具有指数函数形式权因子的有理Bézier曲线退化

Degenerations of Rational Bézier Curves with Weights in the Form of Exponential Function

针对具有指数函数形式权因子的有理Bézier曲线,研究该曲线的退化性质.首先将具有指数函数形式的权因子转化为幂函数形式,并指出它们之间的关系;然后利用有理Bézier曲线的toric退化理论定义正则控制曲线;最后给出权因子趋向于无穷时有理Bézier曲线的退化曲线及其几何性质.实验结果验证了文中提出的退化理论,并指出其与有理Bézier曲线toric退化之间的区别.

For the rational Bézier curve with weights in the form of exponential function, the degeneration ofthe curve is presented in this paper. Firstly, the weights in the form of exponential function are converted intothe form of power function and we indicate the relationship between them. Based on the toric degenerations ofrational Bézier curve, the regular control curve of rational Bézier curve is defined. Finally, the geometric propertyof the degeneration of curve of rational Bézier curve while weights approach to infinity is presented. Experimentalresults verify the presented result and show the differences between it and the toric degenerations ofrational Bézier curve.