Cutting corners preserves Lipschitz continuity

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1994 English Publisher:Springer Science and Business Media LLCJournal:Applied Mathematics, volume 9, pages 31-34 (issn: 1005-1031, eissn: 1993-0445,

Copyright policy )

Authors: Feng, Yuyu; Kozak, Jernej;

doi: 10.1007/bf02662023

Cutting corners preserves Lipschitz continuity

- Summary
- Subjects
- Metrics

Abstract

In this note the author proves that the corner cutting procedure preserves continuity properties, i.e., a sequence of polygons obtained in this way belongs to the Lipschitz class of the same constant and exponent. As a consequence this also holds for all functions or curves obtained as the limit of this procedure, such as the Bernstein polynomials, Bézier and spline parametric curves.

Related Organizations

University of Ljubljana
Slovenia

Keywords

Bézier splines, Computer-aided design (modeling of curves and surfaces), corner cutting method, parametric curves, Lipschitz continuity, Bernstein polynomials

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average