G1-smooth planar parameterization of complex domains for isogeometric analysis
G1-smooth planar parameterization of complex domains for isogeometric analysis
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DOI：
10.1016/j.cma.2023.116330
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发表时间：
2023-09-15
影响因子：
7.2
通讯作者：
Chen，Falai
中科院分区：
文献类型：
--
作者：
Pan，Maodong;Zou，Ruijie;Chen，Falai
构造高质量的复杂域参数化仍然是等几何分析中的一个重大挑战。为了解决这个问题，我们提出了一种适用于任意拓扑结构平面域的G1-光滑参数化方法.首先，我们生成一个粗略的分解给定的复杂形状，利用提取的骨架的域没有内部奇异性。然后，我们执行更精细的域划分，以获得更准确的边界表示。矩形和三角形Bézier补丁被用来表示的几何形状。其次，通过对相邻面片施加G1连续性约束，构造了全局G1连续的初始参数化。最后，我们使用拟保角映射技术分别提高每个面片的参数化质量。各种例子来证明所提出的方法的能力，并证明其优越性比现有的多补丁参数化。
The construction of high-quality parameterizations for complex domains remains a significant challenge in isogeometric analysis. To address this issue, we propose a G 1-smooth parameterization method for planar domains with arbitrary topology. Firstly, we generate a coarse decomposition of the given complex shape without internal singularities utilizing the extracted skeleton of the domain. We then perform a finer domain partition to obtain more accurate boundary representations. Both rectangular and triangular Bézier patches are employed to represent the geometry. Secondly, by imposing G 1 continuity constraints on the adjacent patches, we construct an initial parameterization that is globally G 1 continuous. Finally, we enhance the parameterization quality of each patch separately using the quasi-conformal mapping technique. Various examples are presented to justify the capability of the proposed method and to demonstrate its superiority over existing multi-patch parameterizations.