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Given a planar curve defined by means of a real rational parametrization, weprove that the affine values of the parameter generating the real singularitiesof the offset are real roots of a univariate polynomial that can be derivedfrom the parametrization of the original curve, without computing or making useof the implicit equation of the offset. By using this result, a finite setcontaining all the real singularities of the offset, and in particular all thereal self-intersections of the offset, can be computed. We also report onexperiments carried out in the computer algebra system Maple, showing theefficiency of the algorithm for moderate degrees.

A new method to compute the singularities of offsets to rational plane curves