27 citations · 113 across the 12 of their papers we have counts for
13 papers
Infinity Branches and Asymptotic Analysis of Algebraic Space Curves: New Techniques and Applications
Sonia Pérez-Díaz, Li-Yong Shen, Xin-Yu Wang +1
Let C represent an irreducible algebraic space curve defined by the real polynomials fi(x1, x2, x3) for i = 1, 2. It is a recognized fact that a birational relationship invariably…
Computing branches and asymptotes of meromorphic functions
M. Fernandez de Sevilla, R. Magdalena Benedicto, S. Perez-Diaz
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 p…
The limit point and the T--function
Angel Blasco, Sonia Pérez-Díaz
Let be a rational parametrization of an algebraic space curve . In this paper, we introduce the notion of limit point, , of the given…
Characterizing the finiteness of the Hausdorff distance between two algebraic curves
Angel Blasco, Sonia Pérez-Díaz
In this paper, we present a characterization for the Hausdorff distance between two given algebraic curves in the -dimensional space (parametrically or implicitly defined) to be…
Asymptotes of Space Curves
Angel Blasco, Sonia Pérez-Díaz
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 implicitl…
Parametrization of translational surfaces
Sonia Perez-Diaz, Liyong Shen
The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition fo…
Asymptotes and Perfect Curves
Angel Blasco, Sonia Pérez-Díaz
We develop a method for computing all the {\it generalized asymptotes} of a real plane algebraic curve over implicitly defined by an irreducible polynomial $f(x,y…
Characterization of Rational Ruled Surfaces
Sonia Perez-Diaza, Liyong Shen
The ruled surface is a typical modeling surface in computer aided geometric design. It is usually given in the standard parametric form. However, it can also be in the forms than t…
Determination and (re)parametrization of rational developable surfaces
Sonia Perez-Diaz, Li-Yong Shen
The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the stan- dard parametric form, but it…
Numerical Reparametrization of Rational Parametric Plane Curves
Sonia Perez-Diaz, Li-Yong Shen
In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be…
Asymptotic Behavior of an Implicit Algebraic Plane Curve
A. Blasco, S. Perez-Diaz
In this paper, we introduce the notion of infinity branches as well as approaching curves. We present some properties which allow us to obtain an algorithm that compares the behavi…
Computing the Singularities of Rational Surfaces
S. Perez-Diaz, J. R. Sendra, C. Villarino
Given a rational projective parametrization $\cP(\ttt,\sss,\vvv)$ of a rational projective surface $\cS$ we present an algorithm such that, with the exception of a finite set (mayb…
Approximate Parametrization of Plane Algebraic Curves by Linear Systems of Curves
Sonia Perez-Diaz, Sonia L. Rueda, Juana Sendra +1
It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance and an -irreducible a…