Tetrahedralization of a Hexahedral Mesh

TL;DR

This paper introduces a generalized algorithm for tetrahedralizing any hexahedral mesh, expanding on existing methods by overcoming face division limitations and applying heuristics for broader applicability.

Contribution

The authors develop a new, flexible tetrahedralization algorithm for hexahedral meshes, extending previous methods and incorporating heuristics for improved generality.

Findings

Algorithm successfully tetrahedralizes complex hexahedral meshes

Outperforms existing methods in flexibility and applicability

Provides a foundation for improved mesh processing techniques

Abstract

Two important classes of three-dimensional elements in computational meshes are hexahedra and tetrahedra. While several efficient methods exist that convert a hexahedral element to a tetrahedral elements, the existing algorithm for tetrahedralization of a hexahedral complex is the marching tetrahedron algorithm which limits pre-selection of face divisions. We generalize a procedure for tetrahedralizing triangular prisms to tetrahedralizing cubes, and combine it with certain heuristics to design an algorithm that can triangulate any hexahedra.