Truncated Hierarchical Loop Subdivision Surfaces and application in isogeometric analysis

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• 作者：Hongmei Kang ; Xin Li ; ^{lixustc@ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Falai Chen ; Jiansong Deng
• 关键词：Loop subdivision ; Local refinement ; Truncation ; Extraordinary vertices ; Isogeometric analysis
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：72
• 期：8
• 页码：2041-2055
• 全文大小：4162 K

文摘

Subdivision Surface provides an efficient way to represent free-form surfaces with arbitrary topology. Loop subdivision is a subdivision scheme for triangular meshes, which is C²$C^2$ continuous except at a finite number of extraordinary vertices with G¹$G^1$ continuous. In this paper we propose the Truncated Hierarchical Loop Subdivision Surface (THLSS), which generalizes truncated hierarchical B-splines to arbitrary topological triangular meshes. THLSS basis functions are linearly independent, form a partition of unity, and are locally refinable. THLSS also preserves the geometry during adaptive h-refinement and thus inherits the surface continuity of Loop subdivision surface. Adaptive isogeometric analysis is performed with the THLSS basis functions on several complex models with extraordinary vertices to show the potential application of THLSS.