The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical prop...The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.展开更多
In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dim...In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.展开更多
A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(F...A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.展开更多
Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermit...Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set, and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the short- coming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a gl-cubic Hermite in- terpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global G2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an al- ternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15（1） （2007）, pp. 41-53].展开更多
For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon'...For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics.展开更多
By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula.And the corresponding error estimates are also provided.
The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonse...The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are also given. In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.展开更多
An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlik...An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation,the present method employs different surface points sets and influence radius for each volume point movement,accompanied with efficient geometry searching strategy.The deformed surface points,also called Control Points (CPs),are stored in each processor.The displacement of spatial points is interpolated by using only 20-50 nearest control points,and the local influence radius is set to 5-20 times the maximum displacement of control points.To shorten the searching time for the nearest control point clouds,an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique.Besides,an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications.Three 3D cases,including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements,are used to test the present mesh deformation method.The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 450 and more than 80% parallel efficiency with 1024 MPI processors.In addition,the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.展开更多
The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal ...The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal dimension of L(x).展开更多
The object of this short survey is to revive interest in the technique of fractal interpolation. In order to attract the attention of numerical analysts, or rather scientific community of researchers applying various ...The object of this short survey is to revive interest in the technique of fractal interpolation. In order to attract the attention of numerical analysts, or rather scientific community of researchers applying various approximation techniques, the article is interspersed with comparison of fractal interpolation functions and diverse conventional interpolation schemes. There are multitudes of interpolation methods using several families of functions: polynomial, exponential, rational, trigonometric and splines to name a few. But it should be noted that all these conventional nonrecursive methods produce interpolants that are differentiable a number of times except possibly at a finite set of points. One of the goals of the paper is the definition of interpolants which are not smooth, and likely they are nowhere differentiable. They are defined by means of an appropriate iterated function system. Their appearance fills the gap of non-smooth methods in the field of approximation. Another interesting topic is that, if one chooses the elements of the iterated function system suitably, the resulting fractal curve may be close to classical mathematical functions like polynomials, exponentials, etc. The authors review many results obtained in this field so far, although the article does not claim any completeness. Theory as well as applications concerning this new topic published in the last decade are discussed. The one dimensional case is only considered.展开更多
This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to...This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.展开更多
Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function.In this paper,we first present an example to explain a relationship betwee...Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function.In this paper,we first present an example to explain a relationship between iteration procedure and fractal function.Then we discuss conditions that vertical scaling factors must obey in one typical case.展开更多
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their...In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.展开更多
The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen-...The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.展开更多
A new interpolation algorithm for Head-Related Transfer Function （HRTF） is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical ha...A new interpolation algorithm for Head-Related Transfer Function （HRTF） is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition （SVD） is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance.展开更多
Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the com...Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.展开更多
The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability ...The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable.展开更多
Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling fa...Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket （SG）. As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5 ：△=0 on SG ／ {q1, q2, q3}, and u（qi）=ai, i = 1, 2, 3, where qi, i=1, 2, 3, are boundary points of SG.展开更多
In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by ...In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.展开更多
基金supported by the National Science and Technology Major Projects(No.2011ZX05020-008)Well Logging Advanced Technique and Application Basis Research Project of Petrochina Company(No.2011A-3901)
文摘The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.
基金Supported by the National Natural Science Foundation of China and the Natural Science Foundtion of Zhejiang Province.
文摘In this paper, a new iterated function system consisting of non-linear affinemaps is constructed. We investigate the fractal interpolation functions generated bysuch a system and get its differentiability, its box dimension, its packing dimension,and a lower bound of its Hansdorff dimension.
基金co-supported by the National Key R&D Program of China(Nos.2018YFF01012401-05)the National Natural Science Foundation of China(No.51975243)+2 种基金Jilin Provincial Department of Education(No.JJKH20180084KJ),Chinathe Fundamental Research Funds for the Central Universities and Jilin Provincial Department of Science&Technology Fund Project,China(Nos.20170101043JC and 20180520072JH)Graduate Innovation Fund of Jilin University,China(No.101832018C184).
文摘A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.
基金partially supported by the CSIR India(Grant No.09/084(0531)/2010-EMR-I)the SERC,DST India(Project No.SR/S4/MS:694/10)
文摘Hermite interpolation is a very important tool in approximation theory and nu- merical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set, and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the short- coming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a gl-cubic Hermite in- terpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global G2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an al- ternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15（1） （2007）, pp. 41-53].
文摘For Hermite-Birkhoff interpolation of scattered multidumensional data by radial basis function (?),existence and characterization theorems and a variational principle are proved. Examples include (?)(r)=r^b,Duchon's thin-plate splines,Hardy's multiquadrics,and inverse multiquadrics.
