SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating shortest paths on a convex polytope in three dimensions
Journal of the ACM (JACM)
Designing a data structure for polyhedral surfaces
Proceedings of the fourteenth annual symposium on Computational geometry
Efficient computation of geodesic shortest paths
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Constructing Approximate Shortest Path Maps in Three Dimensions
SIAM Journal on Computing
Practical methods for approximating shortest paths on a convex polytope in R3
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Computing approximate shortest paths on convex polytopes
Proceedings of the sixteenth annual symposium on Computational geometry
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Handling degenerate cases in exact geodesic computation on triangle meshes
The Visual Computer: International Journal of Computer Graphics
Edge-Based Data Structures for Solid Modeling in Curved-Surface Environments
IEEE Computer Graphics and Applications
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Industrial geometry: recent advances and applications in CAD
Computer-Aided Design
Construction of Iso-Contours, Bisectors, and Voronoi Diagrams on Triangulated Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
The complexity of geodesic Voronoi diagrams on triangulated 2-manifold surfaces
Information Processing Letters
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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 (he"1,he"2) 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.