On shortest paths in polyhedral spaces
SIAM Journal on Computing
Proximity and reachability in the plane.
Proximity and reachability in the plane.
Path planning in 0/1/ weighted regions with applications
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
On maximum flows in polyhedral domains
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
The weighted region problem: finding shortest paths through a weighted planar subdivision
Journal of the ACM (JACM)
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
On the shortest paths between two convex polyhedra
Journal of the ACM (JACM)
BUSHWHACK: An Approximation Algorithm for Minimal Paths through Pseudo-Euclidean Spaces
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
New lower bound techniques for robot motion planning problems
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Sculpting potential fields in the BVP path planner
ROBIO'09 Proceedings of the 2009 international conference on Robotics and biomimetics
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We present an algorithm for determining the shortest path between a source and a destination through a planar subdivision in which each region has an associated weight. Distances are measured according to a weighted Euclidean metric: Each region of the subdivision has associated with it a weight, and the weighted distance between two points in a convex region is the product of the corresponding weight and the Euclidean distance between them. Our algorithm runs in time &Ogr;(n7 L) and requires &Ogr;(n3) space, where n is the number of edges of the subdivision, and L is the precision of the problem instance (including the number of bits in a user-specified tolerance ∈, which is the percentage the solution is allowed to differ from an optimal solution). The algorithm uses the fact that shortest paths obey Snell's Law of Refraction at region boundaries, a local optimality property of shortest paths that is well-known from the analogous optics model.