Tetrahedral mesh deformation with positional constraints

Abstract

Deforming a tetrahedral mesh to conform to geometry modifications is a useful process in applications. This paper presents a method for tetrahedral mesh deformation driven by displacement of partial vertices of the mesh. The basic techniques behind the method are radial basis function (RBF)-based interpolation and adaptive mesh refinement. The method is realized by a warping process that transforms the mesh via iterative RBF-based interpolation to avoid the inversion of tetrahedra. Adaptive refinement by locally bisecting potentially inverted tetrahedra is also introduced to assure sufficiently large warping stepsizes. The refinement is performed on both the input mesh and the warped meshes concurrently to maintain the consistency of the topology. As a result, the method can effectively produce an inversion-free and topology compatible deformation mesh that satisfies hard positional constraints. Experimental results show the effectiveness of the method.