  The illumination pattern (or emissivity profile) of the accretion disc due to
the reflection of X-rays in AGN can be understood in terms of relativistic
effects on the rays propagating from a source in a corona surrounding the
central black hole, both on their trajectories and on the accretion disc
itself. Theoretical emissivity profiles due to isotropic point sources as well
as simple extended geometries are computed in general relativistic ray tracing
simulations performed on graphics processing units (GPUs). Such simulations
assuming only general relativity naturally explain the accretion disc
emissivity profiles determined from relativistically broadened emission lines
which fall off steeply (with power law indices of between 6 and 8) over the
inner regions of the disc, then flattening off to almost a constant before
tending to a constant power law of index 3 over the outer disc. Simulations for
a variety of source locations, extents and geometries show how the emissivity
profiles depend on these properties, and when combined with reverberation time
lags allow the location and extent of the primary X-ray source to be
constrained. Comparing the emissivity profile determined from the broadened
iron K emission line in spectra of 1H 0707-495 obtained in January 2008 to
theoretical emissivity profiles and applying constraints from reverberation
lags suggest that there exists an extended region of primary X-ray emission
located as low as 2rg above the accretion disc, extending outwards to a radius
of around 30rg.
