摘要: In this paper we discuss decomposition techniques and data reduction strategies with emphasis on piecewise polynomial curves surfaces. The main idea behind the methods is to transform object (curve or surface) into a sequence of components in order analyze original multiresolutional setting. Data obtained by only keeping coefficients from each component which give “significant” contributions reconstruction original. A new method combining knot removal given. We present several examples show special effect decomposition.
sci-hub.st 参考文章(14)
Tom Lyche, Discrete B-Splines and Conversion Problems Springer, Dordrecht. pp. 117- 134 ,(1990) , 10.1007/978-94-009-2017-0_4
M. Dæhlen, T. Lyche, Box Splines and Applications Geometric Modeling. pp. 35- 93 ,(1991) , 10.1007/978-3-642-76404-2_3
Stephane G. Mallat, Multiresolution approximations and wavelet orthonormal bases of L^2(R) Transactions of the American Mathematical Society. ,vol. 315, pp. 69- 87 ,(1989) , 10.1090/S0002-9947-1989-1008470-5
Welch, A Technique for High-Performance Data Compression IEEE Computer. ,vol. 17, pp. 8- 19 ,(1984) , 10.1109/MC.1984.1659158
T. LYCHE, K. MØRKEN, A Data-Reduction Strategy for Splines with Applications to the Approximation of Functions and Data Ima Journal of Numerical Analysis. ,vol. 8, pp. 185- 208 ,(1988) , 10.1093/IMANUM/8.2.185
W. B. Pennebaker, J. L. Mitchell, G. G. Langdon, R. B. Arps, An overview of the basic principles of the Q-Coder adaptive binary arithmetic coder IBM Journal of Research and Development. ,vol. 32, pp. 717- 726 ,(1988) , 10.1147/RD.326.0717
Tom Lyche, Knut Mørken, Knot removal for parametric B-spline curves and surfaces Computer Aided Geometric Design. ,vol. 4, pp. 217- 230 ,(1987) , 10.1016/0167-8396(87)90013-6
Erlend Arge, Morten Dæhlen, Aslak Tveito, Box spline interpolation; a computational study Journal of Computational and Applied Mathematics. ,vol. 44, pp. 303- 329 ,(1992) , 10.1016/0377-0427(92)90003-G
Wolfgang Dahmen, Charles A. Micchelli, Subdivision algorithms for the generation of box spline surfaces Computer Aided Geometric Design. ,vol. 1, pp. 115- 129 ,(1984) , 10.1016/0167-8396(84)90025-6
Elaine Cohen, Tom Lyche, Richard Riesenfeld, Discrete box splines and refinement algorithms Computer Aided Geometric Design. ,vol. 1, pp. 131- 148 ,(1984) , 10.1016/0167-8396(84)90026-8