How to make projection from altitude and azimuth to screen with screen coordinate system? Thanks to @ohoh for helped translate ra and dec into alt and az. Now that I have this data(altitude and azimuth), how can I plot it in something like this, with the coordinate system going like this?
The example sky map appears to be a stereographic projection; circles of right ascension and declination are projected as circular arcs, and their intersections are projected as right angles.
The example has a 195&deg; field of view, and the eastern and western horizons are mislabeled.

Let the celestial sphere be centered at the origin with radius 1, zenith at (0,&nbsp;0,&nbsp;1), northern horizon at (0,&nbsp;1,&nbsp;0), and eastern horizon at (1,&nbsp;0,&nbsp;0).
Assuming azimuth 0&deg; is north:
$$\begin{align}
x &amp;= \sin \mathrm{Az} \cos \mathrm{Alt} \\
y &amp;= \cos \mathrm{Az} \cos \mathrm{Alt} \\
z &amp;= \sin \mathrm{Alt}
\end{align}$$

To project from the nadir (0,&nbsp;0,&nbsp;-1) onto the plane z&nbsp;=&nbsp;0:
$$ (x', y') = \left( \frac{x}{z + 1}, \frac{y}{z + 1} \right) $$

To fit this between (0,&nbsp;0) and (2R,&nbsp;2R) on a canvas with northern horizon at (R,&nbsp;0) and eastern horizon at (0,&nbsp;R), scale by -R and translate by (R,&nbsp;R):
$$ (X, Y) = (R(1 - x'), R(1 - y')) $$

For a sky map centered overhead, if north is up, east should be on the left.