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 2-manifold surface is represented by a triangle mesh TT, the geodesic metric on TT can be computed exactly using computational geometry methods. Previous work for establishing the geodesic metric on TT only supports using half-edge data structures; i.e., each edge ee in TT is split into two halves (he1,he2)(he1,he2) and each half-edge corresponds to one of two faces incident to ee. In this paper, we prove that the exact-geodesic structures on two half-edges of ee can be merged into one structure associated with ee. 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.