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Volume 37, Issue 5
The Design of Bézier Surface Through Quintic Bézier Asymptotic Quadrilateral

Hui Wang, Chungang Zhu & Caiyun Li

DOI: 10.4208/jcm.1809-m2016-0761

J. Comp. Math., 37 (2019), pp. 721-738.

Published online: 2019-03

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  • Abstract

The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bézier asymptotic quadrilateral interpolated by a smooth Bézier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bézier surfaces is compatible with the CAD systems.

  • Keywords

Asymptotic curves, Bézier surface, Interpolation, Quadrilateral.

  • AMS Subject Headings

65D07

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huiwang@mail.dlut.edu.cn (Hui Wang)

cgzhu@dlut.edu.cn (Chungang Zhu)

caiyun@dlut.edu.cn (Caiyun Li)

  • BibTex
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  • TXT
@Article{JCM-37-721, author = {Wang , HuiZhu , Chungang and Li , Caiyun}, title = {The Design of Bézier Surface Through Quintic Bézier Asymptotic Quadrilateral}, journal = {Journal of Computational Mathematics}, year = {2019}, volume = {37}, number = {5}, pages = {721--738}, abstract = {

The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bézier asymptotic quadrilateral interpolated by a smooth Bézier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bézier surfaces is compatible with the CAD systems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1809-m2016-0761}, url = {http://global-sci.org/intro/article_detail/jcm/13043.html} }
TY - JOUR T1 - The Design of Bézier Surface Through Quintic Bézier Asymptotic Quadrilateral AU - Wang , Hui AU - Zhu , Chungang AU - Li , Caiyun JO - Journal of Computational Mathematics VL - 5 SP - 721 EP - 738 PY - 2019 DA - 2019/03 SN - 37 DO - http://doi.org/10.4208/jcm.1809-m2016-0761 UR - https://global-sci.org/intro/article_detail/jcm/13043.html KW - Asymptotic curves, Bézier surface, Interpolation, Quadrilateral. AB -

The asymptotic curve is widely used in astronomy, mechanics and numerical optimization. Moreover, it shows great application potentials in architecture. We focus on the problem how to cover bounded asymptotic curves by a freeform surface. The paper presents the necessary and sufficient conditions for quadrilateral with non-inflection being asymptotic boundary curves of a surface. And then, with given corner data, we model quintic Bézier asymptotic quadrilateral interpolated by a smooth Bézier surface of bi-eleven degree. We handle the available degrees of freedom during the construction to get an optimized result. Some representative surfaces bounded by asymptotic curves with lines or inflections are also discussed by examples. The presented interpolation scheme for the construction of tensor-product Bézier surfaces is compatible with the CAD systems.

Wang , HuiZhu , Chungang and Li , Caiyun. (2019). The Design of Bézier Surface Through Quintic Bézier Asymptotic Quadrilateral. Journal of Computational Mathematics. 37 (5). 721-738. doi:10.4208/jcm.1809-m2016-0761
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