Inversion Free and Topology Compatible Tetrahedral Mesh Warping Driven by Boundary Surface Deformation

Warping a tetrahedral mesh driven by boundary surface deformation is useful in many applications. Although some methods have been developed to transform the mesh to conform to the deformed boundary surface, it is still a challenging problem to construct an inversion free warped mesh maintaining a compatible topology. In this paper, these two problems are solved by a novel method that combines radial basis function (RBF)-based warping and adaptive mesh refinement. We iteratively transform the mesh using RBF-based warping with a safe step size to ensure that no element is inverted. The use of the RBF-based warping ensures a smooth warping and thus generates a high-quality warped volumetric mesh. To avoid too small step sizes, we refine the elements that are potentially inverted. The refinement is performed on the original and the warped meshes in the same way so as to maintain compatible topology between them. The results of our method can be used in many areas such as finite element simulation and shape interpolation. We demonstrate the effectiveness of our method with a set of examples.