Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications
Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications
复制标题
用于建模和仿真应用的非结构化六面体网格的插值 Catmull-Clark 体积细分
DOI：
10.1016/j.cagd.2020.101867
复制
发表时间：
2020
影响因子：
1.5
通讯作者：
Yongjie Zhang
中科院分区：
文献类型：
--
作者：
Jin Xie;Jinlan Xu;Dong Zhenyu;Gang Xu;Chongyang Deng;Bernard Mourrain;Yongjie Zhang
体积建模是材料建模和等几何仿真的重要课题。基于Catmull-Clark细分体的极限点公式，提出了两种非结构六面体网格上的插值Catmull-Clark细分体方法。第一种方法的基本思想是构造一个新的控制格，其有限体积由CatmullClark细分格式插值原始六面体网格的顶点。新的控制格是由局部推回操作从一个CatmullClark细分步骤与修改的几何规则。该插值方法简单、有效，并涉及多个形状参数来调整极限体积的形状。第二种方法是基于极限点公式的渐进迭代逼近。在每一步迭代中，我们逐步修改原始六面体网格的顶点，以生成一个新的控制格，其有限体积内插原始六面体网格中的所有顶点。文中还给出了迭代过程的收敛性证明。该插值细分体在规则区域内具有C2-光滑性，但在特殊顶点和边附近不具有C2-光滑性.此外，所提出的插值体细分方法不仅可用于几何插值，而且可用于体材料建模领域的材料属性插值。最后给出了几个实例，说明了本文提出的体剖分方法在等几何分析中的应用。
Volumetric modeling is an important topic for material modeling and isogeometric simulation. In this paper, two kinds of interpolatory Catmull-Clark volumetric subdivision approaches over unstructured hexahedral meshes are proposed based on the limit point formula of Catmull-Clark subdivision volume. The basic idea of the first method is to construct a new control lattice, whose limit volume by the CatmullClark subdivision scheme interpolates vertices of the original hexahedral mesh. The new control lattice is derived by the local push-back operation from one CatmullClark subdivision step with modified geometric rules. This interpolating method is simple and efficient, and several shape parameters are involved in adjusting the shape of the limit volume. The second method is based on progressive-iterative approximation using limit point formula. At each iteration step, we progressively modify vertices of an original hexahedral mesh to generate a new control lattice whose limit volume interpolates all vertices in the original hexahedral mesh. The convergence proof of the iterative process is also given. The interpolatory subdivision volume has C 2-smoothness at the regular region except around extraordinary vertices and edges. Furthermore, the proposed interpolatory volumetric subdivision methods can be used not only for geometry interpolation, but also for material attribute interpolation in the field of volumetric material modeling. The application of the proposed volumetric subdivision approaches on isogeometric analysis is also given with several examples.