A Sufficient Convexity Condition for Parametric Bézier Surface over Rectangle

Sai Hao, Xianghuai Dong
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引用次数: 0

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 Bezier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bezier 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.
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矩形上参数曲面的一个充分凸性条件
曲面凹凸性是计算机辅助几何设计中的一个关键问题,在物理模型、工业设计、自动制造等几何建模领域有着广泛的应用。本文提出了矩形上参数Bezier曲面的一个充分凸性条件,并将其作为Bezier控制网格的一个充分凸性条件。用De Casteljau曲面细分算法证明了这一条件,其中递归表达式阐述了控制网格最终收敛于曲面。最后讨论了插值型曲面建模的两个实例,其中一个是一般曲面,另一个是退化曲面。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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