Detecting When an Implicit Equation or a Rational Parametrization Defines a Conical or Cylindrical Surface, or a Surface of Revolution

Given an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e., the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a...

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Bibliographische Detailangaben
Veröffentlicht in:IEEE transactions on visualization and computer graphics. - 1996. - 23(2017), 12 vom: 15. Dez., Seite 2550-2559
1. Verfasser: Alcazar, Juan Gerardo (VerfasserIn)
Weitere Verfasser: Goldman, Ron
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2017
Zugriff auf das übergeordnete Werk:IEEE transactions on visualization and computer graphics
Schlagworte:Journal Article Research Support, Non-U.S. Gov't
Beschreibung
Zusammenfassung:Given an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e., the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a surface of revolution. The algorithms are directly applicable to, and formulated in terms of, the implicit equation or the rational parametrization. When the surface is cylindrical, we show how to compute the direction of its rulings; when the surface is conical, we show how to compute its vertex; and when the surface is a surface of revolution, we show how to compute its axis of rotation directly from the defining equations
Beschreibung:Date Completed 17.12.2018
Date Revised 17.12.2018
published: Print-Electronic
Citation Status PubMed-not-MEDLINE
ISSN:1941-0506
DOI:10.1109/TVCG.2016.2625786