Computational geometry: an introduction
Computational geometry: an introduction
On shortest paths in polyhedral spaces
SIAM Journal on Computing
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
On shortest paths amidst convex polyhedra
SIAM Journal on Computing
SIAM Journal on Computing
Determining the separation of preprocessed polyhedra: a unified approach
Proceedings of the seventeenth international colloquium on Automata, languages and programming
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Approximate Euclidean shortest path in 3-space
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A single-exponential upper bound for finding shortest paths in three dimensions
Journal of the ACM (JACM)
On the shortest paths between two convex polyhedra
Journal of the ACM (JACM)
Approximate shortest paths and geodesic diameters on convex polytopes in three dimensions
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Practical methods for approximating shortest paths on a convex polytope in R3
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Approximating Shortest Paths on a Nonconvex Polyhedron
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Constructing approximate shortest path maps in three dimensions
Proceedings of the fourteenth annual symposium on Computational geometry
Efficiently approximating the minimum-volume bounding box of a point set in three dimensions
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computing approximate shortest paths on convex polytopes
Proceedings of the sixteenth annual symposium on Computational geometry
Time-minimal paths amidst moving obstacles in three dimensions
Theoretical Computer Science
Computing the Penetration Depth of Two Convex Polytopes in 3D
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Optimized color gamuts for tiled displays
Proceedings of the nineteenth annual symposium on Computational geometry
Sublinear geometric algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Parallel implementation of geometric shortest path algorithms
Parallel Computing - Special issue: High performance computing with geographical data
Approximating shortest path for the skew lines problem in time doubly logarithmic in 1/epsilon
Theoretical Computer Science - Algebraic and numerical algorithm
Determining approximate shortest paths on weighted polyhedral surfaces
Journal of the ACM (JACM)
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
Proceedings of the twenty-second annual symposium on Computational geometry
Shortest paths on realistic polyhedra
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Automated antenna positioning algorithms for wireless fixed-access networks
Journal of Heuristics
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Approximate Euclidean shortest paths amid convex obstacles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
A survey of geodesic paths on 3D surfaces
Computational Geometry: Theory and Applications
Approximate shortest path queries on weighted polyhedral surfaces
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Expansion-Based algorithms for finding single pair shortest path on surface
W2GIS'04 Proceedings of the 4th international conference on Web and Wireless Geographical Information Systems
Exact geodesic metric in 2-manifold triangle meshes using edge-based data structures
Computer-Aided Design
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Given a convex polytope P withn faces in R3, points s,t∈6P, and a parameter 0e≤1, we present an algorithm that constructs a path on6P from s tot whose length is at most1+edPs,t, where dPs,t is the length of the shortest path betweens andt on 6P. The algorithm runs in Onlog1/e+1/e3 time, and is relatively simple. The running time isOn+1/e3 if we only want the approximate shortest pathdistance and not the path itself. We also present an extension of thealgorithm that computes approximate shortest path distances from a givensource point on 6P to all vertices ofP.