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

A natural metric in 2-manifold surfaces is to use geodesic distance. If a 2manifold 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 speeded up by pruning unnecessary wedges during the wedge propagation process; (4) The storage of the MMP algorithm is reduced since less 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 44% running time and 29% storage on average.