In order to get the approximately arc-length parameterized rational Bézier curves, a method for reparameterization of rational Bézier curves is proposed based on a piecewise M?bius parameter transfor-mation. This method constructs the piecewise M?bius transformation applying to the rational Bézier curve, on which the break points are chosen as the locally maximal value points of its curvature. And a metric function is defined by the deviation of new parametric speed from unit-speed with respect to L2norm under the condition of C1continuous parametric speed. Then the expression of this M?bius transformation is ob-tained by minimizing the metric function. Numerical examples show that rational Bézier curves with piece-wise M?bius transformation have good parameters very close to the arc-length parameter.%为了得到近似弧长参数的有理Bézier曲线表示, 提出基于分段M?bius参数变换的有理Bézier曲线的重新参数化方法. 该方法将曲线的曲率极大值点作为分段点构造分段 M?bius 参数函数; 在保证参数速率 C1的连续条件下,用新参数速率关于单位速率偏离变量的 L2范数作为度量标准函数; 通过最小化该目标函数求得分段 M?bius 函数的具体表示. 实例结果表明, 通过分段M?bius变换后, 有理Bézier曲线的参数具有很好的弧长参数近似效果.
展开▼
