TITLE:
A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle
AUTHORS:
Sai Hao, Xianghuai Dong
KEYWORDS:
Convexity Condition, Bézier Surface, De Casteljau Arithmetic, Interpolation-Type Surface
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.10 No.2,
June
16,
2020
ABSTRACT: 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 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.