全局各向异性四边形主导网格重建方法

摘要

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡.为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格.重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样；再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除；如此循环,直至达到理想的采样密度.该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征.同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格.%This paper proposes an anisotropic quad-dominant remeshing algorithm suitable for meshes of arbitrary topology. It takes an approach to the challenging problem of obtaining an anisotropic quad-dominant mesh. The method consists of operations that sample surface geometry by dense principle curvature lines and sort curvature-lines by variations of surface normal and volume related to them. The anisotropic sampling of curvature lines is then obtained by implementing a prioritization scheme of curvature lines elimination. The strategy is simple and straightforward to implement. It is flexible to produce anisotropic quad-dominant meshes ranging from dense to coarse too. The resulting meshes exhibit better anisotropic distribution than comparable methods while maintaining high geometric fidelity.