Gagniere, S.Han, Y.Chen, Y.Hyde, D.Marquez‐Razon, A.Teran, J.Fedkiw, R.Alliez, PierreWimmer, Michael2024-03-232024-03-2320241467-8659https://doi.org/10.1111/cgf.14986https://diglib.eg.org/handle/10.1111/cgf14986The 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.Attribution-NonCommercial-NoDerivatives 4.0 Internationalmesh generationmodelling10.1111/cgf.1498617 pages