SIAM Journal on Computing
Computing the geodesic diameter of a 3-polytope
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
The number of shortest paths on the surface of a polyhedron
SIAM Journal on Computing
Nonoverlap of the star unfolding
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Queries on Voronoi diagrams of moving points
Computational Geometry: Theory and Applications
Star Unfolding of a Polytope with Applications
SIAM Journal on Computing
Two-point Euclidean shortest path queries in the plane
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An Optimal Algorithm for Euclidean Shortest Paths in the Plane
SIAM Journal on Computing
Finding All Shortest Path Edge Sequences on a Convex Polyhedron
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
An Optimal-Time Algorithm for Shortest Paths on a Convex Polytope in Three Dimensions
Discrete & Computational Geometry
Approximate shortest path queries on weighted polyhedral surfaces
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Short-Cuts on star, source and planar unfoldings
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
The geodesic diameter of polygonal domains
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Fréchet distance with speed limits
Computational Geometry: Theory and Applications
Constant-time O(1) all pairs geodesic distance query on triangle meshes
SIGGRAPH Asia 2011 Sketches
Constant-time all-pairs geodesic distance query on triangle meshes
I3D '12 Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Querying two boundary points for shortest paths in a polygonal domain
Computational Geometry: Theory and Applications
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We develop algorithms to compute edge sequences, Voronoi diagrams, shortest path maps, the Fréchet distance, and the diameter of a polyhedral surface. Distances on the surface are measured by the length of a Euclidean shortest path. Our main result is a linear factor speedup for the computation of all shortest path edge sequences and the diameter of a convex polyhedral surface. This speedup is achieved with kinetic Voronoi diagrams. We also use the star unfolding to compute a shortest path map and the Fréchet distance of a non-convex polyhedral surface.