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Approximate ESPs on Surfaces of Polytopes Using a Rubberband Algorithm
Advances in Image and Video Technology
Let p and q be two points on the surface of a polytope Π. This paper provides a rubberband algorithm for computing a Euclidean shortest path between p and q (a so-called surface ESP) that is contained on the surface of Π. The algorithm has κ1(ε)·κ2(ε)·O(n 2 ) time complexity, where n is the number of vertices of Π, κi(ε) = (L0 i −Li)/ε, for the true length Li of some shortest path with initial (polygonal path) length L0 i (used when approximating this shortest path), for i = 1, 2. Rubberbanddoi:10.1007/978-3-540-77129-6_23 dblp:conf/psivt/LiKF07 fatcat:pvnmn5qlwzafxnasjciczc6t5a