An implicitization algorithm with fewer variables

In this paper we present a general implicitization algorithm for rational parameterizations, using Gröbner Bases, which: (i) is valid for general parametric varieties (i.e. allowing both rational or polynomial parameterizations), (ii) computes the greatest ideal of polynomials vanishing over the var...

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Bibliographic Details
Published in:Computer aided geometric design Vol. 12; no. 3; pp. 251 - 258
Main Authors: Alonso, Cesar, Gutierrez, Jaime, Recio, Tomas
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.05.1995
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Artificial intelligence
Computer science; control theory; systems
Exact sciences and technology
Gröbner bases
Implicitization
Parametric varieties
Pattern recognition. Digital image processing. Computational geometry
Theoretical computing
Gröbner bases
Implicitization
Parametric varieties
Computational geometry
Parametrization
Gröbner basis
Algorithm performance
ISSN:0167-8396, 1879-2332
Online Access:Get full text
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Summary:In this paper we present a general implicitization algorithm for rational parameterizations, using Gröbner Bases, which: (i) is valid for general parametric varieties (i.e. allowing both rational or polynomial parameterizations), (ii) computes the greatest ideal of polynomials vanishing over the variety and (iii) uses only as many variables as the number of parameters plus coordinates. We give examples of the performance of our algorithm in the CoCoa system, comparing the obtained results with other algorithms.
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content type line 23
ISSN:0167-8396
1879-2332
DOI:10.1016/0167-8396(95)91147-R