A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle

• 作者: Xianghuai Dong
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Convexity Condition Bézier Surface De Casteljau Arithmetic Interpolation-Type Surface
• 年，卷（期）: 2020,（2）
• 页码范围: 252-265
• 页数: 14页
• 分类号: O17

摘要

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.