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 - <p style="text-align: justify;">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.</p>