Rates of convergence of control polygons

Authors:
Elaine Cohen;Larry L. Schumaker
Affiliations:
Dept. of Computer Science, University of Utah, Salt Lake City, UT 84112, U.S.A.;Center for Approximation Theory, Texas A&M University, College Station, RX 77843, U.S.A.
Venue:
Computer Aided Geometric Design
Year:
1985

Citing 2
Cited 5

A survey of curve and surface methods in CAGD

Computer Aided Geometric Design
A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces

IEEE Transactions on Pattern Analysis and Machine Intelligence

On Chebyshevian spline subdivision

Journal of Approximation Theory
On the degree elevation of Bernstein polynomial representation

Journal of Computational and Applied Mathematics
L-system specification of knot-insertion rules for non-uniform B-spline subdivision

Computer Aided Geometric Design
The Bernstein polynomial basis: A centennial retrospective

Computer Aided Geometric Design
A content-aware bridging service for publish/subscribe environments

Journal of Systems and Software

Quantified Score

Hi-index	0.00

Visualization

Abstract

It is well known (cf. [Farin '77] for a proof) that the sequence of control polygons associated with the Bernstein-Bezier representation of a curve using polynomials of degree n converges to the curve as n goes to infinity. Similarly, it was shown in [Lane & Riesenfeld '80] that if a uniform floating B-spline curve is uniformly refined, then the resulting sequence of control polygons also converges to the curve. In this paper we present a simple general method for treating such convergence questions which actually provides precise rates of convergence. We illustrate the method by applying it to B-spline curves which are refined by increasing the degrees and/or refining the knot sequences.