基于极小化二阶导矢确定节点

构造参数拟合曲线的关键问题之一是为每个数据点指定一个参数值（节点）。提出了一种确定节点的新方法。对于每个数据点，新方法由相邻的三个数据点构造一条二次多项式曲线，二次曲线的节点通过极小化其二阶导矢的平方确定。两个相邻数据点间的节点区间由两条二次曲线确定。为使节点计算公式能有效反映出相邻数据点的变化情况，新方法改进了修正弦长方法并应用于节点计算。新方法是一个局部化方法，因此适合于曲线曲面的交互设计。实验结果说明，新方法比其他节点计算方法有效。

Determining knots by minimizing second derivative vector

One of key problems of constructing parametric fitting curves is to compute a knot for each point. A new method for determining knots was presented. Corresponding to each data point, the new method constructed a quadratic curve that passed three consecutive points; the knots of the quadratic curve were determined by minimizing the second derivative vector of the curve. The knot interval between two adjacent points was determined by the two quadratic curves. The new method determined the knots with a local way, which made it useful in interactive design of curve and surface. The experimental results in this paper show that the new method is more effective than the other existing methods.