Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures

• Published in: Computer aided design Vol. 45; no. 3; pp. 695 - 704
• Main Author: Liu, Yong-Jin
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.03.2013
• Subjects: 2-manifold; Algorithms; Computer aided design; Data structures; Design engineering; Edge-based data structure; Exact geodesic; Mathematical analysis; Running; Triangle meshes; Triangles; Wedges; Triangle meshes; 2-manifold; Exact geodesic; Edge-based data structure
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/j.cad.2012.11.005

A natural metric in 2-manifold surfaces is to use geodesic distance. If a 2-manifold surface is represented by a triangle mesh T, the geodesic metric on T can be computed exactly using computational geometry methods. Previous work for establishing the geodesic metric on T only supports using half-edge data structures; i.e., each edge e in T is split into two halves (he1,he2) and each half-edge corresponds to one of two faces incident to e. In this paper, we prove that the exact-geodesic structures on two half-edges of e can be merged into one structure associated with e. Four merits are achieved based on the properties which are studied in this paper: (1) Existing CAD systems that use edge-based data structures can directly add the geodesic distance function without changing the kernel to a half-edge data structure; (2) To find the geodesic path from inquiry points to the source, the MMP algorithm can be run in an on-the-fly fashion such that the inquiry points are covered by correct wedges; (3) The MMP algorithm is sped up by pruning unnecessary wedges during the wedge propagation process; (4) The storage of the MMP algorithm is reduced since fewer wedges need to be stored in an edge-based data structure. Experimental results show that when compared to the classic half-edge data structure, the edge-based implementation of the MMP algorithm reduces running time by 44% and storage by 29% on average. ► We prove exact-geodesic structures on half-edges can be merged into one edge-based structure. ► Practical merging operations using edge-based data structure are presented. ► The merged structure saves storage and simplifies the computation of exact geodesic metric.