Data transformation of angles such that $90^\circ$ is equal to $-90^\circ$ Is there a transformation I can perform on a dataset of angles (from $-90^\circ$ to $90^\circ$) such that the transformation of $-90^\circ$ is equal to that of $90^\circ$? I am only interested in what these angles represent geometrically, so $-90^\circ$ and $90^\circ$ are both a vertical line. I just don't know how to convey this mathematically. 
Furthermore, this transformation needs to reflect the actual geometrical interpretation of these angles. For example, $-80^\circ$ and $80^\circ$ are only $20^\circ$ apart (whereas in the number line they are $160^\circ$ apart).
Thanks. 

Assuming all angles are $\phi \in [-90°, +90°]$, the following transformation may do the trick: $$T(\phi) = sign(\phi) \cdot 90°-\phi$$
$$sign(x) := \begin{cases}
-1 & \text{if } x < 0 \\
\ \ \ 0 & \text{if } x = 0 \\
\ \ \ 1 & \text{if } x > 0 \end{cases}$$
Examples:
$T(+90°) = 90°-90°=0$
$T(-90°) = -90°-(-90°)=0$
$T(80°)-T(-80°) = 90°-80° - (-90°+80°) =  10°-(-10°)=20°$
