  Continuing work initiated in an earlier publication [Phys. Rev. D 69, 084007
(2004)], we construct a system of light-cone coordinates based at a geodesic
world line of an arbitrary curved spacetime. The construction involves (i) an
advanced-time or a retarded-time coordinate that labels past or future light
cones centered on the world line, (ii) a radial coordinate that is an affine
parameter on the null generators of these light cones, and (iii) angular
coordinates that are constant on each generator. The spacetime metric is
calculated in the light-cone coordinates, and it is expressed as an expansion
in powers of the radial coordinate in terms of the irreducible components of
the Riemann tensor evaluated on the world line. The formalism is illustrated in
two simple applications, the first involving a comoving world line of a
spatially-flat cosmology, the other featuring an observer placed on the axis of
symmetry of Melvin's magnetic universe.
