Partitioning a polygonal region into trapezoids
Journal of the ACM (JACM)
On shortest paths amidst convex polyhedra
SCG '86 Proceedings of the second annual symposium on Computational geometry
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On the shortest paths between two convex polyhedra
Journal of the ACM (JACM)
Decomposing polygonal regions into convex quadrilaterals
SCG '85 Proceedings of the first annual symposium on Computational geometry
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
The Power of Non-Rectilinear Holes
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
On shortest paths in polyhedral spaces
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
The complexity of elementary algebra and geometry
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Approximating shortest paths on a convex polytope in three dimensions
Proceedings of the twelfth annual symposium on Computational geometry
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)
Constructing approximate shortest path maps in three dimensions
Proceedings of the fourteenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
Time-minimal paths amidst moving obstacles in three dimensions
Theoretical Computer Science
Movement Planning in the Presence of Flows
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Approximate Euclidean shortest paths amid convex obstacles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A Genetic Algorithm for Shortest Path Motion Problem in Three Dimensions
ICIC '07 Proceedings of the 3rd International Conference on Intelligent Computing: Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence
Automatic generation of computeranimation: using AI for movie animation
Automatic generation of computeranimation: using AI for movie animation
Approximate ESPs on surfaces of polytopes using a rubberband algorithm
PSIVT'07 Proceedings of the 2nd Pacific Rim conference on Advances in image and video technology
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We derive a single-exponential time upper bound for finding the shortest path between two points in 3-dimensional Euclidean space with (nonnecessarily convex) polyhedral obstacles. Prior to this work, the best known algorithm required double-exponential time. Given that the problem is known to be PSPACE-hard, the bound we present is essentially the best (in the worst-case sense) that can reasonably be expected.