Practical 3D Frame Field Generation

摘要

Given a tetrahedral mesh, the algorithm described in this articlernproduces a smooth 3D frame field, i.e. a set of three orthogonalrndirections associated with each vertex of the input mesh. The fieldrnvaries smoothly inside the volume, and matches the normals of thernvolume boundary. Such a 3D frame field is a key component forrnsome hexahedral meshing algorithms, where it is used to steer thernplacement of the generated elements.rnWe improve the state-of-the art in terms of quality, efficiency andrnreproducibility. Our main contribution is a non-trivial extension inrn3D of the existing least-squares approach used for optimizing a 2Drnframe field. Our algorithm is inspired by the method proposed byrnHuang et al. [2011], improved with an initialization that directlyrnenforces boundary conditions. Our initialization alone is a fast andrneasy way to generate frames fields that are suitable for remeshingrnapplications. For better robustness and quality, the field can be furtherrnoptimized using nonlinear optimization as in Li et al [2012].rnWe make the remark that sampling the field on vertices instead ofrntetrahedra significantly improves both performance and quality.