Short and Smooth Polygonal Paths

Automatic graph drawers need to compute paths among vertices of a simple polygon which besides remaining in the interior need to exhibit certain aesthetic properties. Some of these require the incorporation of some information about the polygonal shape without being too far from the actual shortest path. We present an algorithm to compute a locally convex region that “contains” the shortest Euclidean path among two vertices of a simple polygon. The region has a boundary shape that “follows” the shortest path shape. A cubic Bezier spline in the region interior provides a “short and smooth” collision free curve between the two given vertices. The obtained results appear to be aesthetically pleasant and the methods used may be of independent interest. They are elementary and implementable. Figure 7 is a sample output produced by our current implementation.