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.