Morphing Simple Polygons

In this paper we investigate the problem of morphing (i.e., continuously deforming) one simple polygon into another. We assume that our two initial polygons have the same number of sides n , and that corresponding sides are parallel. We show that a morph is always possible through an interpolating simple polygon whose n sides vary but stay parallel to those of the two original ones. If we consider a uniform scaling or translation of part of the polygon as an atomic morphing step, then we show that O(n log n) such steps are sufficient for the morph. Furthermore, the sequence of steps can be computed in O(n log n) time. Received May 25, 1999, and in revised form November 15, 1999.