Morphing

Computational models are used everywhere, from games to movies (special effects and computer graphics animation). Deformations are the basic tool for animating objects, so we focus on a particular aspect of the morphing research field.

Transporting deformations from a mesh to a different one is a typical task of the shape analysis. In particular, it is necessary to perform such a kind of transport when performing group-wise statistical analyses in shape or size and shape spaces. The key point is: given two different meshes X and Y undergoing two different deformations (called diffeomorphisms), when it is possible to say that they are undergoing a similar deformation?

A naive possible answer could be that the displacement field is the same, but this gives different results from one an animator expects. We assume a different point of view: two templates undergo the same deformation if, given a bijective map between the two underlying affine spaces (i.e., we can map points on one mesh to points in another), the local metric (non linear strain) induced by the two diffeomorphisms is the same for corresponding points.

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The source code will be available soon under the BSD license.