Tetrisation of triangular meshes and its application in shape blending

TL;DR

This paper introduces a novel tetrahedralization method for triangular meshes, improving shape deformation techniques by better handling rotations and providing a rotation-invariant error function, with applications in shape blending.

Contribution

It presents a new tetrahedralization approach, a Lie algebra based interpolation, and a rotation-invariant error function to enhance ARAP shape deformation methods.

Findings

Improved handling of large-angle rotations in shape deformation.

Enhanced global transformation compilation with a new error function.

Developed a shape blender demonstrating the method's effectiveness.

Abstract

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.