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中文摘要：
针对非均匀采样点拟合时的光滑B样条曲线构造问题,提出一种基于已知控制顶点和节点向量求解未知控制顶点来构造光滑B样条曲线的方法.首先对所有控制顶点进行基函数极值参数化,再将已知控制顶点作为型值点进行光滑样条曲线插值,并在此曲线上通过利用参数化结果求值得到未知控制顶点.该方法通过控制顶点所在曲线的光顺性提高最终生成曲线的连续性和光滑性.最后通过实例说明,采用文中方法所构造的B样条曲线具有较好的光顺性.
英文摘要：
In order to overcome the problem resulted from none-uniform sampled data set,this paper presents a method to calculate unknown control points using given control points and knots to generate a smooth B-spline curve.It is based on the basis-function-maximum-value parameterization introduced in this paper.This method first parameterizes all control points;then regards given control points as data points to create a fit curve by interpolation;and finally obtains the unknown control points by evaluating the corresponding parameters directly,which improves the continuity and smoothness of the generated B-spline curve.The examples in the last section illustrate the feasibility of this method.
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