用三次NURBS表示圆弧与整圆的算法研究

CUBIC NURBS REPRESENTATION OF ARC AND CIRCLE

提出了一种实用的三次ＮＵＲＢＳ曲线表示圆弧及整圆的方法，并得出了各种情况下现成可用的结果。该方法用４个控制顶点所决定的一段ＮＵＲＢＳ曲线来表示一段小于１８０°的圆弧段；对于大于１８０°的圆弧则采用两段三次ＮＵＲＢＳ曲线来表示，当圆心角为３６０°时，则得到了整圆的表示。文中所述的方法统一、简单、符合对圆弧ＮＵＲＢＳ表示的要求。

This paper presents a method for cubic NURBS representation of arc and circle,and puts forward ready made results under different circumstances.In the method,an arc having central angle less than 180° is represented by a segment of NURBS curve determined by four control points,for an arc having central angle greater than 180°,two segments of NURBS curves are used for the representation.When the central angle equals to 360°,the circle representation can then be obtained.The method described in this paper is simple and consistent,and meets the demands of arc NURBS representation.