3D POLYLLA: Polyhedral meshing algorithm based on terminal-edge regions and terminal-face regions

TL;DR

This paper extends the Polylla polygonal mesh algorithm from 2D to 3D, introducing two versions that generate volumetric meshes with arbitrarily shaped polyhedra using terminal-edge and terminal-face regions.

Contribution

The work presents the first 3D extension of Polylla, including new concepts like terminal-face regions and a three-phase process for volumetric mesh generation.

Findings

Two versions of Polylla 3D are proposed and described.

The second version successfully extends the 2D process to 3D with similar phases.

The algorithms enable generation of complex 3D polyhedral meshes.

Abstract

Polylla is a polygonal mesh algorithm that generates meshes with arbitrarily shaped polygons using the concept of terminal-edge regions. Until now, Polylla has been limited to 2D meshes, but in this work, we extend Polylla to 3D volumetric meshes. We present two versions of Polylla 3D. The first version generates terminal-edge regions, converts them into polyhedra, and repairs polyhedra that are joined by only an edge. This version differs from the original Polylla algorithm in that it does not have the same phases as the 2D version. In the second version, we define two new concepts: longest-face propagation path and terminal-face regions. We use these concepts to create an almost direct extension of the 2D Polylla mesh with the same three phases: label phase, traversal phase, and repair phase.