C~l Curve Interpolation Using Parametric Cubic RationalPolynomial

摘要

A new method is presented for constructing the parametric cubic rational curve to interpolate a set of data points. At each data point, a quadratic rational Bezier curve is constructed, between the two adjacent points, a cubic rational polynomial curve segment is constructed by the combination of the two quadratic rational Bezier curves, all the cubic rational curve segment form the whole C1 interpolation curve. The constructed C~1 cubic rational curve has the precision of the conic section, i.e., ifthe given data points are taken from a conic section, then the constructed curve reproduces the conic section exactly.