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\title{IRAM Memo 2023-1\\[3\bigskipamount]
  Review of the spatial projections support in \mbox{\sc gildas}\\
  Compatibility with FITS}%
\author{S. Bardeau$^{1}$, J. Pety$^{1,2}$\\[0.5cm]
  1. IRAM (Grenoble) \\
  2. Observatoire de Paris}%
\date{22-nov-2023 \\
  version 1.0} \makeindex{}



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$\displaystyle \phi$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1772}%
$\displaystyle \frac{x}{\cos y}$%
\lthtmlindisplaymathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1781}%
$\displaystyle \alpha$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1785}%
$\displaystyle \alpha_p +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1786}%
$\displaystyle (-\cos\theta\sin(\phi-\phi_p),
\sin\theta\cos\delta_p-\cos\theta\sin\delta_p\cos(\phi-\phi_p))$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1788}%
$\displaystyle \delta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1792}%
$\displaystyle \sin^{-1}(\sin\theta\sin\delta_p+\cos\theta\cos\delta_p\cos(\phi-\phi_p))$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1800}%
$\displaystyle \phi_p +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1801}%
$\displaystyle (-\cos\delta\sin(\alpha-\alpha_p),
\sin\delta\cos\delta_p-\cos\delta\sin\delta_p\cos(\alpha-\alpha_p))$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1807}%
$\displaystyle \sin^{-1}(\sin\delta\sin\delta_p+\cos\delta\cos\delta_p\cos(\alpha-\alpha_p))$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1814}%
$\displaystyle \phi \cos \theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1826}%
$\displaystyle \phi_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1830}%
$\displaystyle 0^\circ$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1832}%
$\displaystyle \delta_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1836}%
$\displaystyle +90^\circ$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1838}%
$\displaystyle \alpha_p$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1842}%
$\displaystyle \alpha_0 - 180^\circ$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1844}%
$ \phi_{\text{SFL},0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1846}%
$\displaystyle \phi_{\text{SFL},0} = \text{atan2}(-\cos\delta\sin(\alpha-\alpha_0-180^\circ),
-\cos\delta\cos(\alpha-\alpha_0-180^\circ))
= \alpha-\alpha_0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1848}%
$ (-y,-x) =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1849}%
$ (y,x) + 180^\circ$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1851}%
$ \theta_{\text{SFL},0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1853}%
$\displaystyle \theta_{\text{SFL},0} = \sin^{-1}(\sin\delta)
= \delta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1856}%
$\displaystyle x_{\text{SFL},0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1860}%
$\displaystyle (\alpha-\alpha_0) \cos \delta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1862}%
$\displaystyle y_{\text{SFL},0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1871}%
$\displaystyle x^\prime_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1875}%
$\displaystyle x_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1876}%
$\displaystyle = (\alpha-\alpha_0) \cos \delta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1878}%
$\displaystyle y^\prime_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1882}%
$\displaystyle y_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1883}%
$\displaystyle + \delta_0 = \delta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1885}%
$ (x^\prime_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1886}%
$ ,y^\prime_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1887}%
$ ) =
(x_{\text{SFL},0},y_{\text{SFL},0})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1889}%
$ x_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1890}%
$ = x_{\text{SFL},0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1892}%
$ y_$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1893}%
$ = y_{\text{SFL},0} - \delta_0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1896}%
$ (3600,-1800), (3600,+1800)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1898}%
$ (-200,0)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1906}%
$ \delta_0 \ne 0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}


\end{document}
