Suppose I want to smoothly transform a cow into a horse. Today, we’ll consider how this can be done.
When morphing between two shapes, there are basically two problems we need to consider. First, we need to establish correspondences between points on the surfaces. Second, we need to interpolate between corresponding positions on the source and target shape. The following two papers each focus on one of these problems.
A. Lee, D. Dobkin, W. Sweldens, and P. Schröder. Multiresolution mesh morphing. In Proceedings of SIGGRAPH 99. [PDF]
M. Alexa, D. Cohen-Or, and D. Levin. As-rigid-as-possible shape interpolation. In Proceedings of SIGGRAPH 2000. [PDF]
Surface morphing methods obviously draw inspiration from image morphing methods. Probably the most influential image morphing paper was written by Beier and Neely in 1992.
Here’s a rather different approach to morphing based on variational implicit surfaces.
We might also want to be able to morph shapes in such a way that self-intersection never occurs.
C. Gotsman and V. Surazhsky. Guaranteed intersection-free polygon morphing. Computers and Graphics, 25(1):67-75, 2001. [PDF]
V. Surazhsky and C. Gotsman. Controllable morphing of compatible planar triangulations. ACM Transactions on Graphics, 20(4):203-231, 2001. [PDF]
Recent work on bijective mappings between surfaces provides another nice way of establishing correspondences.