NumCosmoMathSkyFootprintRectangular

Rectangular sky footprint in right ascension and declination.

A NcmSkyFootprint covering the rectangle $[\mathrm{ra}\mathrm{min}, \mathrm{ra}\mathrm{max}] \times [\mathrm{dec}\mathrm{min}, \mathrm{dec}\mathrm{max}]$ (degrees). Positions are sampled uniformly on the sphere patch: right ascension uniform in its range and declination uniform in $\sin(\mathrm{dec})$. The area is $\Delta\mathrm{ra}\,[\sin(\mathrm{dec}\mathrm{max}) - \sin(\mathrm{dec}\mathrm{min})]$, with $\Delta\mathrm{ra}$ in radians, and the density of ncm_sky_footprint_density() is \begin{equation} p(\mathrm{ra}, \mathrm{dec}) = \frac{\cos(\mathrm{dec})}{\Delta\mathrm{ra}\, \frac{180}{\pi}\left[\sin(\mathrm{dec}\mathrm{max}) - \sin(\mathrm{dec}\mathrm{min})\right]} \end{equation} inside the rectangle, with $\Delta\mathrm{ra}$ in degrees.

The limits must satisfy $-90 \le \mathrm{dec}\mathrm{min} < \mathrm{dec}\mathrm{max} \le 90$ and $0 < \mathrm{ra}\mathrm{max} - \mathrm{ra}\mathrm{min} \le 360$; other values abort. Right ascension is compared as given, without wrapping at 0 or 360 degrees: a patch across $\mathrm{ra} = 0$ is set with a negative $\mathrm{ra}\mathrm{min}$ (or $\mathrm{ra}\mathrm{max} > 360$), and positions must use the same convention. A limit that is not given, at construction or later as NULL, spans the whole sphere in that coordinate: $[0, 360]$ in right ascension and $[-90, 90]$ in declination.