Dual Contouring for domains with topology ambiguity

This paper describes an automatic and robust approach to generate quality triangular and tetrahedral meshes for complicated domains with topology ambiguity. In previous works, we developed an octree-based Dual Contouring (DC) method to construct surface and volumetric meshes for complicated domains. However, topology ambiguity exists and causes non-conformal meshes. In this study, we discuss all possible topology configurations and develop an extension of DC which guarantees the correct topology. We first generate one base mesh with the previous DC method. Then we analyze all the octree leaf cells and categorize them into 31 topology groups. In order to discriminate these cells, we compute the values of their face and body saddle points based on a tri-linear representation inside the cells. Knowing the correct categorization, we are able to modify the base mesh and introduce more minimizer points within the same cell. With these minimizer points we update the mesh connectivities to preserve the correct topology. This method is further extended to 3D tetrahedral mesh generation via an advancing front technique. Finally we use a Laplacian smoothing technique to improve the mesh quality; for tetrahedral mesh a combination of edge-contraction, smoothing and optimization is also applied. Our main contribution is the topology categorization and mesh modification. We have applied our algorithm to three complicated domains and obtained good results.