Coarse Quad Layouts Through Robust Simplification of Cross Field Separatrix Partitions

Abstract: Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions and limit cycles, negating some of the benefits a quad layout can provide in quad meshing. We introduce three novel methods to improve on a pipeline for coarse quad partitioning. First, we formulate an efficient method to compute high-quality cross fields on curved surfaces by extending the diffusion generated method from Viertel and Osting (SISC, 2019). Next, we introduce a method for accurately computing the trajectory of streamlines through singular triangles that prevents tangential crossings. Finally, we introduce a robust method to produce coarse quad layouts by simplifying the partitions obtained via naive separatrix tracing. Our methods are tested on a database of 100 objects and the results are analyzed. The algorithm performs well both in terms of efficiency and visual results on the database when compared to state-of-the-art methods.