Perturbing Bezier coefficients for best constrained degree reduction in the L-2-norm
This paper first shows how the Bezier coefficients of a given degree n polynomial are perturbed so that it can be reduced to a degree m (< n) polynomial with the constraint that continuity of a prescribed order is preserved at the two endpoints. The perturbation vector, which consists of the perturbation coefficients, is determined by minimizing a weighted Euclidean norm. The optimal degree n - I approximation polynomial is explicitly given in Bezier form. Next the paper proves that the problem of finding a best L-2-approximation over the interval [0, 1] for constrained degree reduction is equivalent to that of finding a minimum perturbation vector in a certain weighted Euclidean norm. The relevant weights are derived. This result is applied to computing the optimal constrained degree reduction of parametric Bezier curves in the L-2-norm. (C) 2003 Elsevier Inc. All rights reserved.
degree reduction l-2-norm bezier form endpoint constraints least squares perturbation