  A variety of problems in computational physics and engineering require the
convolution of the heat kernel (a Gaussian) with either discrete sources,
densities supported on boundaries, or continuous volume distributions. We
present a unified fast Gauss transform for this purpose in two dimensions,
making use of an adaptive quad-tree discretization on a unit square which is
assumed to contain all sources. Our implementation permits either free-space or
periodic boundary conditions to be imposed, and is efficient for any choice of
variance in the Gaussian.
