  In factorization formulae for cross sections of scattering processes,
final-state jets are described by jet functions, which are a crucial ingredient
in the resummation of large logarithms. We present an approach to calculate
generic one-loop jet functions, by using the geometric subtraction scheme. This
method leads to local counterterms generated from a slicing procedure; and
whose analytic integration is particularly simple. The poles are obtained
analytically, up to an integration over the azimuthal angle for the
observable-dependent soft counterterm. The poles depend only on the soft limit
of the observable, characterized by a power law, and the finite term is written
as a numerical integral. We illustrate our method by reproducing the known
expressions for the jet function for angularities, the jet shape, and jets
defined through a cone or $k_T$ algorithm. As a new result, we obtain the
one-loop jet function for an angularity measurement in $e^+e^-$ collisions,
that accounts for the formally power-suppressed but potentially large effect of
recoil. An implementation of our approach is made available as the GOJet
Mathematica package accompanying this paper.
