened state to that of spherical particles. New semi-empirical models for the viscosity and normal stress difference coefficients are presented for the shear-thickened state. The results of this study indicate that cubic particles offer new and unique opportunities to formulate colloidal dispersions for field-responsive materials.
Wavelet subdivision methods gems for rendering curves and surfaces
Chui, Charles
2010-01-01
OVERVIEW Curve representation and drawing Free-form parametric curves From subdivision to basis functions Wavelet subdivision and editing Surface subdivision BASIS FUNCTIONS FOR CURVE REPRESENTATION Refinability and scaling functions Generation of smooth basis functions Cardinal B-splines Stable bases for integer-shift spaces Splines and polynomial reproduction CURVE SUBDIVISION SCHEMES Subdivision matrices and stencils B-spline subdivision schemes Closed curve rendering Open curve rendering BASIS FUNCTIONS GENERATED BY SUBDIVISION MATRICES Subdivision operators The up-sampling convolution ope
Mitra, Sunanda
1992-11-01
Different approaches to computational stereo to represent human stereo vision have been developed over the past two decades. The Marr-Poggio theory of human stereo vision is probably the most widely accepted model of the human stereo vision. However, recently developed motion stereo models which use a sequence of images taken by either a moving camera or a moving object provide an alternative method of achieving multi-resolution matching without the use of Laplacian of Gaussian operators. While using image sequences, the baseline between two camera positions for a image pair is changed for the subsequent image pair so as to achieve different resolution for each image pair. Having different baselines also avoids the inherent occlusion problem in stereo vision models. The advantage of using multi-resolution images acquired by camera positioned at different baselines over those acquired by LOG operators is that one does not have to encounter spurious edges often created by zero-crossings in the LOG operated images. Therefore in designing a computer vision system, a motion stereo model is more appropriate than a stereo vision model. However, in some applications where only a stereo pair of images are available, recovery of 3D surfaces of natural scenes are possible in a computationally efficient manner by using cepstrum matching and regularization techniques. Section 2 of this paper describes a motion stereo model using multi-scale cepstrum matching for the detection of disparity between image pairs in a sequence of images and subsequent recovery of 3D surfaces from depth-map obtained by a non convergent triangulation technique. Section 3 presents a 3D surface recovery technique from a stereo pair using cepstrum matching for disparity detection and cubic B-splines for surface smoothing. Section 4 contains the results of 3D surface recovery using both of the techniques mentioned above. Section 5 discusses the merit of 2D cepstrum matching and cubic B-spline
Institute of Scientific and Technical Information of China (English)
寇淑清; 杨慎华; 黄良驹; 傅沛福
2001-01-01
The 3-D tool surface description together with the automatic 3-D meshing methods and the contact search is carried out for the FEM numerical simulation of complicated massive forming based on the cubic B-spline. The complex geometry for die-cavity and forging surface is described; the spline technique for 3-D mesh generation as well as piecewise mesh generation is proposed and the region-section search algo rithm is done for the advantages of B-spline such as visualization, localization, generalization, flexibility and adaptation for graphic model.%以三次B样条曲面描述为基础，对体成形数值模拟中的复杂模具型腔、锻件三维网格自动划分、锻件与模具接触的状态进行了一体化研究。利用B样条曲面的直观性、局部性、通用性和造型灵活性，构造了复杂模具型腔及锻件边界，提出了三维网格样条生成法、改进的分块样条生成法及接触判断区域层次搜索技术。
Calculation of Press Fitting Force for Involute Spline Fit%渐开线花键配合压装力计算
Institute of Scientific and Technical Information of China (English)
王宋军; 陈启云; 李慧军; 由毅; 冯擎峰
2013-01-01
The involute spline coupling is widely applied in automobile industry due to strong transmission torque and high centering accuracy.To assure the concentricity of internal and external splines, the coupling method of major diameter center-ing spline interference fit is mostly adopted between gears and shafts in a vehicle transmission.However, there are no fit cate-gories and calculating method of press fitting force in China′s involute spline fit standard.In this paper, the press fitting force of major diameter centering involute spline is calculated using the press coupling calculation method on a smooth cylindrical surface, thus the basis for establishing the press fitting process of involute spline is provided.% 渐开线花键联结因其传递扭矩大、定心精度高等优点，在汽车行业得到广泛应用。为保证内、外花键同轴度，在汽车变速器中齿轮与轴多采用大径定心的花键过盈配合联结方式。在我国渐开线花键配合标准中没有此配合类别及其压装力计算方法。笔者试以光滑圆柱面过盈联结计算方法计算大径定心的渐开线花键配合压装力，为制定渐开线花键压装工艺提供依据。
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.
Adaptive sampling for real-time rendering of large terrain based on B-spline wavelet
Kalem, Sid Ali; Kourgli, Assia
2017-05-01
This paper describes a central processing unit (CPU)-based technique for terrain geometry rendering that could relieve graphics processing unit (GPU) from processing the appropriate level of detail (LOD) of the geometric surface. The proposed approach alleviates the computational load on the CPU and approaches GPU-based efficiency. As the datasets of realistic terrains are usually huge for real-time rendering, we suggest using a training stage to handle large tiled QuadTree terrain representation. The training stage is based on multiresolution wavelet decomposition and is used to limit the region of error control inside the tile. Maximum approximation errors are then calculated for each tile at different resolutions. Maximum world-space errors of the tile at different resolutions permit selection of the appropriate resolution of downsampling that will represent the tile at the run time. Tests and experiments demonstrate that B-spline 0 and B-spline 1 wavelets, well known for their properties of localization and their compact support, are suitable for fast and accurate localization of the maximum approximation error. The experimental results demonstrate that the proposed approach drastically reduces computation time in the CPU. Such a technique should also be used on low/medium end PCs, and embedded systems that are not equipped with the latest models of graphic hardware.
Ultrahard nanotwinned cubic boron nitride.
Tian, Yongjun; Xu, Bo; Yu, Dongli; Ma, Yanming; Wang, Yanbin; Jiang, Yingbing; Hu, Wentao; Tang, Chengchun; Gao, Yufei; Luo, Kun; Zhao, Zhisheng; Wang, Li-Min; Wen, Bin; He, Julong; Liu, Zhongyuan
2013-01-17
Cubic boron nitride (cBN) is a well known superhard material that has a wide range of industrial applications. Nanostructuring of cBN is an effective way to improve its hardness by virtue of the Hall-Petch effect--the tendency for hardness to increase with decreasing grain size. Polycrystalline cBN materials are often synthesized by using the martensitic transformation of a graphite-like BN precursor, in which high pressures and temperatures lead to puckering of the BN layers. Such approaches have led to synthetic polycrystalline cBN having grain sizes as small as ∼14 nm (refs 1, 2, 4, 5). Here we report the formation of cBN with a nanostructure dominated by fine twin domains of average thickness ∼3.8 nm. This nanotwinned cBN was synthesized from specially prepared BN precursor nanoparticles possessing onion-like nested structures with intrinsically puckered BN layers and numerous stacking faults. The resulting nanotwinned cBN bulk samples are optically transparent with a striking combination of physical properties: an extremely high Vickers hardness (exceeding 100 GPa, the optimal hardness of synthetic diamond), a high oxidization temperature (∼1,294 °C) and a large fracture toughness (>12 MPa m(1/2), well beyond the toughness of commercial cemented tungsten carbide, ∼10 MPa m(1/2)). We show that hardening of cBN is continuous with decreasing twin thickness down to the smallest sizes investigated, contrasting with the expected reverse Hall-Petch effect below a critical grain size or the twin thickness of ∼10-15 nm found in metals and alloys.
