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Volume 27 Issue 2
Feb.  2005
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Qinghua ZHANG, Guohong PANG, Xintai LI, Xueqiu ZHANG. Optimal Granularity Selection Method Based on Cost-sensitive Sequential Three-way Decisions[J]. Journal of Electronics & Information Technology, 2021, 43(10): 3001-3009. doi: 10.11999/JEIT200821
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.

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

  • Received Date: 2003-10-09
  • Rev Recd Date: 2004-02-16
  • Publish Date: 2005-02-19
  • 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.
  • 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]袁亚湘,孙文瑜.最优化理论与方法.北京:科学出版社,1997:183-199.[12]关治,陈景良.数值计算方法.北京:清华大学出版社,1990:423-430.
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