C1 cubic splines on Powell-Sabin triangulations

被引：12
|
作者：
Groselj, Jan [1 ]
krajnc, Marjeta [1 ,2 ]
机构：
[1] Univ Ljubljana, FMF, Ljubljana, Slovenia
[2] IMFM, Ljubljana, Slovenia
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 272卷
关键词：
Nested spline spaces; Powell Sabin triangulation; Normalized B-splines; Control structure; QUASI-INTERPOLANTS; CONSTRUCTION; TRIANGLES; SPACE;
D O I：
10.1016/j.amc.2015.07.013
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A bivariate C-1 cubic spline space on a triangulation with Powell Sabin refinement which extends the well-known C-1 quadratic spline space and has a nested structure is introduced. A construction of a locally supported basis that forms a partition of unity is presented based on choosing particular triangles and line segments in the domain. Further, it is shown how these objects can be determined in order to obtain nonnegative basis functions under a natural restriction On the Powell-Sabin refinement. Geometrically intuitive B-spline representation is proposed which makes these splines a useful tool for CAGD applications. (C) 2015 Elsevier Inc. All rights reserved.
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页码：114 / 126
页数：13
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