Shape Spaces from Mesh Morphing

This work concentrates on the extension of classical mesh morphing (between two shapes) to the linear combination of an aribitrary number of shapes. In this setting, several meshes are bases of a linear space. All base meshes are expected to have the same topology, while their geometries differ. Elements of the space are generated by linearly combining the geometries of the bases. The description of particular shapes as a compound of other shape makes sense for two reasons: First, the description could be compact, if the shape complexity is large relative to the number of bases. Second, the description has semantics if the base shapes are meaningful. Applications of such spaces of meshes are geometric animations and information visualization. In particular, the transformation of a given key frame animation to a comapratively small basis is developed.