Minimizing turns for discrete movement in the interior of a polygon

The problem of movement in two-dimensional Euclidean space that is bounded by a (not necessarily convex) polygon is considered. Movement is restricted to be along straight line segments, and the objective is to minimize the number of bends or "turns" in a path. Most past work on this problem has addressed the movement between a source point and a destination point. An O(n \ast \log (n)) time algorithm is presented for computing a data structure that represents the minimal-turn paths from a source point to all other points in the polygon. An advantage of this algorithm is that it uses relatively simple data structures and is practical to implement. Another advantage is that it is easily generalized to accommodate the movement of a disk of radius r > 0.