Results 1 to 10 of about 129,549 (262)
On the geometry and the topology of parametric curves [PDF]
Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020 We consider the problem of computing the topology and describing the geometry of a parametric curve in R. We present an algorithm, PTOPO, that constructs an abstract graph that is isotopic to the curve in the embedding space. Our method exploits the benefits of the parametric representation and does not resort to implicitization.
Katsamaki, Christina +3 more
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Symbolic parametrization of curves
Journal of Symbolic Computation, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
J. Rafael Sendra, Franz Winkler 0001
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Parametric curves with Pythagorean binormal
Advances in Computational Mathematics, 2014 The authors present a new class of rational spatial curves with rational binormal. They call this new class PB curves. Also, the construction of this kind of curves (PB curves) is presented based upon the dual curve representation and the Euler-Rodrigues frame obtained from quaternion polynomials.
Jernej Kozak +2 more
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Radical parametrizations of algebraic curves by adjoint curves
Journal of Symbolic Computation, 2011 We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less o equal to 4 and they are defined over an algebraically closed field of characteristic zero. In addition, we also present an algorithm for parametrizing by radicals any irreducible plane curve of degree $d$ having at least a point of ...
J. Rafael Sendra, David Sevilla
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Parametrizations of elliptic curves by Shimura curves and by classical modular curves [PDF]
Proceedings of the National Academy of Sciences, 1997 Fix an isogeny class 𝒜 of semistable elliptic curves over Q. The elements of 𝒜 have a common conductor N , which is a square-free positive integer. Let D be a divisor of N which is the product of an even number of primes—i.e., the discriminant of an indefinite ...
Ribet, Kenneth A., Takahashi, Shuzo
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Implicitization of Parametric Curves by Matrix Annihilation [PDF]
International Journal of Computer Vision, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hulya Yalcin +2 more
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On the Choice of Pencils in the Parametrization of Curves
Journal of Symbolic Computation, 1992 The main result of this paper is an algorithm which takes as input a plane curve of genus 0 with only ordinary singularities, defined over an infinite perfect field \(K\), and outputs a parametrizaton of the curve defined at worst over a quadratic extension of \(K\).
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Parametric Curves for Graphic Design Systems [PDF]
The Computer Journal, 1983 One important requirement of a graphic design system is to be able to draw a visually pleasing curve passing through a sequence of discrete points in the Euclidean plane. These points are normally provided as input by the graphic designer or the graphic artist.
Pijush K. Ghosh, Sudhir P. Mudur
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Parametrizations for Families of ECM-Friendly Curves [PDF]
Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, 2017 We provide a new family of elliptic curves that results in a one to two percent performance improvement of the elliptic curve integer factoriza-tion method. The speedup is confirmed by extensive tests for factors ranging from 15 to 63 bits.
Gélin, Alexandre +2 more
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Degrees of Parametrizations of Elliptic Curves by Shimura Curves
Journal of Number Theory, 2001 Let \(N\) be a square-free positive integer and \((D,M)\) a pair of positive integers such that \(N=DM\) and the number of prime factors of \(D\) is even. Consider the Shimura curve \(X_0^D(M)\) associated with an Eichler order of level \(M\) in an indefinite quaternion algebra of discriminant \(D\) defined over the field of rational numbers \(\mathbb ...
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