基于型值点拟合的非均匀有理B样条曲线曲面延拓算法

提出了一种用于非均匀有理B样条曲线曲面延拓的算法,采用＂先离后合＂的思想,首先对需要延拓的非均匀有理B样条基线进行分析,构造出一系列的基线型值点;然后将延拓点加入到型值点序列中,再对新的型值点序列进行插值,创建出延拓曲线;最后对生成的延拓曲线的控制顶点序列进行优化操作,以保证所创建的延拓曲线拥有最佳的几何数据结构,从而为下一次延拓打下坚实的基础。算法通过在型值点构造过程中调节容差检验值,使得延拓操作能够适应任意精度的运算场合,从而在运算速度与精度之间达到最佳平衡。讨论了非均匀有理B样条曲线曲面延拓的几种不同形式,以及相应延拓点的计算方式,并给出了运用该算法的运行结果。

Algorithm of NURBS curve & surface extension based on characteristic-points fitting

A new algorithm of Non Uniform Rational B-Spline(NURBS) extension was proposed.A sequence of characteristic-points was created based on the analysis of the NURBS curves to be extended firstly.By inserting the extending points into the sequence of characteristic-points,a new extending curve was interpolated.Finally,an optimization procedure was applied on the new extending curve to have a very simple data structure to proceed to next extending procedure more easily.Particularly,a tolerance value was presented to adjust the accuracy of calculating procedure,so that the best balance between speed and accuracy of the calculating was achieved.Moreover,some forms of the NURBS extension were discussed and the methods of extending points calculating were presented,and results of the algorithm were also provided.