A new method to compute the singularities of offsets to rational plane curves
Algebraic Geometry
2015-06-12 v3
Abstract
Given a planar curve defined by means of a real rational parametrization, we prove that the affine values of the parameter generating the real singularities of the offset are real roots of a univariate polynomial that can be derived from the parametrization of the original curve, without computing or making use of the implicit equation of the offset. By using this result, a finite set containing all the real singularities of the offset, and in particular all the real self-intersections of the offset, can be computed. We also report on experiments carried out in the computer algebra system Maple, showing the efficiency of the algorithm for moderate degrees.
Keywords
Cite
@article{arxiv.1502.04518,
title = {A new method to compute the singularities of offsets to rational plane curves},
author = {Juan Gerardo Alcázar and Jorge Caravantes and Gema M. Diaz-Toca},
journal= {arXiv preprint arXiv:1502.04518},
year = {2015}
}