11 results on '"Perfect curves"'
Search Results
2. Computing branches and asymptotes of meromorphic functions.
- Author
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Fernández de Sevilla, M., Magdalena-Benedicto, R., and Pérez-Díaz, S.
- Abstract
In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily compute the whole branch and all the generalized asymptotes of a “special” curve defined in n-dimensional space by a parametrization that is not necessarily rational. So, some new concepts and methods are established for this type of curves. The approach is based on the notion of perfect curves introduced from the concepts and results presented in previous papers. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. A simple formula for the computation of branches and asymptotes of curves and some applications
- Author
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M. Fernández de Sevilla, Elena Campo-Montalvo, Sonia Pérez-Díaz, Universidad de Alcalá. Departamento de Automática, Universidad de Alcalá. Departamento de Ciencias de la Computación, and Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
- Subjects
Infinity branches ,Perfect curves ,Matemáticas ,Modeling and Simulation ,Parametrization ,Automotive Engineering ,Aerospace Engineering ,Asymptotes ,Computer Graphics and Computer-Aided Design ,Mathematics ,Curves - Abstract
In this paper, we obtain a simple formula based on the computation of some derivatives for determining the branches and the asymptotes of curves that are defined by a parametrization. For this purpose, we use some previous results and notions presented in Blasco and Pérez-Díaz, 2014a, Blasco and Pérez-Díaz, 2014b, Blasco and Pérez-Díaz, 2015, Blasco and Pérez-Díaz, 2020. From these results, we show how the generalized asymptotes of the input curve can be easily computed and we present some applications related to the ramification index and degree of the asymptote, the infinity form and the multiplicity of the infinity points. Furthermore, we show how to construct all the families of parametric curves having some given asymptotes. We develop this method for the plane case but it can be trivially adapted for dealing with rational curves in n-dimensional space. In addition, the formulaes presented can be similarly obtained for curves defined by a parametrization not necessarily rational., Agencia Estatal de Investigación
- Published
- 2022
4. Determining the asymptotic family of an implicit curve
- Author
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Campo Montalvo, Elena, Fernández De Sevilla Vellón, María De Los Ángeles, Magdalena Benedicto, Rafael, Pérez Díaz, Sonia, Universidad de Alcalá. Departamento de Automática, Universidad de Alcalá. Departamento de Ciencias de la Computación, and Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
- Subjects
Infinity branches ,Perfect curves ,Matemáticas ,Parametric plane curve ,Modeling and Simulation ,Approaching curves ,Automotive Engineering ,Aerospace Engineering ,Implicit algebraic plane curve ,Asymptotes ,Computer Graphics and Computer-Aided Design ,Mathematics - Abstract
In this paper we deal with the following problem: given an algebraic plane curve C, implicitly defined, we determine its “asymptotic family”, that is, the set of algebraic curves that have the same asymptotic behavior as C., Agencia Estatal de Investigación
- Published
- 2022
5. Asymptotes and perfect curves.
- Author
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Blasco, Angel and Pérez-Díaz, Sonia
- Subjects
- *
ASYMPTOTES , *GENERALIZATION , *PLANE curves , *ALGEBRAIC curves , *IRREDUCIBLE polynomials , *SET theory , *MATHEMATICAL analysis - Abstract
We develop a method for computing all the generalized asymptotes of a real plane algebraic curve implicitly defined by an irreducible polynomial . The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco and Pérez-Díaz (2013). In addition, we study some properties concerning perfect curves and in particular, we provide a necessary and sufficient condition for a plane curve to be perfect. Finally, we show that the equivalent class of generalized asymptotes for a branch of a plane curve can be described as an affine space for a certain m. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
6. A new approach for computing the asymptotes of a parametric curve
- Author
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Sonia Pérez-Díaz, Angel Blasco, and Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
- Subjects
Infinity branches ,Perfect curves ,Matemáticas ,Applied Mathematics ,010103 numerical & computational mathematics ,Implicit algebraic plane curve ,Space (mathematics) ,Asymptotes ,01 natural sciences ,010101 applied mathematics ,Computational Mathematics ,Parametric plane curve ,Approaching curves ,Applied mathematics ,Algebraic curve ,0101 mathematics ,Asymptote ,Parametric equation ,Mathematics - Abstract
In this paper, we summarize two algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. The approach is based on the notion of perfect curves introduced from the concepts and results presented in previous papers of the same authors. From these results, we derive a new and efficient method that allows to easily compute all the generalized asymptotes of an algebraic curve parametrically defined in n-dimensional space., Agencia Estatal de Investigación