AHT Bézier Curves and NUAHT B-Spline Curves
Institute of Scientific and Technical Information of China (English)
Gang Xu; Guo-Zhao Wang
2007-01-01
In this paper, we present two new unified mathematics models of conics and polynomial curves, called algebraic hyperbolic trigonometric ( AHT) Bézier curves and non-uniform algebraic hyperbolic trigonometric ( NUAHT) B-sptine curves of order n, which are generated over the space span{sin t, cos t, sinh t, cosh t, 1, t,..., tn-5}, n ≥ 5. The two kinds of curves share most of the properties as those of the Bézier curves and B-spline curves in polynomial space. In particular, they can represent exactly some remarkable transcendental curves such as the helix, the cycloid and the catenary. The subdivision formulae of these new kinds of curves are also given. The generations of the tensor product surfaces are straightforward. Using the new mathematics models, we present the control mesh representations of two classes of minimal surfaces.
Cubic Curves, Finite Geometry and Cryptography
Bruen, A A; Wehlau, D L
2011-01-01
Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a `shared secret' related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.
Generalized Vaidya spacetime for cubic gravity
Ruan, Shan-Ming
2015-01-01
We present a kind of generalized Vaidya solutions of a new cubic gravity in five dimensions whose field equations in spherically spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally we present the first law and second law hold in this gravity. Although all the results are analogue to those in Lovelock gravity, we in fact introduce the contribution of new cubic term in five dimensions where cubic Lovelock term is just zero.
Cubical sets as a classifying topos
DEFF Research Database (Denmark)
Spitters, Bas
Coquand’s cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. We show that the underlying cube category is the opposite of the Lawvere theory of De...... Morgan algebras. The topos of cubical sets itself classifies the theory of ‘free De Morgan algebras’. This provides us with a topos with an internal ‘interval’. Using this interval we construct a model of type theory following van den Berg and Garner. We are currently investigating the precise relation...
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.
Institute of Scientific and Technical Information of China (English)
周西军
2003-01-01
Non-uniform rational B-spline (NURBS) curves and surfaces are becoming increasingly widespread. The author have explored G1 continuity condition between adjacent NURBS surface patches along common cubic boundary curve. On the basis of the research performed, this paper presents a G2 continuity condition between adjacent NURBS patches along common cubic boundary curve and deduces a specific algorithm for contro1 points and weights of NURBS patch. For making another NURBS patch and one given NURBS patch to attain G2, according to algorithm condition, one can adjust another patch control points and weights. It is much more convenient for engineers to apply.%非均匀有理B样条(NURBS)曲线、曲面造型理论是当前最先进的几何造型方法之一,大量基于NURBS的实用造型系统得到发展.对NURBS而言,虽然具有参数连续性,但为了实用需要,仍需构造具有一定光滑程度的合成曲面,满足局部设计和修改的目的.在作者给出的具有公共三次曲线的NURBS曲面片G1光滑拼接算法基础上,给出了具有公共三次曲线的NURBS曲面片G2光滑拼接条件,得到了相应控制顶点、权系数的具体算法;对于一个已知NURBS曲面,构造另一个NURBS曲面,使其达到G2拼接是简单易行的.
Complexity of Approximation by Conic Splines (Extended Abstract)
Petitjean, Sylvain; Ghosh, Sunayana; Vegter, Gert
2007-01-01
In this paper we show that the complexity, i.e., the number of elements, of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε^−1/4 + O(1), or c2ε^−1/5 + O(1), respectively. The constants c1 and c2 are expressed in
A B-spline Galerkin method for the Dirac equation
Froese Fischer, Charlotte; Zatsarinny, Oleg
2009-06-01
The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y=-λy, that can also be written as a pair of first-order equations y=λz, z=-λy. Expanding both y(r) and z(r) in the B basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the B basis and z(r) in the dB/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method ( B,B) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.
Quintic spline smooth semi-supervised support vector classification machine
Institute of Scientific and Technical Information of China (English)
Xiaodan Zhang; Jinggai Ma; Aihua Li; Ang Li
2015-01-01
A semi-supervised vector machine is a relatively new learning method using both labeled and unlabeled data in classifi-cation. Since the objective function of the model for an unstrained semi-supervised vector machine is not smooth, many fast opti-mization algorithms cannot be applied to solve the model. In order to overcome the difficulty of dealing with non-smooth objective functions, new methods that can solve the semi-supervised vector machine with desired classification accuracy are in great demand. A quintic spline function with three-times differentiability at the ori-gin is constructed by a general three-moment method, which can be used to approximate the symmetric hinge loss function. The approximate accuracy of the quintic spline function is estimated. Moreover, a quintic spline smooth semi-support vector machine is obtained and the convergence accuracy of the smooth model to the non-smooth one is analyzed. Three experiments are performed to test the efficiency of the model. The experimental results show that the new model outperforms other smooth models, in terms of classification performance. Furthermore, the new model is not sensitive to the increasing number of the labeled samples, which means that the new model is more efficient.
Fast space-variant elliptical filtering using box splines.
Chaudhury, Kunal Narayan; Munoz-Barrutia, Arrate; Unser, Michael
2010-09-01
The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based upon a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using preintegration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based upon the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.
MOVING SCREW DISLOCATION IN CUBIC QUASICRYSTAL
Institute of Scientific and Technical Information of China (English)
ZHOU Wang-min; SONG Yu-hai
2005-01-01
The elasticity theory of the dislocation of cubic quasicrystals is developed.The governing equations of anti-plane elasticity dynamics problem of the quasicrystals were reduced to a solution of wave equations by introducing displacement functions,and the analytical expressions of displacements, stresses and energies induced by a moving screw dislocation in the cubic quasicrystalline and the velocity limit of the dislocation were obtained. These provide important information for studying the plastic deformation of the new solid material.
Semisymmetric Cubic Graphs of Order 162
Indian Academy of Sciences (India)
Mehdi Alaeiyan; Hamid A Tavallaee; B N Onagh
2010-02-01
An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, we inquire the existence of connected semisymmetric cubic graphs of order 162. It is shown that for every odd prime , there exists a semisymmetric cubic graph of order 162 and its structure is explicitly specified by giving the corresponding voltage rules generating the covering projections.
Cubical version of combinatorial differential forms
DEFF Research Database (Denmark)
Kock, Anders
2010-01-01
The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.......The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....
Institute of Scientific and Technical Information of China (English)
LI She-Qiang; FU Xing-Qiu; HU Bing; DENG Jia-Jun; CHEN Lei
2009-01-01
The oxidation of formic acid on edge-truncated cubic platinum nanoparticles/C catalysts is investigated. X-ray photoelectron spectroscopy analysis indicates that the surface of edge-truncated cubic platinum nanoparticles is composed of two types of coordination sites. The oxidation behavior of formic acid on edge-truncated cubic platinum nanoparticles/C is investigated using cyclic voltammetry. The apparent activation energies are found to be 54.2, 55.0, 61.8, 69.5, 71.9, 69.26, 65.28kJ/mol at 0.15, 0.3, 0.4, 0.5, 0.6, 0.65, 0.7 V, respectively. A specific surface area activity of 1.76mA·cm~(-2) at 0.4 V indicates that the edge-truncated cubic Platinum nanoparticles are a promising anode catalyst for direct formic acid fuel cells.
