Degree formulae for offset curves

Authors:
Fernando San Segundo;J. Rafael Sendra
Affiliations:
Departamento de Matemáticas, Universidad de Alcalá, Ap. Correos 20, E-28871 Madrid, Spain;Departamento de Matemáticas, Universidad de Alcalá, Ap. Correos 20, E-28871 Madrid, Spain
Venue:
Journal of Pure And Applied Algebra
Year:
2005

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Abstract

In this paper, we present three different formulae for computing the degree of the offset of a real irreducible affine plane curve C given implicitly, and we see how these formulae particularize to the case of rational curves. The first formula is based on an auxiliary curve, called I, that is defined depending on a non-empty Zariski open subset of R2. The second formula is based on the resultant of the defining polynomial of C, and the polynomial defining generically I. The third formula expresses the offset degree by means of the degree of C and the multiplicity of intersection of C and the hodograph H to C, at their intersection points.