Parametrization of approximate algebraic curves by lines

Authors:
Sonia Pérez-Díaz;Juana Sendra;J. Rafael Sendra
Affiliations:
Departmento de Matemáticas, Universidad de Alcalá, Facultad de Ciencias, Apartado de Correos 20, E-28871 Madrid, Spain;Departamento de Matemáticas, Universidad Carlos III, E-28911 Madrid, Spain;Departmento de Matemáticas, Universidad de Alcalá, Facultad de Ciencias, Apartado de Correos 20, E-28871 Madrid, Spain
Venue:
Theoretical Computer Science - Algebraic and numerical algorithm
Year:
2004

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Abstract

It is well known that irreducible algebraic plane curves having a singularity of maximum multiplicity are rational and can be parametrized by lines. In this paper, given a tolerance ε 0 and an ε-irreducible algebraic plane curve L of degree d having an ε-singularity of multiplicity d - 1, we provide an algorithm that computes a proper parametrization of a rational curve that is exactly parametrizable by lines. Furthermore, the error analysis shows that under certain initial conditions that ensures that points are projectively well defined, the output curve lies within the offset region of L at distance at most 2√2ε1(2d)exp(2).