We present a robust framework to conduct material modeling suitable for continuously varying materials with a local material composition control. The geometry and attribute representations are defined using two trivariate T-splines based on the same parametric domain. The optimization process decreases the mismatch of geometry and attribute between the input tetrahedral mesh and the trivariate T-splines, which consists of two alternately executed procedures: progressive fitting and octree-based adaptive refinement. Control points are dynamically updated without constructing large matrices as used in finite element method. To improve computational efficiency of the optimization, adaptive refinement is carried out only in those regions that undergo fine-scale deformation and an octree-based subdivision is directly used to insert control points in the parametric domain. The proposed framework was implemented on medical and synthetic examples to show the robustness of the material modeling framework. The comparison between trivariate T-splines with adaptive refinement and trivariate NURBS with uniform refinement demonstrates the computational efficiency.

我们提出了一个健壮的框架来进行材料建模，该模型适用于具有局部材料成分控制的连续变化的材料。使用基于相同参数域的两个三元T样条定义几何和属性表示。优化过程减少了输入四面体网格和三元T样条之间的几何形状和属性不匹配，该过程由两个交替执行的过程组成：渐进拟合和基于八叉树的自适应细化。控制点可以动态更新，而无需构造有限元方法中使用的大型矩阵。为了提高优化的计算效率，自适应细化仅在发生小规模变形的区域中进行，并且基于八叉树的细分直接用于在参数域中插入控制点。所提出的框架是在医学和合成实例上实现的，以显示材料建模框架的鲁棒性。具有自适应细化的三变量T样条与具有均匀细化的三变量NURBS之间的比较证明了计算效率。