Complex Bézier curves and the geometry of polynomials

Rachid Ait-Haddou*, Taishin Nomura

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations

Abstract

In this paper, we study the shape of the control polygon of a complex Bézier curve over a complex interval. We show that the location of the complex roots of the polynomial dictates geometrical constraints on the shape of the control polygon. Along the work, new proofs and generalizations of the Walsh coincidence Theorem and the Grace Theorem are given. Applications of the geometry of the control polygon of complex polynomials to Bernstein type inequalities are discussed.

Original languageEnglish (US)
Title of host publicationCurves and Surfaces - 7th International Conference, Curves and Surfaces 2010, Revised Selected Papers
Pages43-65
Number of pages23
DOIs
StatePublished - Jan 16 2012
Event7th International Conference on Curves and Surfaces, Curves and Surfaces 2010 - Avignon, France
Duration: Jun 24 2010Jun 30 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6920 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other7th International Conference on Curves and Surfaces, Curves and Surfaces 2010
CountryFrance
CityAvignon
Period06/24/1006/30/10

Keywords

  • Bernstein type inequalities
  • Complex Bézier curves
  • Grace Theorem
  • Walsh coincidence Theorem
  • complex de Casteljau algorithm
  • polar derivative

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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