The As-Rigid-As-Possible (ARAP) shape deformation framework is a versatile technique for morphing, surface modelling, and mesh editing. We discuss an improvement of the ARAP framework in a few aspects: 1. Given a triangular mesh in 3D space, we introduce a method to associate a tetrahedral structure, which encodes the geometry of the original mesh. 2. We use a Lie algebra based method to interpolate local transformation, which provides better handling of rotation with large angle. 3. We propose a new error function to compile local transformations into a global piecewise linear map, which is rotation invariant and easy to minimise. We implemented a shape blender based on our algorithm and its MIT licensed source code is available online.
@article{arxiv.1601.04816,
title = {Tetrisation of triangular meshes and its application in shape blending},
author = {Shizuo Kaji},
journal= {arXiv preprint arXiv:1601.04816},
year = {2016}
}