Trigonometric Extension of the Geometric Correction Factor: Prototype
  for adding precision to adaptive ray tracing in ENZO
  In this paper, we describe a method designed to add precision to radiation
simulations in the adaptive mesh refinement cosmological hydrodynamics code
ENZO. We build upon the geometric correction factor described in
\textit{ENZO+MORAY: radiation hydrodynamics adaptive mesh refinement
simulations with adaptive ray tracing} (Wise and Abel 2011) which accounts for
partial coverage of a ray's solid angle with a cube. Because of this geometric
mismatch in the methods to approximate this, there are artifacts in the
radiation field. Here, we address the two-dimensional extension, which acts as
a sufficient estimate of the three-dimensional case and, in practice, the
Hierarchical Equal Area isoLatitude Pixelization of the sphere (HEALPix)
(Gorski 2005). We will demonstrate the value of an extension to the geometric
correction factor and lay the groundwork for a future implementation to ENZO to
improve simulations of radiation from point sources.
