Volumetric Mapping of Genus Zero Objects via Mass Preservation

TL;DR

This paper introduces a volume-preserving mapping technique for genus zero objects onto a cube, enabling high-quality hexahedral mesh generation useful for shape analysis, registration, and finite element applications.

Contribution

The method provides a novel volume-preserving mapping approach that guarantees a one-to-one correspondence and produces quality hexahedral meshes for genus zero solids.

Findings

Successfully maps complex 3D models onto a cube with volume preservation.

Generates high-quality hexahedral meshes suitable for computational applications.

Demonstrates effectiveness on various 3D solid models.

Abstract

In this work, we present a technique to map any genus zero solid object onto a hexahedral decomposition of a solid cube. This problem appears in many applications ranging from finite element methods to visual tracking. From this, one can then hopefully utilize the proposed technique for shape analysis, registration, as well as other related computer graphics tasks. More importantly, given that we seek to establish a one-to-one correspondence of an input volume to that of a solid cube, our algorithm can naturally generate a quality hexahedral mesh as an output. In addition, we constrain the mapping itself to be volume preserving allowing for the possibility of further mesh simplification. We demonstrate our method both qualitatively and quantitatively on various 3D solid models