Offsets, Conchoids and Pedal Surfaces

Sendra Pons, Juana and Peternell, Martin and Gotthart, Lukas and Sendra Pons, J. Rafael (2015). Offsets, Conchoids and Pedal Surfaces. "Journal of Geometry", v. 106 (n. 2); pp. 321-339. ISSN 0047-2468.


Title: Offsets, Conchoids and Pedal Surfaces
  • Sendra Pons, Juana
  • Peternell, Martin
  • Gotthart, Lukas
  • Sendra Pons, J. Rafael
Item Type: Article
Título de Revista/Publicación: Journal of Geometry
Date: July 2015
ISSN: 0047-2468
Volume: 106
Freetext Keywords: Offset surfaces, conchoid surfaces, pedal surfaces, inverse pedal surfaces, Darboux and Dupin cyclides.
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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We discuss three geometric constructions and their relations, namely the offset, the conchoid and the pedal construction. The offset surface F d of a given surface F is the set of points at fixed normal distance d of F. The conchoid surface G d of a given surface G is obtained by increasing the radius function by d with respect to a given reference point O. There is a nice relation between offsets and conchoids: The pedal surfaces of a family of offset surfaces are a family of conchoid surfaces. Since this relation is birational, a family of rational offset surfaces corresponds to a family of rational conchoid surfaces and vice versa. We present theoretical principles of this mapping and apply it to ruled surfaces and quadrics. Since these surfaces have rational offsets and conchoids, their pedal and inverse pedal surfaces are new classes of rational conchoid surfaces and rational offset surfaces.

Funding Projects

Government of SpainMTM2011-25816-C02-01UnspecifiedUnspecifiedAlgoritmos y aplicaciones en geometría de curvas y superficies

More information

Item ID: 36189
DC Identifier:
OAI Identifier:
DOI: 10.1007/s00022-014-0251-1
Official URL:
Deposited by: Memoria Investigacion
Deposited on: 17 Mar 2016 11:59
Last Modified: 31 May 2019 15:09
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