Mandoline: Robust Cut-Cell Generation for Arbitrary Triangle Meshes

摘要

Although geometry arising “in the wild” most often comes in the formof a surface representation, a plethora of geometrical and physical applicationsrequire the construction of volumetric embeddings either of thegeometry itself or the domain surrounding it. Cartesian cut-cell-based meshgeneration provides an attractive solution in which volumetric elementsare constructed from the intersection of the input surface geometry witha uniform or adaptive hexahedral grid. This choice, especially common incomputational fluid dynamics, has the potential to efficiently generate accurate,surface-conforming cells; unfortunately, current solutions are oftenslow, fragile, or cannot handle many common topological situations. Wetherefore propose a novel, robust cut-cell construction technique for trianglesurface meshes that explicitly computes the precise geometry of the intersectioncells, even on meshes that are open or non-manifold. Its fundamentalgeometric primitive is the intersection of an arbitrary segment with an axisalignedplane. Beginning from the set of intersection points between trianglemesh edges and grid planes, our bottom-up approach robustly determinescut-edges, cut-faces, and finally cut-cells, in a manner designed to guaranteetopological correctness. We demonstrate its effectiveness and speed on awide range of input meshes and grid resolutions, and make the code availableas open source.