A New Method On Approximation Of Rational Curves By Parametric Polynomials

In computer aided geometric design, computer aided design and computer aided manu-facturing, curve and surface modeling is one of the important parts. It mainly studies on the representing,showing, designing and analyzing of curve/surface in computer imaging system. Between the rational curves/surface and polynomial curves/surface has many resemblance in calculation method and geometric quality. According to the resemblance, a series of studies on approximation of rational curves/surface and circular arcs by polynomial curves/surface has been acquired a lot of achievements. A new method for approximation of rational curves by poly-nomial curves is proposed. The parametric equation of the rational curve can be transformed into an implicit algebraic equation through the resultant method. Then the approximation problem is transformed into an optimization problem with polynomial objective function. Solve this problem to get the parameters so that the polynomial curve is determined. Finally, some examples are given to show the effectiveness of these methods. Numerical examples show that our method is simpler in calculating and have better approximation results. Additionally, we obtain smaller error between the curves defined by Hausdorff distance. Circular arcs is a special kind of rational curve, we simply introduced some methods for circular arc by quartic polynomial curves.