ABSTRACT
Piecewise rational curves are widely used in computer-aided geometric design and geometric modeling. This has various reasons, for instance that parametric representations by rational functions comply with industrial standards. In [33], [34], the authors describe a method to approximate an (not necessarily rational) algebraic curve by pieces of rational cubics. By approximation theory, the best approximation by rational curves is one which intersects the given curve in the maximal number of points. The idea in [33], [34] is to take four points in the interior of the curve which is to be approximated, and to search for an arc of a rational cubic that interpolates the curve segment at these four points and at the tangents of the two ends. If a solution exists, it can be easily found by solving a linear system.
