![]() Their semi-regularity is a better fit for parallelized computation and makes their construction considerably more intricate due to the constraints implied by the global semi-regular lattice structure. Hex-meshes feature considerably fewer cells than tet-meshes for the same simulation accuracy, which is a desirable criterion for specific numerical solvers or finite element simulations. The same rivalry arises for volumetric meshes, where hexahedral meshes are often preferred over tetrahedral meshes. The resulting algorithm allows for an efficient evaluation with parallel algorithms on GPU hardware and completes even large reconstructions within minutes.ĭue to reduced element count and more harmonic structures, quad-meshes are often preferable over triangular-meshes for specific tasks like solving partial differential equations or CAD applications. ![]() We introduce specialized operations on the three-dimensional graph structure to enforce consistency during the relaxation. The extracted geometry incorporates regularity as well as feature alignment, following sharp edges and curved boundary surfaces. We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the norm for cubical cells. In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre-computations and can start directly from surfaces or samples. We exemplify the ease of construction of at-most-hexa meshes by proposing a frugal and straightforward method to generate high-quality meshes of this kind, starting directly from hulls or point clouds, for example, from a 3D scan. In this work, we introduce a strict subset of general hex-dominant meshes, which we term ‘at-most-hexa meshes’, in which most cells are still hexahedral, but no cell has more than six boundary faces, and no face has more than four sides. ![]() Hex-dominant meshes, where most but not all cell elements have a hexahedral structure, constitute an attractive compromise, potentially unlocking benefits from both structures, but their generality makes their employment in downstream applications difficult. Hex-meshes are more intricate to construct due to the global structure of the meshing, but feature much better regularity, alignment, are more expressive, and offer the same simulation accuracy with fewer elements. ![]() Tetrahedral meshes and (pure) hex-meshes are two popular formats in scenarios like CAD applications, offering opposite advantages and disadvantages. Still, their construction bears several additional challenges compared to boundary-based representations. Volumetric polyhedral meshes are required in many applications, especially for solving partial differential equations on finite element simulations. ![]()
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