Multiresolution analysis over triangles, based on quadratic Hermite interpolation

被引:18
作者
Dæhlen, M [1 ]
Lyche, T [1 ]
Morken, K [1 ]
Schneider, R [1 ]
Seidel, HP [1 ]
机构
[1] Univ Oslo, Dept Informat, N-0316 Oslo, Norway
关键词
multivariate splines; triangulations; wavelets;
D O I
10.1016/S0377-0427(00)00373-3
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Given a triangulation T of R-2, a recipe to build a spline space S(T) over this triangulation, and a recipe to refine the triangulation T into a triangulation T', the question arises whether S(T) subset of S(T'), i.e., whether any spline surface over the original triangulation T can also be represented as a spline surface over the refined triangulation T'. In this paper we will discuss how to construct such a nested sequence of spaces based on Powell-Sabin 6-splits for a regular triangulation. The resulting spline space consists of piecewise C-1-quadratics, and refinement is obtained by subdividing every triangle into four subtriangles at the edge midpoints. We develop explicit formulas for wavelet transformations based on quadratic Hermite interpolation, and give a stability result with respect to a natural norm. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:97 / 114
页数:18
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