有理参数曲线的C1分段根式弧角重新参数化算法研究

Research on C~1 Piecewise Radical Arc Angle Re-parameterization Algorithm for Rational Parametric Curves

曲线和曲面的参数化与重新参数化是计算机辅助几何设计研究中的基本问题。针对一类角速度函数在单位区间上存在零点的有理曲线参数表示,研究其近似弧角重新参数化,通过分段根式变换复合分段M?bius变换并结合C1连续的弧角新参数化算法,提出一种基于C1分段根式变换的重新参数化算法。实验表明,该算法能极大提升有理参数表示的角速度均匀度。

Parameterization and re-parameterization of curves and surfaces is a basic problem in computer-aided geometric design.The approximate arc angle re-parameterization is studied for a class of rational curve parameter representation of angular velocity function with zero on unit interval.Based on the piecewise radical transformation and the piecewise M?bius transformation combined with the C~1 arc angle new parameterization algorithm,a re-parameterization algorithm based on the C1piecewise radical transformation was proposed.Experiments show that this algorithm can greatly improve the angular velocity uniformity represented by the rational parameters.