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.
Hodograph computation and bound estimation for rational B-spline curves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is necessary to compute the derivative and estimate the bound of rational B-spline curves in design system, which has not been studied to date. To improve the function of computer aided design (CAD) system, and to enhance the efficiency of different algorithms of rational B-spline curves, the representation of scaled hodograph and bound of derivative magnitude of uniform planar rational B-spline curves are derived by applying Dir function, which indicates the direction of Cartesian vector between homogeneous points, discrete B-spline theory and the formula of translating the product into a summation of B-spline functions. As an application of the result above,upper bound of parametric distance between any two points in a uniform planar rational B-spline curve is further presented.
Bending Angle Prediction Model Based on BPNN-Spline in Air Bending Springback Process
Directory of Open Access Journals (Sweden)
Zhefeng Guo
2017-01-01
Full Text Available In order to rapidly and accurately predict the springback bending angle in V-die air bending process, a springback bending angle prediction model on the combination of error back propagation neural network and spline function (BPNN-Spline is presented in this study. An orthogonal experimental sample set for training BPNN-Spline is obtained by finite element simulation. Through the analysis of network structure, the BPNN-Spline black box function of bending angle prediction is established, and the advantage of BPNN-Spline is discussed in comparison with traditional BPNN. The results show a close agreement with simulated and experimental results by application examples, which means that the BPNN-Spline model in this study has higher prediction accuracy and better applicable ability. Therefore, it could be adopted in a numerical control bending machine system.
Computer generated hologram null test of a freeform optical surface with rectangular aperture
Su, Ping; Ma, Jianshe; Tan, Qiaofeng; Kang, Guoguo; Liu, Yi; Jin, Guofan
2012-02-01
In null computed generated hologram (CGH) test of optical elements, fitting method is needed in null CGH design to generate continuous phase function from the ray-traced discrete phase data. The null CGH for freeform testing usually has a deformed aperture and a high order phase function, because of the aberrations introduced by freeform wavefront propagation. With traditional Zernike polynomial fitting method, selection of an orthogonal basis set and choosing number of terms are needed before fitting. Zernike polynomial fitting method is not suitable in null CGH design for freeform testing; a novel CGH design method with cubic B-spline interpolation is developed. For a freeform surface with 18×18 mm2 rectangular aperture and 630 μm peak-to-valley undulation, the null CGH with a curved rectangular aperture is designed by using the method proposed. Simulation and experimental results proved the feasibility of the novel CGH design method.
A method for determining the median line of measured cylindrical and conical surfaces
Janecki, Dariusz; Zwierzchowski, Jarosław
2015-08-01
The paper presents a novel method for the determination of the median line of the cylindrical and conical surfaces. This method can be incorporated into virtually any cylindricity measurement strategy, including the bird-cage strategy and the helical line strategy. In the study, a median line was determined by minimizing the functional made up of two components. The form of the first component results from the classic definition of the median line provided in the corresponding standard. The other, termed the bending energy, is responsible for ensuring appropriate smoothness of the median line. In order to solve this variational problem, the median line was approximated by means of linear combination of cubic B-spline functions. A simulation and experiments were conducted to establish the suitability of the algorithm developed for the determination of the median line using the helical-line and the cross-section measurement strategy.
THE INSTABILITY DEGREE IN THE DIEMNSION OF SPACES OF BIVARIATE SPLINE
Institute of Scientific and Technical Information of China (English)
Zhiqiang Xu; Renhong Wang
2002-01-01
In this paper, the dimension of the spaces of bivariate spline with degree less that 2r and smoothness order r on the Morgan-Scott triangulation is considered. The concept of the instability degree in the dimension of spaces of bivariate spline is presented. The results in the paper make us conjecture the instability degree in the dimension of spaces of bivariate spline is infinity.
Ziadi, Manel; Ben Hassen-Trabelsi, Aida; Mekni, Sabrine; Aïssi, Balkiss; Alaya, Marwen; Bergaoui, Latifa; Hamdi, Moktar
2017-01-01
This paper opens up a new issue dealing with Luffa cylindrica (LC) lignocellulosic biomass recovery in order to produce 2G bioethanol. LC fibers are composed of three principal fractions, namely, α-cellulose (45.80% ± 1.3), hemicelluloses (20.76% ± 0.3), and lignins (13.15% ± 0.6). The optimization of LC fibers hydrothermal and diluted acid pretreatments duration and temperature were achieved through the cubic central composite experimental design CCD. The pretreatments optimization was monitored via the determination of reducing sugars. Then, the 2G bioethanol process feasibility was tested by means of three successive steps, namely, LC fibers hydrothermal pretreatment performed at 96°C during 54 minutes, enzymatic saccharification carried out by means of a commercial enzyme AP2, and the alcoholic fermentation fulfilled with Saccharomyces cerevisiae. LC fibers hydrothermal pretreatment liberated 33.55 g/kg of reducing sugars. Enzymatic hydrolysis allowed achieving 59.4 g/kg of reducing sugars. The conversion yield of reducing sugar to ethanol was 88.66%. After the distillation step, concentration of ethanol was 1.58% with a volumetric yield about 70%. PMID:28243606
Directory of Open Access Journals (Sweden)
Kaouther Zaafouri
2017-01-01
Full Text Available This paper opens up a new issue dealing with Luffa cylindrica (LC lignocellulosic biomass recovery in order to produce 2G bioethanol. LC fibers are composed of three principal fractions, namely, α-cellulose (45.80% ± 1.3, hemicelluloses (20.76% ± 0.3, and lignins (13.15% ± 0.6. The optimization of LC fibers hydrothermal and diluted acid pretreatments duration and temperature were achieved through the cubic central composite experimental design CCD. The pretreatments optimization was monitored via the determination of reducing sugars. Then, the 2G bioethanol process feasibility was tested by means of three successive steps, namely, LC fibers hydrothermal pretreatment performed at 96°C during 54 minutes, enzymatic saccharification carried out by means of a commercial enzyme AP2, and the alcoholic fermentation fulfilled with Saccharomyces cerevisiae. LC fibers hydrothermal pretreatment liberated 33.55 g/kg of reducing sugars. Enzymatic hydrolysis allowed achieving 59.4 g/kg of reducing sugars. The conversion yield of reducing sugar to ethanol was 88.66%. After the distillation step, concentration of ethanol was 1.58% with a volumetric yield about 70%.
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.
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.
Application of a polynomial spline in higher-order accurate viscous-flow computations
Turner, M. G.; Keith, J. S.; Ghia, K. N.; Ghia, U.
1982-01-01
A quartic spline, S(4,2), is proposed which overcomes some of the difficulties associated with the use of splines S(5,3) and S(3,1) and provides fourth-order accurate results with relatively few grid points. The accuracy of spline S(4,2) is comparable to or better than that of the fourth-order box scheme and the compact differencing scheme. The use of spline S(4,2) is suggested as a possible way of obtaining fourth-order accurate solutions to Navier-Stokes equations.
