Jim Stewart 1 Shortest Path Problems

The topic of this lecture is the application of triangulations to shortest path problems. Only simple polygons will be considered. Given two points inside a polygon, the goal is to find the shortest path lying inside the polygon between the two points; see Fig. 1. One can think of the shortest path as a taut string connecting the two points. We begin with some definitions. Let P be a simple polygon with n vertices. Then π(p, q) is the Euclidean shortest path inside P connecting two points p and q inside P. Also, d(p, q) = |π(p, q)|, which is the length of π(p, q). d(p, q) is a metric and is more commonly referred to as the geodesic distance.