• 计算机视觉与虚拟现实 •

### 球面凸类图形Delaunay三角剖分再分算法及其收敛性分析

1. 昆明理工大学 理学院, 昆明 650500
• 收稿日期:2017-06-29 修回日期:2017-09-04 出版日期:2017-12-10 发布日期:2017-12-18
• 通讯作者: 夏俊
• 作者简介:夏俊(1991-),男,安徽合肥人,硕士研究生,主要研究方向:计算几何;李映华(1978-),男,广东梅州人,讲师,博士,主要研究方向:计算几何。
• 基金资助:
昆明理工大学自然科学基金资助项目（KKSY201507066）。

### Delaunay triangulation subdivision algorithm of spherical convex graph and its convergence analysis

1. School of Science, Kunming University of Science and Technology, Kunming Yunnan 650500, China
• Received:2017-06-29 Revised:2017-09-04 Online:2017-12-10 Published:2017-12-18
• Supported by:
This work is partially supported by the Natural Science Foundation of Kunming University of Science and Technology (KKSY201507066).

Abstract: When calculating curved Ricci Flow, non-convergence emerges due to the existence of undersized angles in triangular meshes. Concerning the problem of non-convergence, a Delaunay triangulation subdivision algorithm of spherical convex graph of enhancing the minimum angle was proposed. First of all, the Delaunay triangulation subdivision algorithm of spherical convex graph was given. The proposed algorithm had two key operations:1) if a Delaunay minor arc was "encroached upon", a midpoint of the Delaunay minor arc was added to segment the Delaunay minor arc; 2) if there was a "skinny" spherical triangle, it was disassembled by adding the center of minor circle of its circumscribed sphere. Then, the convergence criteria of the proposed algorithm was explored on local feature scale and an upper-bound formula of the output vertex was given. The grids based on the output of experiment show that the spherical triangle generated by the grids of the proposed algorithm has no narrow angle, so it is suitable for calculating Ricci Flow.