The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Computational geometry.
Storing the subdivision of a polyhedral surface
SCG '86 Proceedings of the second annual symposium on Computational geometry
There is a planar graph almost as good as the complete graph
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
Compliant motion planning with geometric models
SCG '87 Proceedings of the third annual symposium on Computational geometry
A methodology of autonomous navigation in 3-D space under location uncertainty
IEA/AIE '88 Proceedings of the 1st international conference on Industrial and engineering applications of artificial intelligence and expert systems - Volume 1
A bibliography of quantifier elimination for real closed fields
Journal of Symbolic Computation
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
New methods for computing visibility graphs
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Shortest paths in the plane with polygonal obstacles
Journal of the ACM (JACM)
A single-exponential upper bound for finding shortest paths in three dimensions
Journal of the ACM (JACM)
Rectilinear shortest paths with rectangular barriers
SCG '85 Proceedings of the first annual symposium on Computational geometry
Planning the shortest path for a disc in O(n2log n) time
SCG '85 Proceedings of the first annual symposium on Computational geometry
New lower bound techniques for robot motion planning problems
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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We consider the problem of computing the shortest path between two points in two- or three-dimensional space bounded by polyhedral surfaces. In the 2-D case the problem is easily solved in time O(n2 log n).In the general 3-D case the problem is quite hard to solve, and is not even discrete; we present a doubly-exponential procedure for solving the discrete subproblem of determining the sequence of boundary edges through which the shortest path passes. The main result of this paper involves a favorable special case of the 3-D shortest path problem, namely that of finding the shortest path between two points along the surface of a convex polyhedron. We analyze this problem and solve it in time O(n3 log n).