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.

使四面体网格变形以符合几何形状修改是应用程序中的一个有用过程。本文提出了一种通过网格局部顶点的位移来驱动四面体网格变形的方法。该方法背后的基本技术是基于径向基函数（RBF）的插值和自适应网格细化。该方法是通过变形过程实现的，该变形过程通过基于RBF的迭代插值对网格进行转换，从而避免了四面体的反转。还引入了通过局部平分潜在倒置的四面体的自适应优化，以确保足够大的变形步长。细化是同时对输入网格和扭曲网格执行的，以保持拓扑的一致性。结果是，该方法可以有效地产生满足坚硬位置约束的无反演和拓扑兼容变形网格。实验结果表明了该方法的有效性。