预估校正NURBS实时插补算法的改进

预估校正算法是一类典型的NURBS插补算法，稳定的预估公式和明确的迭代收敛条件是该算法的关键；数学推导证明，现行的二阶预估公式不能保证插补过程中参数u的单调性，插补时将出现方向反转现象；该方法的迭代收敛条件不可能总是成立，在NURBS曲线尖角拐角处可能造成迭代过程发散。本文提出的一阶预估公式可以保证插补过程参数u的单调性，消除插补方向反转现象，和二阶预估公式比较，迭代次数有所增加，速度精度不变。

The Improvements of Predictor-Corrector Real-time NURBS Interpolation Algorithm

Predictor-Corrector Interpolator (PCI) is a kind of typical NURBS interpolation algorithm. Steady predictor and clear iteration convergence expression are the keys of the PCI. It is proven by math deduction that current 2-order predictor cannot assure parameter u monotonicity in interpolation process and interpolation direction would be reverse on some conditions. Iteration convergence expression cannot always be sure. The iteration may be divergence at NURBS curve sharp corner. A 1-order predictor proposed by this paper can guaranty the u monotonicity and eliminate interpolation direction reverse. Compare with 2-order predictor, this method have more iteration cycles while velocity precision is the same as that one.