Planning a purely translational motion for a convex object in two-dimensional space using generalized Voronoi diagrams

Abstract

An O(n log n) algorithm for planning a purely translational motion for a simple convex object amidst polygonal barriers in two-dimensional space is given. The algorithm is based on a new generalization of Voronoi diagrams (similar to that proposed by Chew and Drysdale [1] and by Fortune [2]), and adapts and uses a recent technique of Yap for the efficient construction of these diagrams. © 1987 Springer-Verlag New York Inc.