Rational approximation of offset curves by S-power series

A new algorithm for multi-degree reduction approximating tensor product Bezier surfaces is presented.For a given tensor product Bezier surface,multi-degree reduction algorithm is adopted on the u direction and v direction of the Bezier surface separately.First,the S-power basis is used to express Bezier curves by using transformation matrices,then multi-degree reduction approximating Bezier curves will be achieved by truncating terms of high degree.Approximating Bezier surfaces is achieved by using this method in two different directions of the Bezier surface separately.The approximating surfaces have the constraint of high order interpolations over four corners naturally.Numerical examples are given.