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Applied Mathematics-A Journal of Chinese Universities  2019, Vol. 34 Issue (3): 340-355    DOI: 10.1007/s11766-019-3697-y
    
Gregory Solid Construction for Polyhedral Volume Parameterization by Sparse Optimization
HU Chuan-feng LIN Hong-wei
School of Mathematics, Zhejiang University, Hangzhou 310027, China.
State Key Lab of CAD&CG, Zhejiang University, Hangzhou 310027, China.
Gregory Solid Construction for Polyhedral Volume Parameterization by Sparse Optimization
HU Chuan-feng LIN Hong-wei
School of Mathematics, Zhejiang University, Hangzhou 310027, China.
State Key Lab of CAD&CG, Zhejiang University, Hangzhou 310027, China.
 全文: PDF 
摘要： In isogeometric analysis, it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches, such as trimmed surfaces. In this paper, we develop a Gregory solid based method to parameterize those models. First, we extend the Gregory patch representation to the trivariate Gregory solid representation. Second, the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model, thus generating the polyhedral volume parametrization. To improve the regularity of the polyhedral volume parametrization, we formulate the construction of the trivariate Gregory solid as a sparse optimization problem, where the optimization objective function is a linear combination of some terms, including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid. Then, the alternating direction method of multipliers (ADMM) is used to solve the sparse optimization problem. Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.
关键词： Gregory solid;  Polyhedral volume parametrization;  Sparse optimization;  Regularity;  Isogeometric analysis    
Abstract: In isogeometric analysis, it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches, such as trimmed surfaces. In this paper, we develop a Gregory solid based method to parameterize those models. First, we extend the Gregory patch representation to the trivariate Gregory solid representation. Second, the trivariate Gregory solid representation is employed to interpolate the boundary patches of a geometric model, thus generating the polyhedral volume parametrization. To improve the regularity of the polyhedral volume parametrization, we formulate the construction of the trivariate Gregory solid as a sparse optimization problem, where the optimization objective function is a linear combination of some terms, including a sparse term aiming to reduce the negative Jacobian area of the Gregory solid. Then, the alternating direction method of multipliers (ADMM) is used to solve the sparse optimization problem. Lots of experimental examples illustrated in this paper demonstrate the effectiveness and efficiency of the developed method.
Key words: Gregory solid    Polyhedral volume parametrization    Sparse optimization    Regularity    Isogeometric analysis
出版日期: 2019-09-20
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引用本文:

HU Chuan-feng LIN Hong-wei. Gregory Solid Construction for Polyhedral Volume Parameterization by Sparse Optimization[J]. Applied Mathematics-A Journal of Chinese Universities, 2019, 34(3): 340-355.

HU Chuan-feng LIN Hong-wei. Gregory Solid Construction for Polyhedral Volume Parameterization by Sparse Optimization. Applied Mathematics-A Journal of Chinese Universities, 2019, 34(3): 340-355.

链接本文:

http://www.zjujournals.com/amjcub/CN/10.1007/s11766-019-3697-y    或    http://www.zjujournals.com/amjcub/CN/Y2019/V34/I3/340

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