Paper Info
Title
Approximate parametrization of plane algebraic curves by linear systems of curves
Abstract
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 @e0 and an @e-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of @e-rationality, and we provide an algorithm to parametrize approximately affine @e-rational plane curves by means of linear systems of (d-2)-degree curves. The algorithm outputs a rational parametrization of a rational curve C@? of degree d which has the same points at infinity as C. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that C@? and C are close in practice.
Year
DOI
Venue
2010
10.1016/j.cagd.2009.12.002
Computer Aided Geometric Design
Keywords
Field
DocType
plane algebraic curve,approximate,curve c,empirical analysis,proper degree,linear systems of curves,degree curve,plane algebraic curves,e-irreducible algebraic affine plane,e-rational plane curve,rational parametrization,approximate parametrization,rational curve,linear system,irreducible algebraic curve,theoretical analysis,parametrization
Topology,Discrete mathematics,Family of curves,Algebraic curve,Stable curve,Pure mathematics,Butterfly curve (algebraic),Plane curve,Quartic plane curve,Circular algebraic curve,Mathematics,Polar curve
Journal
Volume
Issue
ISSN
27
2
Computer Aided Geometric Design
Citations 
PageRank 
References 
18
0.93
14
Authors
4
Name
Order
Citations
PageRank
Sonia Pérez-Díaz114715.93
J. Rafael Sendra262168.33
Sonia L. Rueda3486.45
Juana Sendra419319.65