Weighted Squared Volume Minimization (WSVM) for Generating Uniform Tetrahedral Meshes

TL;DR

This paper introduces WSVM, a novel algorithm for generating high-quality, uniform tetrahedral meshes by minimizing a weighted squared volume energy, improving mesh quality automatically without parameter tuning.

Contribution

The paper proposes a new energy-based algorithm, WSVM, that automatically produces uniform and high-quality tetrahedral meshes from surface models, outperforming existing methods.

Findings

WSVM produces meshes with fewer slivers and better uniformity.

The algorithm automatically optimizes mesh quality without parameter tuning.

Evaluations show consistent improvements over existing tetrahedral meshing techniques.

Abstract

This paper presents a new algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes. Drawing inspiration from the principle of minimal surfaces that minimize squared surface area, WSVM employs a new energy function integrating weighted squared volumes for tetrahedral elements. When minimized with constant weights, this energy promotes uniform volumes among the tetrahedra. Adjusting the weights to account for local geometry further achieves uniform dihedral angles within the mesh. The algorithm begins with an initial tetrahedral mesh generated via Delaunay tetrahedralization and proceeds by sequentially minimizing volume-oriented and then dihedral angle-oriented energies. At each stage, it alternates between optimizing vertex positions and refining mesh connectivity through the iterative process. The algorithm operates fully automatically and requires no parameter tuning. Evaluations on a variety of 3D models demonstrate that WSVM consistently produces tetrahedral meshes of higher quality, with fewer slivers and enhanced uniformity compared to existing methods. Check out further details at the project webpage: https://kaixinyu-hub.github.io/WSVM.github.io.