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In this paper we present several formulae for computing the partial degrees of the defining polynomial of the offset curve to an irreducible affine plane curve given implicitly, and we see how these formulae particularize to the case of rational curves. In addition, we present a formula for computing the degree w.r.t the distance variable.
The offset hypersurface <i>O</i><inf><i>d</i></inf>(<i>V</i>), at distance <i>d</i>, to an irreducible hypersurface <i>V</i> is essentially the envelope of the system of spheres centered at the points of <i>V</i> with fixed radius <i>d</i> (for a formal definition, and for basic properties of offsets, see  and ). This type of geometric objects have… (More)
We start recalling the classical and intuitive concept of offset curve. Let C be a plane curve, and let p ∈ C. Let L N be the normal line to C at p (assume for now that this normal line is well defined). Let q 1 , q 2 be the two points of L N at a fixed " distance " d 0 ∈ C * of p. Then, the offset curve (or parallel curve) to C at distance d 0 , is the set… (More)