关键词: 离散曲率, 三角网格, 平均曲率构造向量, Gauss曲率构造角

Abstract: The Meyer method of calculating discrete curvatures for triangular meshes is concise in geometry and requires relatively small amount of calculation, but there is still potential to improve its results. The concepts of mean curvature structural vector and Gauss curvature structural angle are suggested, along with their geometric significance. Based on these analyses, the improved algorithms of the Meyer method are constructed, in which the main steps are simplified and the unnecessary errors are avoided. Simulation results show that the proposed algorithms effectively improve the calculation precision and efficiency of discrete curvatures estimation for triangular meshes.

Key words: discrete curvature, triangulated grid model, mean curvature structural vector, Gauss curvature structural angle