Chebyshev Approximation of Plane Curves by Splines

✍ Scribed by E.F. Eisele

• Publisher: Elsevier Science
• Year: 1994
• Tongue: English
• Weight: 552 KB
• Volume: 76
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1994.1010

✦ Synopsis

Given a parametric plane curve (\mathbf{p}) and any Bézier curve (\mathbf{q}) of degree (n) such that (\mathbf{p}) and (q) have contact of order (k) at the common end points, we use the normal vector field of (\mathbf{p}) to measure the distance of corresponding points of (\mathbf{p}) and (\mathbf{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_{\mathrm{q}}) is an alternant with (2 \cdot(n-k-1)+1) extreme points. Finally, a Remes type algorithm is presented for the numerical computation of a locally best approximation to p. 1994 Academic Press, Inc.