Volumetric parametrization from a level set boundary representation with PHT-splines
Volumetric parametrization from a level set boundary representation with PHT-splines
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DOI：
10.1016/j.cad.2016.08.008
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发表时间：
2017-01-01
影响因子：
4.3
通讯作者：
Timon Rabczuk
中科院分区：
文献类型：
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作者：
Chan, Chiu Ling;Anitescu, Cosmin;Timon Rabczuk
等几何分析中的一个挑战是构造适合分析的体网格，它可以准确地表示给定物理域的几何形状。在本文中，我们提出了一种方法，从基于体素的数据中推导出感兴趣区域的样条基表示。我们展示了一种通过水平集函数获得区域边界表示的有效方法。然后，我们利用边界的几何信息(法矢和曲率)来构造具有分层三次样条线的匹配C-1表示。这种近似是通过单个模板和线性变换(缩放、平移和旋转)来完成的，而不需要求解优化问题。我们用二维和三维的几个例子来说明我们的方法，并在一些标准的基准测试问题上显示了良好的性能。(C)2016爱思唯尔有限公司。保留所有权利。
A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a spline-based representation of a domain of interest from voxel-based data. We show an efficient way to obtain a boundary representation of the domain by a level-set function. Then, we use the geometric information from the boundary (the normal vectors and curvature) to construct a matching C-1 representation with hierarchical cubic splines. The approximation is done by a single template and linear transformations (scaling, translations and rotations) without the need for solving an optimization problem. We illustrate our method with several examples in two and three dimensions, and show good performance on some standard benchmark test problems. (C) 2016 Elsevier Ltd. All rights reserved.