2D Quadrilateral Meshes Quality Improvement

Quadrilateral (or quad) meshes generated by various remeshing and simplification methods for input models with complex structure and boundary configurations often possess elements with minimal quality, which calls for an optimization approach to improve their individual elements’ quality while preserving the boundary features. Many existing methods either fix boundary vertices during optimization or assume a simple boundary configuration. In this paper, we introduce a new quality improvement framework for 2D quad meshes with open boundaries. Our framework aims to optimize the configuration of an embedded polygon constructed based on the one-ring neighbors of each interior vertex. A feature-preserved boundary optimization is also introduced based on the angle configuration of the individual boundary vertices to further improve the quality of the boundary elements. Our framework has been applied to a number of 2D quad meshes with various boundary configurations and compared with other representative methods to demonstrate its advantages.