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

Ladislav KavanUniversity of Pennsylvania

Examples where our approach produces reasonable results. The input polylines are represented by white lines with their orientations indicated by yellow arrows. The number below each image is the Dirichlet energy of the corresponding winding number function. The color maps represent the associated winding num- bers, where higher winding numbers correspond to warmer colors (the actual mapping is slightly adjusted for each image to better visualize the distribution).

Abstract

Jacobson et al. [JKSH13] hypothesized that the local coherency of the generalized winding number function proposed in that work 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 awed and is unfortunately not applicable for most handmade meshes shared on popular mesh repositories such as Google 3D Warehouse.

Publication

Kenshi Takayama, Alec Jacobson, Ladislav Kavan, Olga Sorkine-Hornung. Consistently Orienting Facets in Polygon Meshes by Minimizing the Dirichlet Energy of Generalized Winding Numbers. arXiv, 2014.

Links and Downloads

Paper

BibTeX

Acknowledgements

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.