Detecting Similarity of Plane Rational Curves

A novel and deterministic algorithm is presented to detect whether two given planar rational curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and the particular case of equal curves yields all symmetries. A complete theoretical description of the method is provided, and the method has been implemented and tested in the Sage system. Note of the authors: The final version of this paper was published as “Juan Gerardo Alcázar, Carlos Hermoso, Georg Muntingh: Detecting similarity of rational plane curves. Journal of Computational Applied Mathematics 269: 1-13 (2014).”