Automatic Shape Control of Triangular B-Splines of Arbitrary Topology
Institute of Scientific and Technical Information of China (English)
Ying He; Xian-Feng Gu; Hong Qin
2006-01-01
Triangular B-splines are powerful and flexible in modeling a broader class of geometric objects defined over arbitrary, non-rectangular domains. Despite their great potential and advantages in theory, practical techniques and computational tools with triangular B-splines are less-developed. This is mainly because users have to handle a large number of irregularly distributed control points over arbitrary triangulation. In this paper, an automatic and efficient method is proposed to generate visually pleasing, high-quality triangular B-splines of arbitrary topology. The experimental results on several real datasets show that triangular B-splines are powerful and effective in both theory and practice.
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).
Design Evaluation of Wind Turbine Spline Couplings Using an Analytical Model: Preprint
Energy Technology Data Exchange (ETDEWEB)
Guo, Y.; Keller, J.; Wallen, R.; Errichello, R.; Halse, C.; Lambert, S.
2015-02-01
Articulated splines are commonly used in the planetary stage of wind turbine gearboxes for transmitting the driving torque and improving load sharing. Direct measurement of spline loads and performance is extremely challenging because of limited accessibility. This paper presents an analytical model for the analysis of articulated spline coupling designs. For a given torque and shaft misalignment, this analytical model quickly yields insights into relationships between the spline design parameters and resulting loads; bending, contact, and shear stresses; and safety factors considering various heat treatment methods. Comparisons of this analytical model against previously published computational approaches are also presented.
Heyne, Matthias; Derrick, Donald
2015-12-01
Tongue surface measurements from midsagittal ultrasound scans are effectively arcs with deviations representing tongue shape, but smoothing-spline analysis of variances (SSANOVAs) assume variance around a horizontal line. Therefore, calculating SSANOVA average curves of tongue traces in Cartesian Coordinates [Davidson, J. Acoust. Soc. Am. 120(1), 407-415 (2006)] creates errors that are compounded at tongue tip and root where average tongue shape deviates most from a horizontal line. This paper introduces a method for transforming data into polar coordinates similar to the technique by Mielke [J. Acoust. Soc. Am. 137(5), 2858-2869 (2015)], but using the virtual origin of a radial ultrasound transducer as the polar origin-allowing data conversion in a manner that is robust against between-subject and between-session variability.
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.
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
Dry Powder Precursors of Cubic Liquid Crystalline Nanoparticles (cubosomes)
Spicer, Patrick T.; Small, William B.; Small, William B.; Lynch, Matthew L.; Burns, Janet L.
2002-08-01
Cubosomes are dispersed nanostructured particles of cubic phase liquid crystal that have stimulated significant research interest because of their potential for application in controlled-release and drug delivery. Despite the interest, cubosomes can be difficult to fabricate and stabilize with current methods. Most of the current work is limited to liquid phase processes involving high shear dispersion of bulk cubic liquid crystalline material into sub-micron particles, limiting application flexibility. In this work, two types of dry powder cubosome precursors are produced by spray-drying: (1) starch-encapsulated monoolein is produced by spray-drying a dispersion of cubic liquid crystalline particles in an aqueous starch solution and (2) dextran-encapsulated monoolein is produced by spray-drying an emulsion formed by the ethanol-dextran-monoolein-water system. The encapsulants are used to decrease powder cohesion during drying and to act as a soluble colloidal stabilizer upon hydration of the powders. Both powders are shown to form (on average) 0.6 μm colloidally-stable cubosomes upon addition to water. However, the starch powders have a broader particle size distribution than the dextran powders because of the relative ease of spraying emulsions versus dispersions. The developed processes enable the production of nanostructured cubosomes by end-users rather than just specialized researchers and allow tailoring of the surface state of the cubosomes for broader application.
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.
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
The Adaptive LASSO Spline Estimation of Single-Index Model
Institute of Scientific and Technical Information of China (English)
LU Yiqiang; ZHANG Riquan; HU Bin
2016-01-01
In this paper,based on spline approximation,the authors propose a unified variable selection approach for single-index model via adaptive L1 penalty.The calculation methods of the proposed estimators are given on the basis of the known lars algorithm.Under some regular conditions,the authors demonstrate the asymptotic properties of the proposed estimators and the oracle properties of adaptive LASSO (aLASSO) variable selection.Simulations are used to investigate the performances of the proposed estimator and illustrate that it is effective for simultaneous variable selection as well as estimation of the single-index models.
Gravity Aided Navigation Precise Algorithm with Gauss Spline Interpolation
Directory of Open Access Journals (Sweden)
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.
Superhard BC(3) in cubic diamond structure.
Zhang, Miao; Liu, Hanyu; Li, Quan; Gao, Bo; Wang, Yanchao; Li, Hongdong; Chen, Changfeng; Ma, Yanming
2015-01-01
We solve the crystal structure of recently synthesized cubic BC(3) using an unbiased swarm structure search, which identifies a highly symmetric BC(3) phase in the cubic diamond structure (d-BC(3)) that contains a distinct B-B bonding network along the body diagonals of a large 64-atom unit cell. Simulated x-ray diffraction and Raman peaks of d-BC(3) are in excellent agreement with experimental data. Calculated stress-strain relations of d-BC(3) demonstrate its intrinsic superhard nature and reveal intriguing sequential bond-breaking modes that produce superior ductility and extended elasticity, which are unique among superhard solids. The present results establish the first boron carbide in the cubic diamond structure with remarkable properties, and these new findings also provide insights for exploring other covalent solids with complex bonding configurations.
Cubical Cohomology Ring of 3D Photographs
Gonzalez-Diaz, Rocio; Medrano, Belen; 10.1002/ima.20271
2011-01-01
Cohomology and cohomology ring of three-dimensional (3D) objects are topological invariants that characterize holes and their relations. Cohomology ring has been traditionally computed on simplicial complexes. Nevertheless, cubical complexes deal directly with the voxels in 3D images, no additional triangulation is necessary, facilitating efficient algorithms for the computation of topological invariants in the image context. In this paper, we present formulas to directly compute the cohomology ring of 3D cubical complexes without making use of any additional triangulation. Starting from a cubical complex $Q$ that represents a 3D binary-valued digital picture whose foreground has one connected component, we compute first the cohomological information on the boundary of the object, $\\partial Q$ by an incremental technique; then, using a face reduction algorithm, we compute it on the whole object; finally, applying the mentioned formulas, the cohomology ring is computed from such information.
Pandithevan, Ponnusamy
2015-02-01
In tissue engineering, the successful modeling of scaffold for the replacement of damaged body parts depends mainly on external geometry and internal architecture in order to avoid the adverse effects such as pain and lack of ability to transfer the load to the surrounding bone. Due to flexibility in controlling the parameters, layered manufacturing processes are widely used for the fabrication of bone tissue engineering scaffold with the given computer-aided design model. This article presents a squared distance minimization approach for weight optimization of non-uniform rational B-spline curve and surface to modify the geometry that exactly fits into the defect region automatically and thus to fabricate the scaffold specific to subject and site. The study showed that though the errors associated in the B-spline curve and surface were minimized by squared distance method than point distance method and tangent distance method, the errors could be minimized further in the rational B-spline curve and surface as the optimal weight could change the shape that desired for the defect site. In order to measure the efficacy of the present approach, the results were compared with point distance method and tangent distance method in optimizing the non-rational and rational B-spline curve and surface fitting for the defect site. The optimized geometry then allowed to construct the scaffold in fused deposition modeling system as an example. The result revealed that the squared distance-based weight optimization of the rational curve and surface in making the defect specific geometry best fits into the defect region than the other methods used. © IMechE 2015.
