准均匀B样条曲面小波分解的快速算法

Fast algorithm for wavelet decomposition of quasi-uniform B-spline surfaces

准均匀 B样条曲线小波分解与重构的快速算法可以拓广到张量积 B样条曲面 ,而曲面小波分解与重构的快速算法是曲面多分辨造型的关键。该文在介绍准均匀 B样条曲线小波分解快速算法的基础上 ,建立张量积 B样条曲面多分辨率表示的概念 ,并用数学形式严格描述曲面小波分解与重构的快速算法。该算法具有线性计算复杂度 ,是研究曲面多分辨编辑、光顺与显示的基础 。

A fast algorithm for wavelet decomposition and reconstruction of quasi uniform bicubic B spline surfaces is a key part of B spline multiresolution modeling. This paper introduces some basic concepts for multiresolution representation of B spline surfaces and gives a fast algorithm for wavelet decomposition and reconstruction of quasi uniform B spline surfaces. The algorithm is precisely described by mathematics, and it can be performed in linear time. It is the basis of the multiresolution editing, fairing and displaying of B spline surfaces and is useful for engineers engaged in computer aided geometry design (CAGD).