高阶中心差分偏移量方法构造细分求和规则阶数问题
Maximal Sum Rule Orders of Subdivision Schemes Based on High-Order Central Difference Type Offset Vectors
摘要:
曲线细分是曲线造型的有力工具。采用添加差分形式的偏移量是构造细分格式的一种重要方法。本文讨论了采用高阶中心差分形式的偏移量所能够构造的细分格式求和规则的最高阶数问题。
Abstract:
Subdivision method is a powerful tool for curve modeling. A popular method to construct a new subdivision scheme is to add central difference type offset vector to the initial subdivision scheme. This paper investigates maximal orders of sum rule of subdivisions constructed from high-order central difference type offset vectors.
参考文献
|
[1]
|
Maillot, J. and Stam, J. (2001) A Unified Subdivision Scheme for Polygonal Modeling. Computer Graphics Forum, 20, 471-479.
[Google Scholar] [CrossRef]
|
|
[2]
|
Lin, S., et al. (2013) A New Interpolation Subdivision Scheme for Triangle/Quad Mesh. Graphical Models, 75, 247-254.
[Google Scholar] [CrossRef]
|
|
[3]
|
Pan, J., Chen, K. and Chen, Q. (2012) Shape-Controlled Ternary Interpolating Subdivision Scheme Based on Approximating Subdivision. 2012 IEEE 4th International Conference on Digital Home (ICDH), 23-25 November 2012, Guangzhou.
[Google Scholar] [CrossRef]
|
|
[4]
|
檀结庆, 童广悦, 张莉. 基于插值细分的逼近细分法[J]. 计算机辅助设计与图形学学报, 2015(7): 1162-1166.
|
|
[5]
|
Luo, Z. and Qi, W. (2013) On Interpolatory Subdivision from Approximating Subdivision Scheme. Applied Mathematics and Computation, 220, 339-349.
[Google Scholar] [CrossRef]
|
|
[6]
|
Jiang, Q.T., Oswald, P. and Riemenschneider, S.D. (2003) Square Root 3-Subdivision Schemes: Maximal Sum Rule Orders. Constructive Approximation, 19, 437-463.
[Google Scholar] [CrossRef]
|
|
[7]
|
Han, B. and Jia, R.Q. (1998) Optimal Interpolatory Subdivision Schemes in Multidimensional Spaces. SIAM Journal on Numerical Analysis, 36, 105-124.
[Google Scholar] [CrossRef]
|
|
[8]
|
亓万锋, 王金玲. 偏移量构造细分格式的最高求和规则[J]. 辽宁师范大学学报(自然科学版), 2017, 40(1): 14-19.
|