给出一种二次B样条曲线插值方法.利用数据点的参数化和节点向量的自由度,构造在各数据点满足切向约束的二次B样条插值曲线,直观地控制插值曲线达到预期形状.用文中方法构造插值曲线是一个递推过程,不必预先确定数据点参数值和节点向量、不必解线性方程组,而是在插值过程中根据数据点及其切向的约束条件递推地确定数据点的参数值、节点和控制顶点.该文方法允许插值曲线各段的连接点与数据点不一致,以使得二次B样条插值曲线的形状更自然.而且在满足数据点切向约束的条件下,还可利用节点进一步调控插值曲线的形状.另外,用文中方法构造的二次B样条插值曲线对于数据点的改变具有较好的局部性质.文中最后给出一些例子将该文方法与其它一些插值方法进行比较,实验结果表明,该文方法是有效的.
In this paper a new interpolation method for quadratic B-spline curves is proposed so as to fully utilize the degrees of freedom provided by parameterization and knot vector to control the shapes of the interpolation curves intuitively by the tangent constraints on data points. Without solving any equation systems, the interpolation procedure of the method is a recursive one in which the parameter values at data points, the knots and the control points are determined recursively according to the data points and the tangent constraints on data points. With the method the connection points of adjacent curve segments are not necessarily coincident with data points, so that the shapes of quadratic B-spline interpolation curves are more natural. Furthermore, under the restriction of the tangent constraints, there are still some degrees of freedom in constructing interpolation curves by the method, the shapes of the interpolation curves can be further ad- justed by the selection of knots. Besides, the quadratic B-spline interpolation curves constructed by the method possess rather good local properties for the relieving disturbances on data points. Some examples are given to compare the method proposed in the paper with several other interpolation methods. The experimental results show that this method is effective.