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
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
A few remarks on recurrence relations for geometrically continuous piecewise Chebyshevian B-splines
Mazure, Marie-Laurence
2009-08-01
This works complements a recent article (Mazure, J. Comp. Appl. Math. 219(2):457-470, 2008) in which we showed that T. Lyche's recurrence relations for Chebyshevian B-splines (Lyche, Constr. Approx. 1:155-178, 1985) naturally emerged from blossoms and their properties via de Boor type algorithms. Based on Chebyshevian divided differences, T. Lyche's approach concerned splines with all sections in the same Chebyshev space and with ordinary connections at the knots. Here, we consider geometrically continuous piecewise Chebyshevian splines, namely, splines with sections in different Chebyshev spaces, and with geometric connections at the knots. In this general framework, we proved in (Mazure, Constr. Approx. 20:603-624, 2004) that existence of B-spline bases could not be separated from existence of blossoms. Actually, the present paper enhances the powerfulness of blossoms in which not only B-splines are inherent, but also their recurrence relations. We compare this fact with the work by G. Mühlbach and Y. Tang (Mühlbach and Tang, Num. Alg. 41:35-78, 2006) who obtained the same recurrence relations via generalised Chebyshevian divided differences, but only under some total positivity assumption on the connexion matrices. We illustrate this comparison with splines with four-dimensional sections. The general situation addressed here also enhances the differences of behaviour between B-splines and the functions of smaller and smaller supports involved in the recurrence relations.
A class of compactly supported symmetric/antisymmetric B-spline wavelets
Institute of Scientific and Technical Information of China (English)
YANG Shouzhi; LOU Zengjian
2005-01-01
An algorithm for constructing a class of compactly supported symmetric/antisymmetric B-spline wavelets is presented.For any m th order and k th order cardinal B-spline Nm (x), Nk (x), if m + k is an even integer, the corresponding m th order B-spline wavelets ψkm (x) can be constructed, which are compactly supported symmetric/antisymmetric. In addition, if ψkm (x), m ＞ 1 is m th Bspline wavelet associated with two spline functions Nm (x) and Nk (x), then (ψkm (x))′( x ) is m - 1th B-spline wavelet associated with Nm-1(x) and Nk+1(x), i.e. (ψkm(x))′(x) =22ψk+1m-1(x). Similarly, ∫x0 ψkm(t)dt, k ＞1 is m + 1th B-spline wavelet associated with Nm + 1 (x) and Nk-1 (x). Using this method, we recovered Chui and Wang' s spline wavelets. Since a class of B-spline wavelets are symmetric/antisymmetric, their linear phase property is assured. Several examples are also presented.
On O(1) Gaussian filtering using box splines
Chauhdury, Kunal N
2011-01-01
It is well-known that box filters can be efficiently computed using pre-integrations and local finite-differences [Crow1984,Heckbert1986,Viola2001]. Several image processing algorithms based on this idea have been proposed in the literature. By generalizing this idea and by combining it with a non-standard variant of the Central Limit Theorem, a constant-time or O(1) algorithm was proposed in [Chaudhury2010] that allowed one to perform space-variant filtering using Gaussian-like kernels . The algorithm was based on the observation that both isotropic and anisotropic Gaussians could be approximated using certain bivariate splines called box splines. The attractive feature of the algorithm was that it allowed one to continuously control the shape and size of the filter, and that it had a fixed computational cost per pixel, irrespective of the size of the filter. The algorithm, however, had the drawback that it offered only a limited control on the covariance and accuracy of the Gaussian approximation. In this w...
B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy
Directory of Open Access Journals (Sweden)
Shilpa Dilipkumar
2015-03-01
Full Text Available An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy. A comparative study of the proposed technique with the state-of-art maximum likelihood (ML and maximum-a-posteriori (MAP with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED.
Liu, C.; Yuan, F.; Gen, Z.; Wang, L.; Cui, Y. G.; Wan, J. F.; Zhang, J. H.; Rong, Y. H.
2016-06-01
Temperature-dependence surface relief during cubic↔tetragonal martensitic transformation (MT) in Mn69.4Fe26.0Cu4.6 antiferromegnetic shape memory alloy was studied by means of in-situ atomic force microscopy. The surface morphology memory effect was found and the crystallography reversibility of the transformation and its shearing characters were directly verified. Twin shearing is suggested as the main mechanism of formation of tent-type surface relief. The surface relief angle (θα|θβ)<0.5° was firstly measured and might be the smallest compared with that in other shape memory alloys. A Landau model was proposed to consider the shearing strain related with surface relief of MT varying with the coupling effect between second-order antiferromagnetic transition and first-order MT. According to this model, the Mn69.4Fe26.0Cu4.6 alloy belongs to the weak coupling system and this kind of weak coupling effect makes the main contribution to the small relief angle.
Rounaghi, Mohammad Mahdi; Abbaszadeh, Mohammad Reza; Arashi, Mohammad
2015-11-01
One of the most important topics of interest to investors is stock price changes. Investors whose goals are long term are sensitive to stock price and its changes and react to them. In this regard, we used multivariate adaptive regression splines (MARS) model and semi-parametric splines technique for predicting stock price in this study. The MARS model as a nonparametric method is an adaptive method for regression and it fits for problems with high dimensions and several variables. semi-parametric splines technique was used in this study. Smoothing splines is a nonparametric regression method. In this study, we used 40 variables (30 accounting variables and 10 economic variables) for predicting stock price using the MARS model and using semi-parametric splines technique. After investigating the models, we select 4 accounting variables (book value per share, predicted earnings per share, P/E ratio and risk) as influencing variables on predicting stock price using the MARS model. After fitting the semi-parametric splines technique, only 4 accounting variables (dividends, net EPS, EPS Forecast and P/E Ratio) were selected as variables effective in forecasting stock prices.
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。
Counting rational points on cubic curves
Institute of Scientific and Technical Information of China (English)
HEATH-BROWN; Roger; TESTA; Damiano
2010-01-01
We prove upper bounds for the number of rational points on non-singular cubic curves defined over the rationals.The bounds are uniform in the curve and involve the rank of the corresponding Jacobian.The method used in the proof is a combination of the "determinant method" with an m-descent on the curve.
Anisotropy of a cubic ferromagnet at criticality
Kudlis, A.; Sokolov, A. I.
2016-10-01
Critical fluctuations change the effective anisotropy of cubic ferromagnet near the Curie point. If the crystal undergoes phase transition into orthorhombic phase and the initial anisotropy is not too strong, reduced anisotropy of nonlinear susceptibility acquires at Tc the universal value δ4*=2/v* 3 (u*+v*) where u* and v* are coordinates of the cubic fixed point on the flow diagram of renormalization group equations. In the paper, the critical value of the reduced anisotropy is estimated within the pseudo-ɛ expansion approach. The six-loop pseudo-ɛ expansions for u*, v*, and δ4* are derived for the arbitrary spin dimensionality n . For cubic crystals (n =3 ) higher-order coefficients of the pseudo-ɛ expansions obtained turn out to be so small that use of simple Padé approximants yields reliable numerical results. Padé resummation of the pseudo-ɛ series for u*, v*, and δ4* leads to the estimate δ4*=0.079 ±0.006 , indicating that detection of the anisotropic critical behavior of cubic ferromagnets in physical and computer experiments is certainly possible.
