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

TL;DR

This paper investigates a method to orient polygon mesh facets by minimizing the Dirichlet energy of generalized winding numbers, but finds it fundamentally flawed for practical meshes.

Contribution

It formulates a concise energy minimization approach for facet orientation but demonstrates its limitations in real-world mesh applications.

Findings

The energy minimization approach is computationally efficient.

The method is not suitable for most handmade meshes.

Fundamental flaws limit practical applicability.

Abstract

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.