At‐Most‐Hexa Meshes

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