Multiresolution analysis over triangle meshes: method and data structure

A robust and efficient algorithm is presented to build multiresolution models (MRMs) of arbitrary meshes without requirement of subdivision connectivity. To overcome the sampling difficulty of arbitrary meshes, edge contraction and vertex expansion are used as downsampling and upsampling methods. Our MRMs of a mesh are composed of a base mesh and a series of edge split operations, which are organized as a directed graph. Each split operation encodes two parts of information. One is the modification to the mesh, and the other is the dependency relation among splits. Such organization ensures the efficiency and robustness of our MRM algorithm. Examples demonstrate the functionality of our method.

准均匀B样条曲面小波分解的快速算法

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 。