可弦长参数化的复有理曲线

Complex Rational Curves with Chord Length Parameterization

鉴于Bézier曲线的弦长参数化在参数曲线的点逆向工程中有着重要的应用,利用复有理Bézier曲线这个工具推导了2次和3次复有理Bézier曲线可弦长参数化的一些充分条件;进一步地,给出了选择控制顶点和权因子来构造可弦长参数化曲线的算法.文中构造的可弦长参数化2次复有理Bézier曲线通过其所有控制顶点;构造的可弦长参数化3次复有理Bézier曲线除了插值给定的端点及其切向之外,还提供2个自由度调节曲线的形状.数值例子结果表明,文中所推导的对复有理施以弦长参数化的方法是十分有效的.

Chord length parameterization of Bézier curves has important applications in the point inverse mapping of parametric curves.Using the tool of complex rational Bézier curves,this paper derives some sufficient conditions that quadratic and cubic complex rational Bézier curves can be parameterized by chord length.In addition,this paper presents the algorithms to construct curves with chord length parameterization by choosing appropriate control points and weights.The quadratic complex rational Bézier curve with chord length parameterizations constructed in this paper passes through all its control points.Apart from the given endpoints and the corresponding given tangent vectors,the constructed cubic complex rational Bézier curve with chord length parameterizations offers other two degrees of freedom to modify the shape of the curve.Numerical examples demonstrate that our method is efficient to construct complex rational with chord length parameterization.