Euclidean Shortest Paths in a Simple Polygon

Let p and q be two points in a simple polygon Π. This chapter provides two rubberband algorithms for computing a shortest path between p and q that is contained in Π. The two algorithms use previously known results on triangular or trapezoidal decompositions of simple polygons, and have either O (n) or O (n log n) time complexity (where the super-linear time complexity is only due to preprocessing, i.e. for the trapezoidal decomposition of the simple polygon Π).