- Published
- 2020
7. A simple formula for the computation of branches and asymptotes of curves and some applications.
- Author
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Campo-Montalvo, Elena, Fernández de Sevilla, Marián, and Pérez-Díaz, Sonia
- Subjects
- *
PARAMETRIC equations - Abstract
• We obtain a simple formula for determining the branches of parametric curves. • We obtain a simple formula for determining the asymptotes of parametric curves. • The formula is based on the computation of some simple derivatives. • We present applications related to the ramification index and the infinity points. • We construct all the families of parametric curves having some given asymptotes. In this paper, we obtain a simple formula based on the computation of some derivatives for determining the branches and the asymptotes of curves that are defined by a parametrization. For this purpose, we use some previous results and notions presented in Blasco and Pérez-Díaz (2014a,b, 2015, 2020). From these results, we show how the generalized asymptotes of the input curve can be easily computed and we present some applications related to the ramification index and degree of the asymptote, the infinity form and the multiplicity of the infinity points. Furthermore, we show how to construct all the families of parametric curves having some given asymptotes. We develop this method for the plane case but it can be trivially adapted for dealing with rational curves in n -dimensional space. In addition, the formulaes presented can be similarly obtained for curves defined by a parametrization not necessarily rational. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
8. A survey on recent advances and future challenges in the computation of asymptotes
- Author
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Pérez Díaz, Sonia, Blasco Lorenzo, Ángel, and Universidad de Alcalá. Departamento de Física y Matemáticas
- Subjects
Infinity branches ,Perfect curves ,Matemáticas ,Parametric plane curve ,Approaching curves ,Implicit algebraic plane curve ,Asymptotes ,Mathematics - Abstract
In this paper, we summarize two algorithms for computing all the generalizedasymptotes of a plane algebraic curve implicitly or parametrically de-fined. The approach is based on the notion of perfect curve introducedfrom the concepts and results presented in [Blasco and Pérez-Díaz(2014)],[Blasco and Pérez-Díazz(2014-b)] and [Blasco and Pérez-Díaz(2015)]. From these results, we derive a new method that allow to easily compute horizontal and vertical asymptotes., Agencia Estatal de Investigación
- Published
- 2019
9. A new approach for computing the asymptotes of a parametric curve.
- Author
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Blasco, Angel and Pérez-Díaz, Sonia
- Subjects
- *
PARAMETRIC equations , *ASYMPTOTES , *PLANE curves - Abstract
In this paper, we summarize two algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. The approach is based on the notion of perfect curves introduced from the concepts and results presented in previous papers of the same authors. From these results, we derive a new and efficient method that allows to easily compute all the generalized asymptotes of an algebraic curve parametrically defined in n -dimensional space. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
10. Asymptotes of space curves
- Author
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Angel Blasco, Sonia Pérez-Díaz, and Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
- Subjects
Infinity branches ,Plane curve ,Matemáticas ,media_common.quotation_subject ,Computation ,Asymptotes ,Mathematics - Algebraic Geometry ,FOS: Mathematics ,14H50, 14Q05, 68W30 ,Algebraic number ,Algebraic Geometry (math.AG) ,media_common ,Mathematics ,Algebraic space curve ,Perfect curves ,Plane (geometry) ,Applied Mathematics ,Mathematical analysis ,Convergent branches ,Infinity ,Computational Mathematics ,Algebraic space ,Algebraic curve ,Asymptote - Abstract
In this paper, we generalize the results presented in [5] for the case of real algebraic space curves. More precisely, given an algebraic space curve C (parametrically or implicitly defined), we show how to compute the generalized asymptotes. The approach is based on the notion of perfect curve introduced from the concepts and results presented in [4]., Comment: 30 pages, 9 figures. arXiv admin note: text overlap with arXiv:1307.6153
- Published
- 2015
11. Asymptotes and Perfect Curves
- Author
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Blasco Lorenzo, Ángel, Pérez Díaz, Sonia, and Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
- Subjects
Class (set theory) ,Pure mathematics ,Infinity branches ,Perfect curves ,Matemáticas ,Irreducible polynomial ,Plane curve ,Aerospace Engineering ,Implicit algebraic plane curve ,Asymptotes ,Computer Graphics and Computer-Aided Design ,Real plane ,Mathematics - Algebraic Geometry ,Modeling and Simulation ,Automotive Engineering ,FOS: Mathematics ,Affine space ,Algebraic curve ,Asymptote ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
We develop a method for computing all the generalized asymptotes of a real plane algebraic curve C implicitly defined by an irreducible polynomial f ( x , y ) ∈ R [ x , y ] . The approach is based on the notion of perfect curve introduced from the concepts and results presented in Blasco and Perez-Diaz (2013) . In addition, we study some properties concerning perfect curves and in particular, we provide a necessary and sufficient condition for a plane curve to be perfect. Finally, we show that the equivalent class of generalized asymptotes for a branch of a plane curve can be described as an affine space R m for a certain m.
- Published
- 2013
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