Algorithm for Curved Surface Mesh Generation Based on Delaunay Refinement

Curved surface mesh generation is a key step for many areas. Here, a mesh generation algorithm for closed curved surface based on Delaunay refinement is proposed. We focus on improving the shape quality of the meshes generated and making them conform to 2-manifold. The Delaunay tetrahedralization of initial sample is generated first, the initial surface mesh which is a subset of the Delaunay tetrahedralization can be achieved. A triangle is refined by inserting a new point if it is large or of bad quality. For each sample, we also check the triangles that adjoin it whether from a topological disk. If not, the largest triangle will be refined. Finally, the surface mesh is updated after a new point is inserted into the sample. The definition of mesh size function for surface mesh generation is also put in this paper. Meshing experiments of some models demonstrate that the new algorithm is advantageous in generating high quality surface mesh, the count of mesh is suitable and can well approximate the curved surface. The presented method can be used for a wide range of problems including computer graphics, computer vision and finite element method.