A New Method for the Morph of Planar Polygons Based on Shape Feature

Abstract

A shape feature-based and intersection-free method for morphing two planar simple polygons with corresponding vertices is presented. Based on the convexity-preserving morph of planar convex polygons and the convexity preserving morph of compatible planar triangulations with different convex boundaries, we present the method in this paper for the morph of two simple planar polygons which embeds the source and target polygons in the compatible planar triangulations whose boundaries are the boundaries of the magnified convex hull of the polygons respectively, then morphs the triangulations with the convexity-preserving method. In contrast with the existing intersection-free method which embeds the polygons in the compatible planar triangulations with identical convex boundaries, our method takes into consideration the geometric contours as well as the differences of the source and target polygons, so the morph is possibly more natural, on the other hand, the algorithm for compatibly triangulating the polygons with a single hole in our method uses further less Steiner vertices, so the efficiency is improved greatly.