基金Supported by the Education Department of Zhejiang Province (Y200806015)
文摘By utilizing symmetric functions,this paper presents explicit representations for Hermite interpolation and its numerical differentiation formula.And the corresponding error estimates are also provided.
文摘The authors introduce nonseparable scaling function interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are also given. In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.
基金supported by the National Key Research and Development Program of China (No.2016YFB0200701)the National Natural Science Foundation of China (Nos. 11532016 and 91530325)
文摘An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation,the present method employs different surface points sets and influence radius for each volume point movement,accompanied with efficient geometry searching strategy.The deformed surface points,also called Control Points (CPs),are stored in each processor.The displacement of spatial points is interpolated by using only 20-50 nearest control points,and the local influence radius is set to 5-20 times the maximum displacement of control points.To shorten the searching time for the nearest control point clouds,an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique.Besides,an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications.Three 3D cases,including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements,are used to test the present mesh deformation method.The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 450 and more than 80% parallel efficiency with 1024 MPI processors.In addition,the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.
文摘The purpose of this paper is to prove a Holder property about the fractal interpolation function L(x), ω(L,δ)=O(δ~α), and an approximate estimate |f-L|≤2{α(h)+||f||/1-h^(2-D)·h^(2-D)}, where D is a fractal dimension of L(x).
文摘The object of this short survey is to revive interest in the technique of fractal interpolation. In order to attract the attention of numerical analysts, or rather scientific community of researchers applying various approximation techniques, the article is interspersed with comparison of fractal interpolation functions and diverse conventional interpolation schemes. There are multitudes of interpolation methods using several families of functions: polynomial, exponential, rational, trigonometric and splines to name a few. But it should be noted that all these conventional nonrecursive methods produce interpolants that are differentiable a number of times except possibly at a finite set of points. One of the goals of the paper is the definition of interpolants which are not smooth, and likely they are nowhere differentiable. They are defined by means of an appropriate iterated function system. Their appearance fills the gap of non-smooth methods in the field of approximation. Another interesting topic is that, if one chooses the elements of the iterated function system suitably, the resulting fractal curve may be close to classical mathematical functions like polynomials, exponentials, etc. The authors review many results obtained in this field so far, although the article does not claim any completeness. Theory as well as applications concerning this new topic published in the last decade are discussed. The one dimensional case is only considered.
文摘This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.
文摘Parameter identification problem is one of essential problem in order to model effectively experimental data by fractal interpolation function.In this paper,we first present an example to explain a relationship between iteration procedure and fractal function.Then we discuss conditions that vertical scaling factors must obey in one typical case.
文摘In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.
文摘The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.
基金Supported by Shanghai Natural Science Foundation, Shanghai Leading Academic Discipline Project, and STCSM of China (No. 08ZR1408300, S30108, and 08DZ2231100)
文摘A new interpolation algorithm for Head-Related Transfer Function （HRTF） is proposed to realize 3D sound reproduction via headphones in arbitrary spatial direction. HRTFs are modeled as a weighted sum of spherical harmonics on a spherical surface. Truncated Singular Value Decomposition （SVD） is adopted to calculate the weights of the model. The truncation number is chosen according to Frobenius norm ratio and the partial condition number. Compared with other interpolated methods, our proposed approach not only is continuous but exploits global information of available directions. The HRTF from any desired direction can be and interpolated results demonstrate that our obtained more accurately and robustly. Reconstructed proposed algorithm acquired better performance.
基金Supported by the National Natural Science Foundation of China (No.60875046)by Program for Changjiang Scholars and Innovative Research Team in University(No.IRT1109)+5 种基金the Key Project of Chinese Ministry of Education (No.209029)the Program for Liaoning Excellent Talents in University(No.LR201003)the Program for Liaoning Science and Technology Research in University (No.LS2010008,2009S008,2009S009,LS2010179)the Program for Liaoning Innovative Research Team in University(Nos.2009T005,LT2010005,LT2011018)Natural Science Foundation of Liaoning Province (201102008)by "Liaoning BaiQianWan Talents Program(2010921010,2011921009)"
文摘Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.
文摘The sufficient conditions of Holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable.
基金Supported by the National Natural Science Foundation of China(11271327)Zhejiang Provincial National Science Foundation of China(LR14A010001)
文摘Abstract. In this paper, we first characterize the finiteness of fractal interpolation functions （FIFs） on post critical finite self-similar sets. Then we study the Laplacian of FIFs with uniform vertical scaling factors on the Sierpinski gasket （SG）. As an application, we prove that the solution of the following Dirichlet problem on SG is a FIF with uniform vertical scaling factor 1/5 ：△=0 on SG ／ {q1, q2, q3}, and u（qi）=ai, i = 1, 2, 3, where qi, i=1, 2, 3, are boundary points of SG.
文摘In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.
