A Robust Grid‐Based Meshing Algorithm for Embedding Self‐Intersecting Surfaces
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Date
2024
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© 2024 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd.
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.
Description
@article{10.1111:cgf.14986,
journal = {Computer Graphics Forum},
title = {{A Robust Grid‐Based Meshing Algorithm for Embedding Self‐Intersecting Surfaces}},
author = {Gagniere, S. and Han, Y. and Chen, Y. and Hyde, D. and Marquez‐Razon, A. and Teran, J. and Fedkiw, R.},
year = {2024},
publisher = {© 2024 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14986}
}