Binomial Squares in Pure Cubic Number Fields
Lemmermeyer, Franz
2011-01-01
Let K = Q(\\omega) with \\omega^3 = m be a pure cubic number field. We show that the elements\\alpha \\in K^\\times whose squares have the form a - \\omega form a group isomorphic to the group of rational points on the elliptic curve E_m: y^2= x^3 - m.
The cactus rank of cubic forms
Bernardi, Alessandra
2011-01-01
We prove that the smallest degree of an apolar 0-dimensional scheme to a general cubic form in $n+1$ variables is at most $2n+2$, when $n\\geq 8$, and therefore smaller than the rank of the form. When n=8 we show that the bound is sharp, i.e. the smallest degree of an apolar subscheme is 18.
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.
Enhanced initial protein adsorption on an engineered nanostructured cubic zirconia
Sabirianov, R F; Namavar, F
2010-01-01
Motivated by experimentally observed biocompatibility enhancement of nanoengineered cubic zirconia ZrO2 coatings to mesenchymal stromal cells, we have carried out computational analysis of the initial immobilization of one of known structural fragment of the adhesive protein (fibronectin) on the corresponding surface. We constructed an atomistic model of the zirconia nano-hillock of 3-fold symmetry based on AFM and TEM images. First-principle quantum-mechanical calculations show a substantial variation of electrostatic potential at the hillock due to the presence of surface features such as edges and vertexes. Using an implemented Monte Carlo simulated annealing method we found the orientation of the immobilized protein on the zirconia surface (both flat and nanostructured) and contribution of the each amino acid residue from the protein sequence to the adsorption energy. Accounting for the variation of the dielectric permittivity at the protein-implant interface we use a model distance-dependent dielectric f...
Kotomin, E A; Piskunov, S; Zhukovskii, Yu F; Eglitis, R I; Gopejenko, A; Ellis, D E
2008-08-07
Combining B3PW hybrid exchange-correlation functional within the density functional theory (DFT) and a supercell model, we calculated from the first principles the electronic structure of both ideal PbZrO(3) (001) surface (with ZrO(2)- and PbO-terminations) and a neutral oxygen vacancy also called the F center. The atomic relaxation and electronic density redistributions are discussed. Thermodynamic analysis of pure surfaces indicates that ZrO(2) termination is energetically more favorable than PbO-termination. The O vacancy on the ZrO(2)-surface attracts approximately 0.3 e (0.7 e in the bulk PbZrO(3)), while the remaining electron density from the missing O(2-) ion is localized mostly on atoms nearest to a vacancy. The calculated defect formation energy is smaller than in the bulk which should lead to the vacancy segregation to the surface. Unlike Ti-based perovskites, the vacancy-induced (deep) energy level lies in PbZrO(3) in the middle of the band gap.
Three-dimensional wavelet transform and multiresolution surface reconstruction from volume data
Wang, Yun; Sloan, Kenneth R., Jr.
1995-04-01
Multiresolution surface reconstruction from volume data is very useful in medical imaging, data compression and multiresolution modeling. This paper presents a hierarchical structure for extracting multiresolution surfaces from volume data by using a 3-D wavelet transform. The hierarchical scheme is used to visualize different levels of detail of the surface and allows a user to explore different features of the surface at different scales. We use 3-D surface curvature as a smoothness condition to control the hierarchical level and the distance error between the reconstructed surface and the original data as the stopping criteria. A 3-D wavelet transform provides an appropriate hierarchical structure to build the volume pyramid. It can be constructed by the tensor products of 1-D wavelet transforms in three subspaces. We choose the symmetric and smoothing filters such as Haar, linear, pseudoCoiflet, cubic B-spline and their corresponding orthogonal wavelets to build the volume pyramid. The surface is reconstructed at each level of volume data by using the cell interpolation method. Some experimental results are shown through the comparison of the different filters based on the distance errors of the surfaces.
Yang, Yu; Yao, Hongwei; Hong, Mei
2015-04-16
Nonlamellar lipid membranes are frequently induced by proteins that fuse, bend, and cut membranes. Understanding the mechanism of action of these proteins requires the elucidation of the membrane morphologies that they induce. While hexagonal phases and lamellar phases are readily identified by their characteristic solid-state NMR line shapes, bicontinuous lipid cubic phases are more difficult to discern, since the static NMR spectra of cubic-phase lipids consist of an isotropic (31)P or (2)H peak, indistinguishable from the spectra of isotropic membrane morphologies such as micelles and small vesicles. To date, small-angle X-ray scattering is the only method to identify bicontinuous lipid cubic phases. To explore unique NMR signatures of lipid cubic phases, we first describe the orientation distribution of lipid molecules in cubic phases and simulate the static (31)P chemical shift line shapes of oriented cubic-phase membranes in the limit of slow lateral diffusion. We then show that (31)P T2 relaxation times differ significantly between isotropic micelles and cubic-phase membranes: the latter exhibit 2 orders of magnitude shorter T2 relaxation times. These differences are explained by the different time scales of lipid lateral diffusion on the cubic-phase surface versus the time scales of micelle tumbling. Using this relaxation NMR approach, we investigated a DOPE membrane containing the transmembrane domain (TMD) of a viral fusion protein. The static (31)P spectrum of DOPE shows an isotropic peak, whose T2 relaxation times correspond to that of a cubic phase. Thus, the viral fusion protein TMD induces negative Gaussian curvature, which is an intrinsic characteristic of cubic phases, to the DOPE membrane. This curvature induction has important implications to the mechanism of virus-cell fusion. This study establishes a simple NMR diagnostic probe of lipid cubic phases, which is expected to be useful for studying many protein-induced membrane remodeling phenomena
Ytterbium: Transition at High Pressure from Face-Centered Cubic to Body-Centered Cubic Structure.
Hall, H T; Barnett, J D; Merrill, L
1963-01-11
Pressure of 40,000 atmospheres at 25 degrees C induces a phase transformation in ytterbium metal; the face-centered cubic structure changes to body-centered cubic. The radius of the atom changes from 1.82 to 1.75 A. At the same time the atom's volume decreases by 11 percent and the volume, observed macroscopically, decreases 3.2 percent.
Cubic optical elements for an accommodative intraocular lens.
Simonov, Aleksey N; Vdovin, Gleb; Rombach, Michiel C
2006-08-21
We present a new accommodative intraocular lens based on a two-element varifocal Alvarez lens. The intraocular lens consists of (1) an anterior element combining a spherical lens for refractive power with a cubic surface for the varifocal effect, and (2) a posterior element with a cubic surface only. The focal length of the IOL lens changes when the superimposed refractive elements shift in opposite directions in a plane perpendicular to the optical axis. The ciliary muscle will drive the accommodation by a natural process of contraction and relaxation. Results of ray-tracing simulations of the model eye with the two-element intraocular lens are presented for on-axis and off-axis vision. The configuration of the lens is optimized to reduce refractive errors as well as effects of misalignment. A prototype with a clear aperture of ~5.7 mm is manufactured and evaluated in air with a Shack-Hartmann wave-front sensor. It provides an accommodation range of ~4 dioptres in the eye at a ~0.75-mm lateral displacement of the optical elements. The experimentally measured on-axis optical performance of the IOL lens agrees with the theoretically predicted performance.
