Field Smoothness-Controlled Partition for Quadrangulation

We propose a novel partition method for reliable feature-aligned quadrangulation. The core insight of the partition is that smooth streamlines distant from singularities are more suitable as patch boundaries. This allows singularities to be enclosed within patches, resulting in straighter patch boundaries and reducing the distorting influence of singularities. Accordingly, we introduce a new patch quality control mechanism that keeps the patch boundaries inside regions with high field smoothness. Combined with other common metrics (e.g., aligning boundaries with field and feature lines), we develop a practical partition algorithm that first iteratively traces paths in field smoothness-controlled regions to form patches and then removes redundant paths to simplify the patch layout. We demonstrate the effectiveness and practicability of our partitions by using them to generate quality quad meshes on a massive test data set. Compared with state-of-the-art methods, our approach produces quad meshes with significantly enhanced quality while maintaining similar reliability, validating the core insight. Code and data for this paper are at https://github.com/AnderLiang/Field-Smoothness-Controlled-Quadrangulation.