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Graph."],"published-print":{"date-parts":[[2019,12,31]]},"abstract":"<jats:p>Although geometry arising \"in the wild\" most often comes in the form of a surface representation, a plethora of geometrical and physical applications require the construction of volumetric embeddings either of the geometry itself or the domain surrounding it. Cartesian cut-cell-based mesh generation provides an attractive solution in which volumetric elements are constructed from the intersection of the input surface geometry with a uniform or adaptive hexahedral grid. This choice, especially common in computational fluid dynamics, has the potential to efficiently generate accurate, surface-conforming cells; unfortunately, current solutions are often slow, fragile, or cannot handle many common topological situations. We therefore propose a novel, robust cut-cell construction technique for triangle surface meshes that explicitly computes the precise geometry of the intersection cells, even on meshes that are open or non-manifold. Its fundamental geometric primitive is the intersection of an arbitrary segment with an axis-aligned plane. Beginning from the set of intersection points between triangle mesh edges and grid planes, our bottom-up approach robustly determines cut-edges, cut-faces, and finally cut-cells, in a manner designed to guarantee topological correctness. We demonstrate its effectiveness and speed on a wide range of input meshes and grid resolutions, and make the code available as open source.<\/jats:p>","DOI":"10.1145\/3355089.3356543","type":"journal-article","created":{"date-parts":[[2019,11,8]],"date-time":"2019-11-08T20:27:58Z","timestamp":1573244878000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":20,"title":["Mandoline"],"prefix":"10.1145","volume":"38","author":[{"given":"Michael","family":"Tao","sequence":"first","affiliation":[{"name":"University of Toronto, Canada"}]},{"given":"Christopher","family":"Batty","sequence":"additional","affiliation":[{"name":"University of Waterloo, Canada"}]},{"given":"Eugene","family":"Fiume","sequence":"additional","affiliation":[{"name":"Simon Fraser University, Canada and University of Toronto, Canada"}]},{"given":"David I. 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