Mesh Generation for Self-intersecting Rational Parametric Surfaces

We propose a mesh generation algorithm for rational parametric surfaces with self-intersections that can generate simplicial complex structured triangular meshes with various metrics. Our algorithm first uses the moving plane method to calculate the singular factors of the surface, which provide the implicit equations of the surface intersections in the parameter domain. Next, we locate the non-generic singular points on intersections using the singular factors and the surface's first fundamental form. This step is crucial for generating a mesh surface with correct topology. We then design a point tracing method for the intersections based on the moving plane method, which ensures that the mesh points generated in the parameter domain include all pre-images of the mesh points on the surface intersections. Finally, we use a particle-based mesh generation method to generate the mesh in the parameter domain. We have conducted extensive experiments to validate our algorithm, and the results demonstrate that our algorithm can generate complex structured mesh surfaces with the same topology as the original parametric surfaces. Compared with representative state-of-the-art methods, our algorithm achieves higher mesh accuracy and quality on most self-intersecting parametric surfaces.