Morphing of Triangular Meshes in Shape Space

TL;DR

This paper introduces a new shape space-based method for morphing between isometric poses of non-rigid objects represented as triangular meshes, ensuring near-isometric transformations without complex minimization.

Contribution

It develops a novel shape space model for mesh morphing, extending it to arbitrary triangulations and isometric skeletons, with proofs and heuristic methods for practical application.

Findings

Linear interpolation in shape space yields most isometric morphs.

The approach works for arbitrary triangulations using heuristics.

No minimization problems are needed for the morphing process.

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.