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Design of Loop’s Subdivision Surfaces by Fourth-Order Geometric PDEs with \(G^1\) Boundary Conditions

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Abstract

In this paper, we present a method for constructing Loop’s subdivision surface patches with given \(G^1\) boundary conditions and a given topology of control polygon, using several fourth-order geometric partial differential equations. These equations are solved by a mixed finite element method in a function space defined by the extended Loop’s subdivision scheme. The method is flexible to the shape of the boundaries, and there is no limitation on the number of boundary curves and on the topology of the control polygon. Several properties for the basis functions of the finite element space are developed.

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Acknowledgments

Guoliang Xu was supported in part by NSFC Funds for Creative Research Groups of China (Grant No. 11021101, 11321061). Qing Pan was supported by a National Natural Science Foundation of China (Grants No. 11171103) and Scientific Research Fund of Hunan Provincial Education Department (No. 12K029).

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Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing , 100190, China

    Guoliang Xu

  2. Key Laboratory of High Performance Computing and Stochastic Information Processing, College of Mathematics and Computer Science, Hunan Normal University, Changsha, China

    Qing Pan

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  1. Guoliang Xu
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  2. Qing Pan
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Correspondence to Qing Pan.

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Xu, G., Pan, Q. Design of Loop’s Subdivision Surfaces by Fourth-Order Geometric PDEs with \(G^1\) Boundary Conditions. J Sci Comput 62, 674–692 (2015). https://doi.org/10.1007/s10915-014-9872-7

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  • DOI: https://doi.org/10.1007/s10915-014-9872-7

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