Abhyankar, Shreeram S. ; Bajaj, Chanderjit (1987) Automatic parameretization of rational curves and surfaces 1: Conics and conicoids Computer-Aided Design, 19 (1). pp. 11-14. ISSN 0010-4485
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/001044...
Related URL: http://dx.doi.org/10.1016/0010-4485(87)90147-3
Abstract
Given the implicit equation for degree two curves (conics) and degree two surfaces (conicoids), algorithms are described here, which obtain their corresponding rational parametric equations (a polynomial divided by another). These rational parameterizations are considered over the fields of rationals, reals and complex numbers. In doing so, solutions are given to important subproblems of finding rational and real points on the given conic curve or conicoid surface. Further polynomial parameterizations are obtained whenever they exist for the conics or conicoids. These algorithms have been implemented on a VAX-780 using VAXIMA.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Geometry; Surfaces; Curves; Conics; Conicoids |
| ID Code: | 166 |
| Deposited On: | 17 Sep 2010 08:33 |
| Last Modified: | 10 May 2011 08:46 |
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