Meshing Force of Misaligned Spline Coupling and the Influence on Rotor System
Directory of Open Access Journals (Sweden)
Guang Zhao
2008-01-01
Full Text Available Meshing force of misaligned spline coupling is derived, dynamic equation of rotor-spline coupling system is established based on finite element analysis, the influence of meshing force on rotor-spline coupling system is simulated by numerical integral method. According to the theoretical analysis, meshing force of spline coupling is related to coupling parameters, misalignment, transmitting torque, static misalignment, dynamic vibration displacement, and so on. The meshing force increases nonlinearly with increasing the spline thickness and static misalignment or decreasing alignment meshing distance (AMD. Stiffness of coupling relates to dynamic vibration displacement, and static misalignment is not a constant. Dynamic behaviors of rotor-spline coupling system reveal the following: 1X-rotating speed is the main response frequency of system when there is no misalignment; while 2X-rotating speed appears when misalignment is present. Moreover, when misalignment increases, vibration of the system gets intricate; shaft orbit departs from origin, and magnitudes of all frequencies increase. Research results can provide important criterions on both optimization design of spline coupling and trouble shooting of rotor systems.
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 Selection of Spectral Variables with B-Spline Compression
Rossi, Fabrice; Wertz, Vincent; Meurens, Marc; Verleysen, Michel
2007-01-01
The large number of spectral variables in most data sets encountered in spectral chemometrics often renders the prediction of a dependent variable uneasy. The number of variables hopefully can be reduced, by using either projection techniques or selection methods; the latter allow for the interpretation of the selected variables. Since the optimal approach of testing all possible subsets of variables with the prediction model is intractable, an incremental selection approach using a nonparametric statistics is a good option, as it avoids the computationally intensive use of the model itself. It has two drawbacks however: the number of groups of variables to test is still huge, and colinearities can make the results unstable. To overcome these limitations, this paper presents a method to select groups of spectral variables. It consists in a forward-backward procedure applied to the coefficients of a B-Spline representation of the spectra. The criterion used in the forward-backward procedure is the mutual infor...
Prediction of longitudinal dispersion coefficient using multivariate adaptive regression splines
Indian Academy of Sciences (India)
Amir Hamzeh Haghiabi
2016-07-01
In this paper, multivariate adaptive regression splines (MARS) was developed as a novel soft-computingtechnique for predicting longitudinal dispersion coefficient (DL) in rivers. As mentioned in the literature,experimental dataset related to DL was collected and used for preparing MARS model. Results of MARSmodel were compared with multi-layer neural network model and empirical formulas. To define the mosteffective parameters on DL, the Gamma test was used. Performance of MARS model was assessed bycalculation of standard error indices. Error indices showed that MARS model has suitable performanceand is more accurate compared to multi-layer neural network model and empirical formulas. Results ofthe Gamma test and MARS model showed that flow depth (H) and ratio of the mean velocity to shearvelocity (u/u^∗) were the most effective parameters on the DL.
Multiquadric Spline-Based Interactive Segmentation of Vascular Networks.
Meena, Sachin; Surya Prasath, V B; Kassim, Yasmin M; Maude, Richard J; Glinskii, Olga V; Glinsky, Vladislav V; Huxley, Virginia H; Palaniappan, Kannappan
2016-08-01
Commonly used drawing tools for interactive image segmentation and labeling include active contours or boundaries, scribbles, rectangles and other shapes. Thin vessel shapes in images of vascular networks are difficult to segment using automatic or interactive methods. This paper introduces the novel use of a sparse set of user-defined seed points (supervised labels) for precisely, quickly and robustly segmenting complex biomedical images. A multiquadric spline-based binary classifier is proposed as a unique approach for interactive segmentation using as features color values and the location of seed points. Epifluorescence imagery of the dura mater microvasculature are difficult to segment for quantitative applications due to challenging tissue preparation, imaging conditions, and thin, faint structures. Experimental results based on twenty epifluorescence images is used to illustrate the benefits of using a set of seed points to obtain fast and accurate interactive segmentation compared to four interactive and automatic segmentation approaches.
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.
Cubic Polynomials with Rational Roots and Critical Points
Gupta, Shiv K.; Szymanski, Waclaw
2010-01-01
If you want your students to graph a cubic polynomial, it is best to give them one with rational roots and critical points. In this paper, we describe completely all such cubics and explain how to generate them.
Use of Pom Pons to Illustrate Cubic Crystal Structures.
Cady, Susan G.
1997-01-01
Describes a method that uses olefin pom pons to illustrate cubic crystal structure. Facilitates hands-on examination of different packing arrangements such as hexagonal close-packed and cubic close-packed structures. (JRH)
Cubic Lienard Equations with Quadratic Damping (Ⅱ)
Institute of Scientific and Technical Information of China (English)
Yu-quan Wang; Zhu-jun Jing
2002-01-01
Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation.
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.
Energy Technology Data Exchange (ETDEWEB)
Daly, Don S.; Anderson, Kevin K.; White, Amanda M.; Gonzalez, Rachel M.; Varnum, Susan M.; Zangar, Richard C.
2008-07-14
Background: A microarray of enzyme-linked immunosorbent assays, or ELISA microarray, predicts simultaneously the concentrations of numerous proteins in a small sample. These predictions, however, are uncertain due to processing error and biological variability. Making sound biological inferences as well as improving the ELISA microarray process require require both concentration predictions and creditable estimates of their errors. Methods: We present a statistical method based on monotonic spline statistical models, penalized constrained least squares fitting (PCLS) and Monte Carlo simulation (MC) to predict concentrations and estimate prediction errors in ELISA microarray. PCLS restrains the flexible spline to a fit of assay intensity that is a monotone function of protein concentration. With MC, both modeling and measurement errors are combined to estimate prediction error. The spline/PCLS/MC method is compared to a common method using simulated and real ELISA microarray data sets. Results: In contrast to the rigid logistic model, the flexible spline model gave credible fits in almost all test cases including troublesome cases with left and/or right censoring, or other asymmetries. For the real data sets, 61% of the spline predictions were more accurate than their comparable logistic predictions; especially the spline predictions at the extremes of the prediction curve. The relative errors of 50% of comparable spline and logistic predictions differed by less than 20%. Monte Carlo simulation rendered acceptable asymmetric prediction intervals for both spline and logistic models while propagation of error produced symmetric intervals that diverged unrealistically as the standard curves approached horizontal asymptotes. Conclusions: The spline/PCLS/MC method is a flexible, robust alternative to a logistic/NLS/propagation-of-error method to reliably predict protein concentrations and estimate their errors. The spline method simplifies model selection and fitting
B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration
Institute of Scientific and Technical Information of China (English)
雷桂媛
2002-01-01
The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O(N-1) is regained by using the B-splines smoothed rejection method in importance sampling.
B-splines smoothed rejection sampling method and its applications in quasi-Monte Carlo integration
Institute of Scientific and Technical Information of China (English)
雷桂媛
2002-01-01
The rejection sampling method is one of the most popular methods used in Monte Carlo methods. It turns out that the standard rejection method is closely related to the problem of quasi-Monte Carlo integration of characteristic functions, whose accuracy may be lost due to the discontinuity of the characteristic functions. We proposed a B-splines smoothed rejection sampling method, which smoothed the characteristic function by B-splines smoothing technique without changing the integral quantity. Numerical experiments showed that the convergence rate of nearly O( N-1 ) is regained by using the B-splines smoothed rejection method in importance sampling.
