Physically based morphing of point‐sampled surfaces

This paper presents an innovative method for naturally and smoothly morphing point‐sampled surfaces via dynamic meshless simulation on point‐sampled surfaces. While most existing literature on shape morphing emphasizes the issue of finding a good correspondence map between two object representations, this research primarily investigates the challenging problem of how to find a smooth, physically‐meaningful transition path between two homeomorphic point‐set surfaces. We analyze the deformation of surface involved in the morphing process using concepts in differential geometry and continuum mechanics. The morphing paths can be determined by optimizing an energy functional, which characterizes the intrinsic deformation of the surface away from its rest shape. As demonstrated in the examples, our method automatically produces a series of natural and physically‐plausible in‐between shapes, which greatly alleviates the shrinking, stretching, and self‐intersection problems that often occur when linear interpolation is employed for the morphing of two objects. We envision that our new technique will continue to broaden the application scope of point‐set surfaces and their dynamic animation. Copyright © 2005 John Wiley & Sons, Ltd.