Mandoline: Robust Cut-Cell Generation for Arbitrary Triangle Meshes SIGGRAPH Asia 2019

MICHAEL TAO¹, CHRISTOPHER BATTY², EUGENE FIUME¹³, DAVID LEVIN¹

¹University of Toronto, ²University of Waterloo, ³Simon Frasier University

Abstract

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.

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BibTeX

@article{Tao:Mandoline:2019,
  title = {Mandoline: Robust Cut-Cell Generation for Arbitrary Triangle Meshes},
  author = {Michael Tao, Christopher Batty, Eugene Fiume, David Levin},
  year = {2019},
  journal = {ACM Transactions on Graphics}, 
}

Acknowledgements

This work is graciously supported by NSERC Discovery Grants (RGPIN-04360–2014 & RGPIN-2017–05524), NSERC Accelerator Grant (RGPAS-2017–507909), Connaught Fund (503114), and the Canada Research Chairs Program. We thank Tim Jeruzalski for his substantial efforts to render our results, as well as Rahul Arora, Nicole Sultanum, and Sarah Kushner for assistance with figure creation, and Ryan Goldade for the fluid crown splash model.