Algorithms for Trigonometric Curves (Simplification, Implicitization, Parameterization)

A trigonometric curve is a real plane curve where each coordinate is given parametrically by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can also be represented implicitly by bivariate poly...

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Veröffentlicht in:Journal of symbolic computation Jg. 26; H. 3; S. 279 - 300
Hauptverfasser: Hong, Hoon, Schicho, Josef
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.09.1998
ISSN:0747-7171, 1095-855X
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Abstract A trigonometric curve is a real plane curve where each coordinate is given parametrically by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can also be represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric representation, (b) computing an implicit representation from a given parametric representation, and (c) computing a parametric representation from a given implicit representation.
AbstractList A trigonometric curve is a real plane curve where each coordinate is given parametrically by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can also be represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric representation, (b) computing an implicit representation from a given parametric representation, and (c) computing a parametric representation from a given implicit representation.
Author Schicho, Josef
Hong, Hoon
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  givenname: Josef
  surname: Schicho
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  organization: Research Institute for Symbolic Computation, Johannes Kepler University, Linz, A-4040, Austria
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Snippet A trigonometric curve is a real plane curve where each coordinate is given parametrically by a truncated Fourier series. The trigonometric curves frequently...
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Title Algorithms for Trigonometric Curves (Simplification, Implicitization, Parameterization)
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