有理Bezier曲线参数化方法研究

摘要

The relationship between the transformation of weights on rational Bézier curve and parameterization of the curve with the shape unchanged is discussed. The correspondence relationship between the parameter of a point on a rational Bézier curve and its weights is given, and (n-1) factors of shape-unchanged are obtained. The parametric transformation formula is derived which has the same influence on parameterization as the weight transformation. Under the two transformations, the shape and the endpoints are unchanged, only the correspondence relationship between the point on a rational Bézier curve and the parameter is changed.%研究了在曲线形状保持不变的条件下，有理n次Bézier曲线的权因子改变与曲线参数化的关系。同时，给出了有理n次Bézier曲线上点的参数与权因子之间的对应关系，导出了有理n次Bézer曲线的n-1个形状不变因子。得到了与权因子变换对参数化有同样影响的参数射影变换，两种变换都不改变曲线的形状和首末端点，仅仅改变了曲线上的点与定义域内点的对应关系。