A Robust Grid-Based Meshing Algorithm for Embedding Self-Intersecting Surfaces

TL;DR

This paper introduces an efficient grid-based algorithm for embedding self-intersecting surfaces into a volumetric hexahedral mesh, simplifying the creation of simulation-ready models despite complex surface intersections.

Contribution

It presents a novel method that handles self-intersecting meshes efficiently using minimal exact arithmetic and introduces topology-aware coarsening and tetrahedralization techniques.

Findings

Handles high degrees of self-intersection efficiently.

Produces volumetric hexahedral meshes from complex surfaces.

Supports user-defined mesh resolution with topology awareness.

Abstract

The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not self-intersecting. However, due to numerical and/or user error, input surfaces are commonly self-intersecting to some degree. The removal of self-intersection is a burdensome task that complicates workflow and generally slows down the process of creating simulation-ready digital assets. We present a method for the creation of a volumetric embedding hexahedron mesh from a self-intersecting input triangle mesh. Our method is designed for efficiency by minimizing use of computationally expensive exact/adaptive precision arithmetic. Although our approach allows for nearly no limit on the degree of self-intersection in the input surface, our focus is on efficiency in the most common case: many minimal self-intersections. The embedding hexahedron mesh is created from a uniform background grid and consists of hexahedron elements that are geometrical copies of grid cells. Multiple copies of a single grid cell are used to resolve regions of self-intersection/overlap. Lastly, we develop a novel topology-aware embedding mesh coarsening technique to allow for user-specified mesh resolution as well as a topology-aware tetrahedralization of the hexahedron mesh.