Mesh Generation for Self-Intersecting Rational Parametric Surfaces

When processing self-intersecting surfaces, existing mesh generation methods encounter issues such as lacking intersection representation, large errors, and diminished triangle quality near intersections. In response to these challenges, a novel mesh generation algorithm for self-intersecting rational parametric surfaces is proposed. Firstly, the moving plane method is utilized to calculate the singular factors of the surface. Secondly, the topologically significant points on the intersections is identified by singular factors and the first fundamental form of the surface. Thirdly, a pairing algorithm for mesh vertices on intersections is developed based on the moving plane method to ensure the neighborhood coordination of mesh intersection. The mesh is finally constructed by a particle-based mesh generation method within the parameter domain. Mesh generation tests are conducted on self-intersecting surfaces with different topologies. The proposed algorithm ensures the correctness of mesh intersection topology. Compared to various typical isotropic mesh generation algorithms that do not pair mesh vertices at intersections, the mean value of minimum angles increased 0.6% on average.