Guaranteed intersection-free polygon morphing

Abstract

We present a method for naturally and continuously morphing two simple planar polygons with corresponding vertices in a manner that guarantees that the intermediate polygons are also simple. This contrasts with all existing polygon morphing schemes who cannot guarantee the non-self-intersection property on a global scale, due to the heuristics they employ. Our method achieves this property by reducing the polygon morphing problem to the problem of morphing compatible planar triangulations of corresponding point sets, which is performed by interpolating vertex barycentric coordinates instead of vertex locations. The reduction involves compatibly triangulating simple polygons and polygons with a single hole. We show how to achieve this using only a small number of extra (Steiner) vertices.