Consistently Orienting Facets in Polygon Meshes by Minimizing the Dirichlet Energy of Generalized Winding Numbers

Technical report, ETH Zurich (2014)
Kenshi Takayama, Alec Jacobson, Ladislav Kavan, and Olga Sorkine-Hornung


Jacobson et al. [JKSH13] hypothesized that the local coherency of the generalized winding number function could be used to correctly determine consistent facet orientations in polygon meshes. We report on an approach to consistently orienting facets in polygon meshes by minimizing the Dirichlet energy of generalized winding numbers. While the energy can be concisely formulated and efficiently computed, we found that this approach is fundamentally flawed and is unfortunately not applicable for most handmade meshes shared on popular mesh repositories such as Google 3D Warehouse.

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We are grateful to Peter Kaufmann, Wenzel Jakob, Nobuyuki Umetani, Melina Skouras, Ilya Baran, and Ryan Schmidt for their advice and feedback. This work was supported in part by the ERC grant iModel (StG-2012-306877), by an SNF award 200021_137879, by an NSF grant IIS-1350330 and by a gift from Adobe Research. Kenshi Takayama's work was funded by JSPS Postdoctoral Fellowships for Research Abroad. Alec Jacobson's work was supported by an Intel Doctoral Fellowship.