Automatic remeshing by mapping a 2D grid on 3D genus-gg meshes based on topological analysis

Remeshing of 3D meshes is important for many CAD, visualization and analysis applications. Current remeshing methods for closed manifold genus-gg meshes usually involve 3D mesh operations, such as splitting and merging the mesh edges, in order to construct a new mesh that will satisfy given geometrical criteria. These 3D operations are local and usually do not lead to the desired new mesh. Indeed, the remeshed model usually does not satisfy regular criteria. Moreover, changing one of the criteria will lead to reactivating the remeshing process from scratch.In this paper, we propose a novel remeshing approach which overcomes the above problems. It can be applied on 3D genus-gg meshes (g>0)(g>0) which are 2D manifold and triangular. The proposed approach is based on continuously mapping a 2D grid on the 3D genus-gg meshes. The criteria of the new mesh can be defined directly on the 2D grid. The remeshing is invariant to the original triangular mesh. The mapping is based on a new parameterization technique, also developed by the authors, which utilizes the topologic analysis of the object. As a result, the mapping of the 2D grid into a 3D mesh minimizes distortion and guarantees continuity. In addition, the 2D grid, element shapes and density can be modified straightforwardly, thus making the approach modular. In the paper, the remeshing approach and the parameterization (mapping) technique are described in detail, and the feasibility of the remeshing method is demonstrated on complex 3D genus-gg objects.