空间均匀有理张力样条参数曲线

Uniform Rational T-Spline Parametric Curve in Space

引入了基于双曲样条函数的、具有张力参数的空间有理等距节点样条参数曲线 ,给出了这种曲线在每个样条子区间上为挠曲线段 (即非平面曲线 )的充分必要条件 ;分析了这种挠曲线段没有尖点、重结点和泛拐点的特性 ;因而在用于空间曲线几何造型时可避免奇异性 .当张力参数趋于零或趋于无穷大时的极限曲线 ,分别是等距节点的有理三次B样条曲线和其控制多边形 ,故张力参数可用于调节曲线的光顺性 .还给出了将权系数用于曲线插值的一种方法 .

Introduced is a kind of space uniform rational spline curve, which possesses tension parameters and is based on hyperbolic spline functions. A necessary and sufficient condition for the curve being torsion curve in every sub-interval is given. Meanwhile the properties that there are no cusp, no loop and no generalized inflection on such curves are analyzed; thus the singularities using the curve in geometric modeling can be avoided. Further, it is found that the limit curve is a uniform rational cubic B-spline curve or the curve’s control polygon when its tension parameters tend to zero or infinity respectively. So the tension parameters can be used to adjust the fairness properties of such curves. Besides, an approach to using weight factors in curve interpolation is also presented.