  A general framework for dealing with irradiation effects in the bolometric
sense --- specifically, reflection with heat absorption and the consequent
redistribution of the absorbed heat, for systems of astrophysical bodies where
the boundaries are used as support for the description of the processes, is
presented. Discussed are its mathematical and physical properties, as well as
its implementation approximations, with a focus on three plausible
redistribution processes (uniform, latitudinal, and local redistribution).
These are tested by extending PHOEBE 2.1 ( http://phoebe-project.org ), the
open-source package for modeling eclipsing binaries, and applied to a toy model
of the known two-body eclipsing systems.
