Rational conchoid and offset constructions: algorithms and implementation

Sendra Pons, Juana and Gómez Sánchez-Pascuala, David and Morán, Valerio (2014). Rational conchoid and offset constructions: algorithms and implementation. In: "12th International Conference on Artificial Intelligence and Symbolic Computation AISC 2014", 11/12/2014 - 13/12/2014, Sevilla, España. ISBN 978-3-319-13769-8. pp. 168-179.

Description

Title: Rational conchoid and offset constructions: algorithms and implementation
Author/s:
  • Sendra Pons, Juana
  • Gómez Sánchez-Pascuala, David
  • Morán, Valerio
Item Type: Presentation at Congress or Conference (Article)
Event Title: 12th International Conference on Artificial Intelligence and Symbolic Computation AISC 2014
Event Dates: 11/12/2014 - 13/12/2014
Event Location: Sevilla, España
Title of Book: Artificial Intelligence and Symbolic Computation : 12th International Conference, AISC 2014, Seville, Spain, December 11-13, 2014. Proceedings. Lecture Notes in Computer Science
Date: 2014
ISBN: 978-3-319-13769-8
Volume: 8884
Subjects:
Freetext Keywords: Offset variety, conchoid variety, rational parametrization, symbolic mathematical software
Faculty: E.T.S.I. y Sistemas de Telecomunicación (UPM)
Department: Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

This paper is framed within the problem of analyzing the rationality of the components of two classical geometric constructions, namely the offset and the conchoid to an algebraic plane curve and, in the affirmative case, the actual computation of parametrizations. We recall some of the basic definitions and main properties on offsets (see [13]), and conchoids (see [15]) as well as the algorithms for parametrizing their rational components (see [1] and [16], respectively). Moreover, we implement the basic ideas creating two packages in the computer algebra system Maple to analyze the rationality of conchoids and offset curves, as well as the corresponding help pages. In addition, we present a brief atlas where the offset and conchoids of several algebraic plane curves are obtained, their rationality analyzed, and parametrizations are provided using the created packages.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainMTM2011-25816-C02-01UnspecifiedUnspecifiedUnspecified

More information

Item ID: 36437
DC Identifier: http://oa.upm.es/36437/
OAI Identifier: oai:oa.upm.es:36437
Official URL: http://www.glc.us.es/aisc2014/
Deposited by: Memoria Investigacion
Deposited on: 29 Feb 2016 18:34
Last Modified: 29 Feb 2016 18:34
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