Constrained polynomial degree reduction in the L2-norm equals best weighted Euclidean approximation of Bézier coefficients

In this paper we show that the best constrained degree reduction of a given Bézier curve f of degree from n to m with Cα−1-continuity at the boundary in L2-norm is equivalent to the best weighted Euclidean approximation of the vector of Bernstein–Bézier (BB) coefficients of f from the vector of degree raised BB coefficients of polynomials of degree m with Cα−1-continuity at the boundary.  2003 Published by Elsevier B.V.