自适应Catmull-Clark细分算法

提出了一种基于Catmull-Clark细分算法的自适应算法,自适应过程由离散点的曲率C来控制,计算多面体中各离散点的曲率,与已给定的曲率值相比较后,得出的可继续细分的点,边,面和不可继续细分的点,边,面用来作为下一次细分的依据,按该步骤迭代可实现局部细化,采用原始Catmull-Clark细分算法,细分过程中网格数量会快速增长;而自适应算法通过选取理想的C值,能够大幅度抑制细分过程中网格数量的快速增长,并能获得与原始算法光顺程度基本一致的曲面。

Adaptive refinements in Catmull-Clark subdivision scheme

An adaptive refinement method based on Catmull-Clark subdivision scheme is presented in the paper. Adaptation process is controlled by the curvature of discrete vertices( C ). Calculating curvature of all the vertices of the whole polyhedron and comparing the calculation with the given curvature, the scheme can determine whether the points, lines and faces enroll in the further subdivision process or not. The local refinements can be realized by repeating the process. The number of meshes grows quickly during the subdivision process when adopting the original scheme. Given a reasonable curvature( C ), the adaptive refinement can remarkably decrease the number of meshes and keep the good fairness of Catumll-Clark surfaces with fewer meshes.