【作者】 黄伟贤； 王国瑾；

【Author】 Huang Weixian,Wang Guojin (Department of Mathematics,Zhejiang University,Hangzhou 310027)

【机构】 浙江大学数学系；

【摘要】 鉴于Bezier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Bezier曲线这个工具,推导了2次和3次复有理Bezier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.本文构造的可弦长参数化2次复有理Bezier曲线通过其所有控制顶点.本文构造的可弦长参数化3次复有理Bezier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表明,本文所推导的对复有理施以弦长参数化的方法是十分有效的.更多还原

【Abstract】 Chord length parameterization of Bezier curves has important applications in the point inverse mapping of parametric curves. Using the tool of complex rational Bezier curves,mis paper derives some sufficient conditions that quadratic and cubic complex rational Bezier curves can be parameterized by chord length.What’s better,the paper presents the algorithms to construct curves with chord length parameterization by choosing appropriate control points and weights.The quadratic complex rational Bezier curve with chord length parameterizations constructed in this paper passes through all its control points.Apart from the given endpoints and the corresponding given tangents,the cubic complex rational Bezier curve with chord length parameterizations constructed in this paper offers other two freedoms to modify the shape of the curve.Numerical examples demonstrate that our method is an efficient way to construct complex rational with chord length parameterization.更多还原