A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle

Sai Hao, Xianghuai Dong
2020 American Journal of Computational Mathematics  
Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bézier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bézier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive
more » ... the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.
doi:10.4236/ajcm.2020.102013 fatcat:bi2io3zz6fbe7h4zz2lk7xaqwq