Path Finding in Free Space Using Sinusoidal Transforms: III

Abstract

This paper investigates the application of a system of spatial representation, called the sinusoidal representation scheme, to the problem of finding a path between two points in a plane strewn with a finite collection of convex obstacles. The main thrust of the argument is that the sinusoidal representation scheme permits the ready extraction of a resructed set of candidates for the shortest path between two points. The structure of the paper is as follows. First, we define a restricted set of paths between a given pair of points which is guaranteed to include all optimal paths. Secondly, we present in detail the sinusoidal representation scheme. Finally, we show how the aforementioned set of paths can be read off from the sinusoidal representation of the scene in question.