Quad Meshing with Coarse Layouts for Planar Domains

Abstract We present a novel method to generate quad meshes with coarse quad layouts for planar domains. Our method contains two steps: (1) domain segmentation and (2) layout generation. Given a planar domain, we propose a novel field-guided segmentation approach to partition it into a collection of rectangle-like polygons. To adapt for domains with complex boundaries, we straighten the boundaries with low distortions before segmentation. Since the polygons are rectangle-like, a robust template-based method is presented to mesh polygons into separate quad meshes that are further used to generate an initial layout. Finally, a new optimization method is developed to reduce the patch numbers and improve quad quality while bounding geometric errors. These technical steps are holistically and harmoniously combined to generate quad meshes containing a small number of quad patches, bounded geometric errors, and high quad quality. We demonstrate the efficacy of our method on various complex models. Compared to other state-of-the-art methods, our method achieves higher quality.