Morphing of Triangular Meshes in Shape Space

Abstract

We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space $\mathcal{S}$. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in $\mathbb{R}^3$. We then extend this shape space to arbitrary triangulations in 3D using a heuristic approach and show the practical use of the approach using experiments. Furthermore, we discuss a modified shape space that is useful for isometric skeleton morphing. All of the newly presented approaches solve the morphing problem without the need to solve a minimization problem.