CHEBYSHEV-APPROXIMATION OF PLANE-CURVES BY SPLINES

Given a parametric plane curve p and any Bezier curve q of degree n such that p and q have contact of order k at the common end points, we use the normal vector field of p to measure the distance of corresponding points of p and q. Applying the theory of nonlinear Chebyshev approximation, we show that the maximum norm of this distance (or error) function rho(q) is locally minimal for q if and only if rho(q) is an alternant with 2 . (n - k - 1) + 1 extreme points. Finally, a Remes type algorithm is presented for the numerical computation of a locally best approximation to p. (C) 1994 Academic Press, Inc.