  Computation of parallel lines (envelopes) to parabolas, ellipses, and
hyperbolas is of importance in structure engineering and theory of mechanisms.
Homogeneous polynomials that implicitly define parallel lines for the given
offset to a conic are found by computing Groebner bases for an elimination
ideal of a suitably defined affine variety. Singularity of the lines is
discussed and their singular points are explicitly found as functions of the
offset and the parameters of the conic. Critical values of the offset are
linked to the maximum curvature of each conic. Application to a finite element
analysis is shown.
  Keywords: Affine variety, elimination ideal, Groebner basis, homogeneous
polynomial, singularity, family of curves, envelope, pitch curve, undercutting,
cam surface
