Curves with rational chord-length parametrization

Sánchez Reyes Fernández, Javier and Fernández Jambrina, Leonardo (2008). Curves with rational chord-length parametrization. "Computer Aided Geometric Design", v. 25 (n. 4-5); pp. 205-213. ISSN 0167-8396.


Title: Curves with rational chord-length parametrization
  • Sánchez Reyes Fernández, Javier
  • Fernández Jambrina, Leonardo
Item Type: Article
Título de Revista/Publicación: Computer Aided Geometric Design
Date: May 2008
ISSN: 0167-8396
Volume: 25
Freetext Keywords: bezier circle,bipolar coordinates,chord-length parametrization,equilateral hyperbola,lemniscate of bernoulli,circle
Faculty: E.T.S.I. Navales (UPM)
Department: Enseñanzas Básicas de la Ingeniería Naval [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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It has been recently proved that rational quadratic circles in standard Bezier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as a straightforward consequence. General curves with chord-length parametrization are simply the analogue in bipolar coordinates of nonparametric curves. This interpretation furnishes a compact explicit expression for all planar curves with rational chord-length parametrization. In addition to straight lines and circles in standard form, they include remarkable curves, such as the equilateral hyperbola, Lemniscate of Bernoulli and Limacon of Pascal. The extension to 3D rational curves is also tackled.

More information

Item ID: 2188
DC Identifier:
OAI Identifier:
DOI: 10.1016/j.cagd.2007.11.003
Official URL:
Deposited by: Memoria Investigacion
Deposited on: 05 Feb 2010 12:40
Last Modified: 20 Apr 2016 11:57
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