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 halfedges
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 onthe-
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.