\section{Map Projections}\label{sec:mapProj}

For the composition of different datasets on the GPU, we must
transform the normals of the sphere into texture coordinates.
Using the buffer of normals, we can calculate the geographic
location of each fragment by using a simple mapping from Cartesian to
spherical coordinates.

Once the geographic coordinates have been determined, they must be
transformed into projection coordinates using either an equirectangular
or polar stereographic projection.  
We modify the forward mapping equation for equirectangular projection~\cite{Eli07} by removing the radius.
This serves to reduce floating point errors from a large planetary radius.
\equation
{
	&p = (\lambda - \lambda_0) \, \cos \phi_0, \\
	&q = \phi,
}
where $\lambda$ and $\phi$ are the longitude and latitude components of
the geographic coordinates and $\lambda_0$ and $\phi_0$ are the center
longitude and latitude of the projection.  



