Combinatorial Methods in Grid based Meshing

TL;DR

This paper introduces a grid-based meshing technique that uses pre-computed optimal subdivisions via Answer Set Programming to generate high-quality, hex-dominant meshes suitable for mechanical engineering geometries, ensuring manufacturability and geometric accuracy.

Contribution

The paper presents a novel grid-based meshing method utilizing pre-computed optimal subdivisions to produce high-quality meshes for complex geometries, addressing manufacturability constraints.

Findings

Successfully generates optimal meshes with up to 35 nodes.

Ensures mesh quality and geometric accuracy through subdivision fitting.

Demonstrates effectiveness with multiple practical examples.

Abstract

This paper describes a novel method of generating hex-dominant meshes using pre-computed optimal subdivisions of the unit cube in a grid-based approach. Our method addresses geometries that are standard in mechanical engineering and often must comply with the restrictions of subtractive manufacturability. A central component of our method is the set of subdivisions we pre-compute with Answer Set Programming. Despite being computationally expensive, we obtain optimal meshes of up to 35 nodes available to our method in a template fashion. The first step in our grid-based method generates a coarse Precursor Mesh for meshing complete parts representing the bar stock. Then, the resulting mesh is generated in a subtractive manner by inserting and fitting the pre-generated subdivisions into the Precursor Mesh. This step guarantees that the elements are of good quality. In the final stage, the mesh nodes are mapped to geometric entities of the target geometry to get an exact match. We demonstrate our method with multiple examples showing the strength of this approach.