APPROXIMATING A COMPOSITE CUBIC CURVE BY ONE WITH FEWER PIECES

An algorithm for approximating P by a single parametric cubic curve Q equals Merge (P//1, P//2) is studied. Typical applications are suggested. Iteratively applying Merge to adjacent pieces of an existing composite G**1 piecewise cubic, provides an approximating one with fewer pieces. Given a sequence of data points, it can be fitted with a standard G**1 piecewise cubic, and then the number of pieces can be reduced to obtain a more efficient one. Finally, some experiments are reported. Unfortunately, this method does not preserve C**2 continuity, but G**1 often suffices and this algorithm may be useful in those cases.