【摘要】 为深入挖掘有理二次Bézier曲线在?0,1?外的拓展性质,针对其标准型,研究参数趋向于?时的极限.首先计算出极限点的位置;然后分别在椭圆和双曲线的情况下,通过比较极限点与已知点的位置、计算有理形式分母的零点、考察极限点处的切向,来探讨极限点的性质;进而得出极限点与中心、肩点共线,以及切线方向与首末控制顶点连线方向平行等结论.实例结果表明,极限点可以作为拓展部分曲线的控制顶点,从而用于整个椭圆的表示.更多还原

【Abstract】 To deeply dig the extended properties of a rational quadratic Bézier curve out of [0,1],this paper used the standard form of the curve and studied the limitation when the parameter tends to ?.It firstly calculated the position of the limit point.Then it separately considered the limit properties under the case of ellipse and hyperbola from comparing the positions of the existing points and the limit point,working out the zeroes of the denominator of the rational form,and considering the tangent direction at the limit point.The example results show that the limit point is collinear with the elliptical center and the shoulder point,the tangent direction at the limit point parallelizes the line between two end control points,the limit point can be regarded as a control point of the extended curve and used for the representation of the whole ellipse,and so on.更多还原