Resolving topology ambiguity for multiple-material domains

This paper describes a novel approach to resolve topology ambiguity in generating quality triangular and tetrahedral meshes for multiple-material domains. In previous works, we developed an octree-based dual contouring method to construct surface and volumetric meshes for complicated domains with topology ambiguity resolved. However, this method is based on enumeration and cannot handle domains with multiple materials. As a follow up, in this study we develop an automatic and efficient approach to resolve topology ambiguity for multiple-material domains. We first use an indicator variable to identify the topology inside each octree leaf cell; whenever one cell is ambiguous, we split the cell into 12 tetrahedra. In the following we analyze each material-change edge to create triangles or boundary tetrahedra with surrounding minimizers. For tetrahedral meshes, in addition to material-change edges we need to analyze each interior edge to create interior tetrahedra. With the ambiguity-free mesh ready, we are able to apply quality improvement techniques to attain good mesh quality. Our main contribution lies in resolving topology ambiguity by analyzing a hybrid octree with both cubic and tetrahedral leaf cells, and this method works for both homogeneous and multiple-material domains. We have applied our algorithm to three complicated material datasets and obtained good results.