有理二次Bézier曲线与带调节参数的三次Bézier曲线的比较

Comparision of Rational Bézier Curve and Its Parameters Adjustment

在给定三个控制点P0,P1,P2的基础上,对有理二次Bézier曲线与带调节参数的三次Bézier曲线进行了比较.一是比较二者接近控制多边形的程度;二是比较二者在控制多边形的凸包内插值一点的情况,分别给出了二者插值的条件,以及在插值条件下给出了权因子和调节参数的计算公式,计算简单,使用方便;三是比较二者偏向控制多边形边P0P1或偏向边P1P2的情况.通过对二者的比较,以后就可以根据实际需要选择适当的曲线,更加有效地对曲线的形状进行调整.

Base on three control point P0 ,P1 and P2 , comparisions are conducted between squared rational Bezier curve and parameters adjustment of cubic Bezier curve for their adjacence in controlling the polygon and the polygon convex interpolation point. Base on the two interpolation condition as well as the power factor and adjustable parameter calculation formula under the interpolation condition given separately, the calculation is simple and easy to use. Through the comparison of controlling the polygon by two kinds of deflection P0P1 and P1P2, the proper curve is selected base on actual requirement, and the curve is adjusted more efficiently.