有理B样条曲线拐点分析的面积坐标法

本文给出了一种分析有理B样条曲线拐点的新方法。特点是通过建立一种新的面积坐标系,简化有理B样条曲线拐点方程的形式。在面积坐标系中,拐点方程结式的次数也由六次降为四次。文中给出了绘图实例。

On Inflection Point of Rational B Spline Curve

In CAGD (computer aided geometric design), rational curve such as rationalB spline curve is often needed2],3]. Designers find it necessary to adjust parame-ters of rational curve to obtain desired shape. Without a mathematical understa-nding of the variation of pararneters on the shape of curve, designers have to relyon experience to adjust the parameters. Adjustment by experience often brings ininflection points which should be avoided as much as possible. Boehm 2] andSederberg 3] do not discuss how to avoid inflection points in adjusting parameters. In this paper, the authors discuss how to avoid bringing in inflection points inadjusting parameters of rational B spline curve. The authors introduce a new areacoordinate system. When a B spline curve is transformed into such a coordinatesystem, the order of the equation dealing with the conditions governing the ap-pearance of inflection points is reduced from six to four. With this simplifiedequation, limits (details are given in section 4 of the full paper) are relativelysimple to obtain and with the aid of such limits CAGD designers can avoidbringing in inflection points when they adjust parameters of rational B splinecurve.