A Fast Quadrilateral Mesh Generation Algorithm Based on Conformal Parameterization

Quadrilateral meshes possess excellent geometric properties and have irreplaceable advantages in fields such as Computational Fluid Dynamics, geometric processing, and the Finite Element Method. However, automatically generating high-quality meshes involves satisfying some conflicting and challenging constraints. This paper addresses this issue by employing conformal parameterization to decompose the difficult-to-solve constraints, thereby reducing the difficulty of mesh generation and solving and proposing a fast quadrilateral mesh generation algorithm (FQMG). Specifically, the FQMG decomposes three constraints oriented towards quadrilateral mesh generation: integrating the seamlessness constraint into the singularity extraction process, transforming the nonlinear parameterization into a linear conformal parameterization to achieve the non-flip constraint, and using a quadratic integer planning method during parameterization to enforce the integer position constraints on cone singularities. Through experimental comparison and analysis, the FQMG algorithm, on average, is at least 50% faster in mesh generation speed than the IFAM algorithm, which prioritizes efficiency. At the same time, the quadrilateral mesh quality obtained is approximated compared to mainstream high-quality mesh generation algorithms such as QuadriFlow.