Dimension of spline spaces with highest order smoothness over hierarchical T-meshes

详细信息    查看全文

• 作者：Meng Wu ; Jiansong Deng ; ^{dengjs@ustc.edu.cn} ; Falai Chen
• 关键词：Dimension formula ; Spline space ; T-mesh ; Homology
• 刊名：Computer Aided Geometric Design
• 出版年：2013
• 出版时间：January, 2013
• 年：2013
• 卷：30
• 期：1
• 页码：20-34
• 全文大小：405 K

文摘

This paper discusses the dimension of spline spaces over a certain type of hierarchical T-mesh. The key step is to establish a bijection between the spline space and a univariate spline space defined in terms of the l-edges of the extended T-mesh with respect to bi-degree . We decompose the univariate spline space into an isomorphic direct sum using the theory of short exact sequences from homological algebra. Using this decomposition, we can obtain a formula for the dimension of the spline space over the required type of hierarchical T-mesh. We also construct a set of basis functions for the spline space.