Volume Quantization with Flexible Singularities for Hexahedral Meshing

Abstract We present a novel algorithm for quantization and subsequent hexahedral mesh generation from seamless volumetric maps. Quantization is the process of choosing integers that represent the numbers of hexahedral elements to be placed in each region of the volume, and transforming the seamless map into an integer‐grid map matching that choice, inducing a hexahedral mesh. Previous work computes such quantizations under the restriction of a fixed predetermined singularity graph. Our novel approach allows for implicit modification and, in particular, simplification of the map's singularity structure wherever that benefits the chosen objective, such as matching target hexahedron sizes as closely as possible. It comes with two novel ingredients: A feature‐focused distortion measure guiding the quantization, and constraints ensuring map injectivity and structure preservation of geometric and topological features, both without relying on a fixed singularity structure. We demonstrate the benefit of the added flexibility offered by this approach: it allows for the generation of hexahedral meshes that more accurately match a desired resolution globally, as well as of meshes exhibiting a simpler block structure.