%0 Journal Article
%A Rueda Pérez, Sonia Luisa
%A Sendra Pons, Juana
%A Sendra Pons, Juan Rafael
%T Rational Hausdorff Divisors: a New approach to the Approximate Parametrization of Curves
%D 2014
%@ 0377-0427
%U http://hdl.handle.net/10017/20518
%X In this paper we introduce the notion of rational Hausdor divisor, we analyze
the dimension and irreducibility of its associated linear system of curves, and we
prove that all irreducible real curves belonging to the linear system are rational
and are at nite Hausdor distance among them. As a consequence, we provide
a projective linear subspace where all (irreducible) elements are solutions to the
approximate parametrization problem for a given algebraic plane curve. Further-
more, we identify the linear system with a plane curve that is shown to be rational
and we develop algorithms to parametrize it analyzing its elds of parametriza-
tion. Therefore, we present a generic answer to the approximate parametrization
problem. In addition, we introduce the notion of Hausdor curve, and we prove
that every irreducible Hausdor curve can always be parametrized with a generic
rational parametrization having coe cients depending on as many parameters
as the degree of the input curve.
%K Hausdorff distance
%K Rational Hausdorff
%K Hausdorff curve
%K Approximate parametrization problem
%K Rational curve
%K Ciencia
%K Matemáticas
%K Science
%K Mathematics
%~ Biblioteca Universidad de Alcala