PH-spline approximation for Bézier curve and rendering offset
Institute of Scientific and Technical Information of China (English)
郑志浩; 汪国昭
2004-01-01
In this paper,a G1, C1, C2 PH-spline is employed as an approximation for a given Bézier curve within error bound and further renders offset which can be regarded as an approximate offset to the Bézier curve. The errors between PH-spline and the Bézier curve, the offset to PH-spline and the offset to the given Bézier curve are also estimated. A new algorithm for constructing offset to the Bézier curve is proposed.
B-splines on 3-D tetrahedron partition in four-directional mesh
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
It is more difficult to construct 3-D splines than in 2-D case. Some results in the three directional meshes of bivariate case have been e xtended to 3-D case and corresponding tetrahedron partition has been constructed. The support of related Bsplines and their recurrent formulas on integration and differentiationdifference are obtained. The results of this paper can be extended into higher dimension spaces, and can be also used in wavelet analysis, because of the relationship between spline and wavelets.
Local atomic structure in cubic stabilized zirconia
Energy Technology Data Exchange (ETDEWEB)
Villella, P.; Conradson, S. D.; Espinosa-Faller, F. J.; Foltyn, S. R.; Sickafus, K. E.; Valdez, J. A.; Degueldre, C. A.
2001-09-01
X-ray-absorption fine structure measurements have been used to elucidate the local atomic structure of quaternary Zr, Y, Er, Ce/U cubic stabilized zirconia. These compounds display more complicated local environments than those reported for simpler binary systems. While the shortest cation-O distances are similar to those found in the binary cubic stabilized compounds, responding to the different sizes of the cations, we have identified large distortions in the first-shell oxygen distribution involving long, 2.8--3.2 {angstrom} cation-O distances that are similar to those found in the amorphous phase of zirconium. The cation-cation distributions are also found to be quite complicated (non-Gaussian) and element specific. The U-near neighbor distances are expanded relative to the Ce ions for which it substitutes, consistent with the larger size of the actinide, and the U-cation distribution is also more complicated. In terms of the effects of this substitution on the other cation sites, the local environment around Y is altered while the Zr and Er local environments remain unchanged. These results point out the importance of collective and correlated interactions between the different pairs of cations and the host lattice that are mediated by the local strain fields generated by the different cations. The presence of pair-specific couplings has not been commonly included in previous analyses and may have implications for the stabilization mechanisms of cubic zirconia.
The special symplectic structure of binary cubics
Slupinski, Marcus
2009-01-01
Let $k$ be a field of characteristic not 2 or 3. Let $V$ be the $k$-space of binary cubic polynomials. The natural symplectic structure on $k^2$ promotes to a symplectic structure $\\omega$ on $V$ and from the natural symplectic action of $\\textrm{Sl}(2,k)$ one obtains the symplectic module $(V,\\omega)$. We give a complete analysis of this symplectic module from the point of view of the associated moment map, its norm square $Q$ (essentially the classical discriminant) and the symplectic gradient of $Q$. Among the results are a symplectic derivation of the Cardano-Tartaglia formulas for the roots of a cubic, detailed parameters for all $\\textrm{Sl}(2,k)$ and $\\textrm{Gl}(2,k)$-orbits, in particular identifying a group structure on the set of $\\textrm{Sl}(2,k)$-orbits of fixed nonzero discriminant, and a purely symplectic generalization of the classical Eisenstein syzygy for the covariants of a binary cubic. Such fine symplectic analysis is due to the special symplectic nature inherited from the ambient excepti...
Method of synthesizing cubic system boron nitride
Energy Technology Data Exchange (ETDEWEB)
Yuzu, S.; Sumiya, H.; Degawa, J.
1987-10-13
A method is described for synthetically growing cubic system boron nitride crystals by using boron nitride sources, solvents for dissolving the boron nitride sources, and seed crystals under conditions of ultra-high pressure and high temperature for maintaining the cubic system boron nitride stable. The method comprises the following steps: preparing a synthesizing vessel having at least two chambers, arrayed in order in the synthesizing vessel so as to be heated according to a temperature gradient; placing the solvents having different eutectic temperatures in each chamber with respect to the boron nitride sources according to the temperature gradient; placing the boron nitride source in contact with a portion of each of the solvents heated at a relatively higher temperature and placing at least a seed crystal in a portion of each of the solvents heated at a relatively lower temperature; and growing at least one cubic system boron nitride crystal in each of the solvents in the chambers by heating the synthesizing vessel for establishing the temperature gradient while maintaining conditions of ultra-high pressure and high temperature.
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.
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.
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.
Motion of a Rigid Rod Rocking Back and Forth Cubic-Quintic Duffing Oscillators
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Karimpour, S.
2012-01-01
In this work, we implemented the first-order approximation of the Iteration Perturbation Method (IPM) for approximating the behavior of a rigid rod rocking back and forth on a circular surface without slipping as well as Cubic-Quintic Duffing Oscillators. Comparing the results with the exact...
Motion of a Rigid Rod Rocking Back and Forth Cubic-Quintic Duffing Oscillators
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Karimpour, S.
2012-01-01
In this work, we implemented the first-order approximation of the Iteration Perturbation Method (IPM) for approximating the behavior of a rigid rod rocking back and forth on a circular surface without slipping as well as Cubic-Quintic Duffing Oscillators. Comparing the results with the exact...
Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application
Institute of Scientific and Technical Information of China (English)
JIA Jin-ming; WEN Xiang-jun
2008-01-01
Inspired by the traditional Wold's nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model,a novel nonlinear partial least squares algorithm based on spline kernel(named SK-PLS)is proposed for nonlinear modeling in the presence of multicollinearity.Based on the iuner-product kernel spanned by the spline basis functions with infinite numher of nodes,this method firstly maps the input data into a high dimensional feature space,and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS"kernel"algorithms in consequence.The linear PLS in the feature space corresponds to a nonlinear PLS in the original input (primal)space.The good approximating property of spline kernel function enhances the generalization ability of the novel model,and two numerical experiments are given to illustrate the feasibility of the proposed method.
Introduction of b-splines to trajectory planning for robot manipulators
Directory of Open Access Journals (Sweden)
Per E. Koch
1988-04-01
Full Text Available This paper describes how B-splines can be used to construct joint trajectories for robot manipulators. The motion is specified by a sequence of Cartesian knots, i.e., positions and orientations of the end effector of a robot manipulator. For a six joint robot manipulator, these Cartesian knots are transformed into six sets of joint variables, with each set corresponding to a joint. Splines, represented as linear combinations of B-splines, are used to fit the sequence of joint variables for each of the six joints. A computationally very simple, recurrence formula is used to generate the 8-splines. This approach is used for the first time to establish the mathematical model of trajectory generation for robot manipulators, and offers flexibility, computational efficiency, and a compact representation.
N2 plasma etching processes of microscopic single crystals of cubic boron nitride
Tamura, Takahiro; Takami, Takuya; Yanase, Takashi; Nagahama, Taro; Shimada, Toshihiro
2017-06-01
We studied the N2 plasma etching of cubic boron nitride (cBN). We have developed experimental techniques for handling 200-µm-size single crystals for the preparation of surfaces with arbitrary crystal indexes, plasma processes, and surface analyses. We successfully prepared smooth surfaces of cBN with roughness smaller than 10 nm and found that the etching behavior was strongly influenced by the surface indexes. The morphology of the etched surfaces can be explained by the chemical stability of (111)B surfaces.