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基于緊支撐徑向基函數(shù)與共軛梯度法的大規(guī)模散亂數(shù)據(jù)快速曲面插值

于秋則,  曹矩,  柳健,  田金文

于秋則, 曹矩, 柳健, 田金文. 基于緊支撐徑向基函數(shù)與共軛梯度法的大規(guī)模散亂數(shù)據(jù)快速曲面插值[J]. 電子與信息學(xué)報(bào), 2005, 27(2): 298-301.
引用本文: 于秋則, 曹矩, 柳健, 田金文. 基于緊支撐徑向基函數(shù)與共軛梯度法的大規(guī)模散亂數(shù)據(jù)快速曲面插值[J]. 電子與信息學(xué)報(bào), 2005, 27(2): 298-301.
Yu Qiu-ze, Cao Ju, Liu Jian, Tian Jin-wen. Rapid Surface Interpolation from Massive Scattered Data Using Compactly Supported Radial Basis Functions and Conjugate Gradient Method[J]. Journal of Electronics & Information Technology, 2005, 27(2): 298-301.
Citation: Yu Qiu-ze, Cao Ju, Liu Jian, Tian Jin-wen. Rapid Surface Interpolation from Massive Scattered Data Using Compactly Supported Radial Basis Functions and Conjugate Gradient Method[J]. Journal of Electronics & Information Technology, 2005, 27(2): 298-301.

基于緊支撐徑向基函數(shù)與共軛梯度法的大規(guī)模散亂數(shù)據(jù)快速曲面插值

Rapid Surface Interpolation from Massive Scattered Data Using Compactly Supported Radial Basis Functions and Conjugate Gradient Method

  • 摘要: 該文提出一種快速大規(guī)模散亂數(shù)據(jù)的曲面插值算法。在此算法中,首先采用緊支撐徑向基函數(shù)(CSRBF)作為插值基函數(shù),采用CSRBF的優(yōu)點(diǎn)是保證構(gòu)成的系數(shù)方程組是對(duì)稱正定而且系數(shù)是稀疏的。這樣可保證系數(shù)方程組一定可解而且可以減少內(nèi)存的開(kāi)銷。其次采用共軛梯度法求解大規(guī)模系數(shù)方程組。該算法在系數(shù)方程組的系數(shù)矩陣A:NN是對(duì)稱正定的情況下,最多迭代N步就可以求得方程組的解,實(shí)驗(yàn)結(jié)果表明該算法的快速性,特別適合大規(guī)模散亂數(shù)據(jù)的曲面的插值。
    Abstract: A novel algorithm for rapid surface interpolation from massive scattered data using Compactly Supported Radial Basis Functions (CSRBF) and conjugate gradient method is presented in this paper, CSRBF is used because it can make the coefficient equations symmetric positive definite (spd), and very sparse. So there must be a solver and a smat 1 storage memory are needed. In solving the system equations, iterative method is used. The conjugate gradient method is used to solve the system equations, because the method converges in at most N steps for a symmetric positive definite N by TV matrix. Experimental results using massive scattered points demonstrate the algorithm is fast. The proposed algorithm is very appropriate for surface interpolation from massive scattered points.
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  • Seungyong Lee, George wolberg, Sung Yong Shin. Scattered data Interpolation with multilevel B-splines[J].IEEE Trans. on Visualization and Computer Graphics.1998, 3(3):228-[2]Franke R, Nielson G M. Scattered data interpolation and applications: A Tutorial and Survey, Geometric Modeling:Methods and Their Application, Hagen H and Roller D, eds.,Berlin: Springer-Verlag, 1991: 131 - 160.[3]Shapiro V. Real functions for representation of rigid solids[J].Computer Aided Geometric Design.1994, 11(2):153-[4]Shepard D. A two dimensional interpolation function for irregularly spaced data. Proc. ACM 23rd Natl Conf., New York,1968:517 - 524.[5]Clough R, Tocher J. Finite element stiffness matrices for analysis of plates in bending. Proceeding Conference Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, 1965:515 - 545.[6]Hardy R. Multiquadratic equations of topography and other irregular surfaces[J].,J. Geophysical Research.1971, 76(8):1905-[7]Dyn N. Interpolation and approximation by radial and related function. Chui C, Schumaker L, Ward J, et al.. Approximation Theory VI, San Diego, Calif.: Academic Press, 1989:211 - 234.[8]Wend H. Piecewise polynomial positive definite and compactly supported radial functions of minimal degree. AICM, 1995, 4:389 - 396.[9]Morse B S. Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions, Shape modeling Conference, Proc. SMI, Geneva, Italy, May 2001:89 - 98.[10]Nikita Kojekine, Ichiro Hagiwara, Savchenko V V. Software tools using CSRBFs for processing scattered data[J].Computers Graphics.2003, 27(2):311-[11]袁亞湘,孫文瑜.最優(yōu)化理論與方法.北京:科學(xué)出版社,1997:183-199.[12]關(guān)治,陳景良.數(shù)值計(jì)算方法.北京:清華大學(xué)出版社,1990:423-430.
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  • 收稿日期:  2003-10-09
  • 修回日期:  2004-02-16
  • 刊出日期:  2005-02-19

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