平面T-Bezier曲线的几何性质分析

Geometric character analysis of planar T-Bézier Curves

以四个控制顶点的平面T-Bezier曲线为主要研究对象,全面分析了平面T-Bezier曲线的奇拐点、尖点和凸性性质。分析结果表明,四个控制顶点的平面T-Bezier曲线的几何特征可描述成下列情形之一:有一个尖点,有一个或两个拐点,有一个二重结点,处处为凸。给出了这几个情形的相应控制多边形表示的充分必要条件,通过图解说明了平面TBezier曲线的几何性质。了解T-Bezier曲线的几何性质,有助于工程设计人员进行平面自由曲线的设计。

The character of the singular infection point, cusp point and convexity of the planar T-Bezier curves created based on four control points is analyzed in detail. The analysis concludes that the geometric character of each T-Bezier curve can be described as one of the cases of one cusp point, one infection point, one infection point or two, one dual loop point, and complete convexity. The necessary and sufficient conditions for control of polygon repre-sentation corresponding to the above mentioned cases are given, and the geometric character of T- Bezier curves is diagrammatically interpreted. Understanding of T- Bezier curve character is of great help to planar free curve design.