Celestial Programming : Convert Between Rectangular And Polar Coordinates
Polar to Rectangular:
$$
\begin{align*}
x& = r \sin \theta \cos \varphi \\
y& = r \sin \theta \sin \varphi \\
z& = r \cos \theta \\
\end{align*}
$$
Rectangular to Polar:
$$
\begin{align*}
r& = \sqrt{x^2 + y^2 + z^2} \\
\cos \theta& = \frac{z}{r} \\
\cos \varphi& = \frac{x}{\sqrt{x^2 + y^2}} \\
\sin \varphi& = \frac{y}{\sqrt{x^2 + y^2}} \\
\tan \varphi& = \frac{y}{x} \\
\end{align*}
$$
- x is Horizontal (left and right).
- y is Depth (in and out of screen).
- z is Vertical (up and down).
- \(\theta\) Vertical (usually lattitude or declination). Range -90° to 90°.
- \(\varphi\) Horizontal (usually longitude or right ascension). Range -180° to 180°, or 0° to 360°
- \(r\) Radius.