DEGREE REDUCTION OF BEZIER CURVES

We provide an simple algorithm for constructing an polynomial Bezier a pproximation of degree n - 1 to an nth degree Bezier curve. This algor ithm makes previous work of Lachance more transparent as formulas are given which express the geometric relationship between the control poi nts. The two curves agree at the two endpoints up to a preselected dif ferentiation order since the method is based on constrained Chebyshev polynomials in order to obtain best constrained approximations. These polynomials then allow a detailed error analysis providing apriori bou nds of the pointwise approximation error. The extension to tensor prod uct surfaces is also briefly discussed.