具有指数函数形式权因子的有理Bézier曲线退化

摘要

For the rational Béziercurve with weights in the form of exponential function, the degeneration of the curve is presented in this paper. Firstly, the weights in the form of exponential function are converted into the form of power function and we indicate the relationship between them. Based on the toric degenerations of rational Béziercurve, the regular control curve of rational Bézier curve is defined. Finally, the geometric prop-erty of the degeneration of curve of rational Bézier curve while weights approach to infinity is presented. Ex-perimental results verify the presented result and show the differences between it and the toric degenerations of rational Béziercurve.%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。