单圆弧样条保形插值算法

该文以插值具有偶数个点的闭多边形为例提出了一种新的圆弧样条插值算法。这种算法具有以下3个特点：（1）生成的圆弧样条曲线具有保形的特点；（2）圆弧样条中圆弧的段数与型值点个数相同。（3）圆弧段之间的连接点不一定在插值的型值点上，这样就能用更多的自由度来控制拟合曲线的形状。同此文中还提出了一个优化的算法来得到光顺的插值曲线，同时还给出了几个例子加以说明。

Shape-Preserving Interpolation by Circular Arc

This paper presents a new circular arc interpolation algorithm, which has the following three features. (1) The resulting arc spline is shape\|preserving, and has the same number of inflections with the original polyline; (2) The segment number of circular arcs is the same as that of data points. Almost all the conventional approach to arc spline interpolating is biarc curve interpolating, which result in about twice the segment number; (3) The connecting points of the arc spline can not be restricted to the interpolated data points, while almost all previous arc spline interpolation methods only consider the connecting points that are on the corresponding data points. As a result of which there are more freedoms to optimize the shape of the fitting curve. In addition to the circular arc interpolation algorithm and simple rules for assignment of the free variables, an optimization method is also presented to choose a fair curve. Several examples of the application of this approach are also presented.