Linear Complexity Hexahedral Mesh Generation

TL;DR

This paper presents a method for efficiently generating hexahedral meshes for certain classes of polyhedra, reducing the problem to a finite case analysis and extending previous results to more complex shapes.

Contribution

It introduces a linear complexity approach for hexahedral mesh generation applicable to topological balls with even-sided quadrilaterals and extends to non-simply-connected polyhedra with bipartite conditions.

Findings

Polyhedra with even quadrilateral sides can be partitioned into O(n) topological cubes.

The techniques reduce the geometric mesh generation problem to finite case analysis.

The approach generalizes to non-simply-connected polyhedra under bipartiteness constraints.

Abstract

We show that any polyhedron forming a topological ball with an even number of quadrilateral sides can be partitioned into O(n) topological cubes, meeting face to face. The result generalizes to non-simply-connected polyhedra satisfying an additional bipartiteness condition. The same techniques can also be used to reduce the geometric version of the hexahedral mesh generation problem to a finite case analysis amenable to machine solution.