  Many systems of interest in general relativistic astrophysics, including
neutron stars, accreting compact objects in X-ray binaries and active galactic
nuclei, core collapse, and collapsars, are assumed to be approximately
spherically symmetric or axisymmetric. In Newtonian or fixed-background
relativistic approximations it is common practice to use spherical polar
coordinates for computational grids; however, these coordinates have
singularities and are difficult to use in fully relativistic models. We
present, in this series of papers, a numerical technique which is able to use
effectively spherical grids by employing multiple patches. We provide detailed
instructions on how to implement such a scheme, and present a number of code
tests for the fixed background case, including an accretion torus around a
black hole.
