**2.1. Coordinate definition and computation**

In the current proposal, we regard the conversion of pixel coordinates to world coordinates as a multi-step process. This is illustrated conceptually in Fig. 1, which shows only the steps to be discussed here. Later extensions may interpose additional steps as required. For example, Paper II divides the final step into two with the computation of intermediate spherical coordinates that are subsequently converted to celestial coordinates via a spherical rotation. Paper IV interposes optional distortion corrections between the first and/or second steps of Fig. 1. Generally these are intended to account for small residuals that cannot be described by one of the standard world coordinate transformations. These may arise in a variety of ways; naturally (e.g. aberration or atmospheric refraction), via complex instrumental response functions (e.g. data cubes produced by a Fabry-Perot interferometer for which surfaces of constant wavelength are curved), by the intrinsic nature of the system under study (e.g. surface coordinates of the asteroid Eros), or as a result of instrumental peculiarities.