====== Brightness ======

In the simplest terms the "brightness" of a pixel is its luminosity value as perceived by a human eye (making infrared and gamma rays \(0\) "bright"). There are quite a few competing standards and definitions of what the means exactly, but for our purposes we will use the \(L\) component of the HSL color space as our "brightness" value of a pixel.

Again, in the simplest terms, increasing or reducing pixel's brightness can be interpreted as adding or subtracting a fixed "gain" value (others may argue that a more natural approach would be to use a multiplier, while others still may bring the "vibrancy" approach into picture).

===== In RGB color space =====
The mathematically correct way to do the brightness is to first convert into HSL color space, adjust the L (luma) component, and then convert back into RGB. That gives the correct result but costs way too many transistors and cycles. So we've got to improvise!

==== Algorithm ====
Here's the algorithm to follow, assuming \(R, G, B \in [0..4095]\) and \(br \in [-1024..+1023]\):
  - calculate luminosity
  - adjust the brightness additively and clamp the value to range \([0..4095]\)
  - figure out the slope for each components based on whether luma is below or above 50% and set chroma components to values that correspond to that 50% luma
  - figure out if the new luma is going to cross the 50% boundary and if so - "flip the slopes"
  - recalculate RGB components

==== Calculation reference ====

To calculate luminosity we just find the max and min of the triplet and get a simple average:
\[L = \frac{min(R, G, B)+max(R, G, B)}{2}\]

Brightness adjustment is a trivial addition, clamping the value to its proper limits:

\[
L` = L + br \\
L` \in [0..4095]
\]

The slope \(k_R\) for the red component calculation depends on whether \(L\) is above or below the middle:
\[
k_{R} =
\begin{cases}
R / L & \text{if} \; L \leq 2047 \\
\frac{R - 4095}{L - 4095} & \text{if} \; L > 2047
\end{cases}
\]

Finding the "middle point" value also depends on whether the \(L\) is above or below the middle:
\[
R =
\begin{cases}
k_R * 2047 & \text{if} \; L \leq 2047 \\
4095 - k_R * 2047 & \text{if} \; L > 2047
\end{cases}
\]

If we are crossing the middle luma boundary as the result of this adjustment - flip the slope:
\[
k_R = 2 - k_R
\]

Applying the new \(L`\) to R component and clamping the result is trivial:

\[
R` = k_R * (L` - 2047) + R \\
R` \in [0..4095]
\]

\(G\) and \(B\) calculations are similar to \(R\).

===== In HSL color space =====
When using the HSL color space the adjustment is as simple as elementary school's arithmetic operation. Namely - just a simple addition.

With that the implementation of the Brightness adjustment can be as simple as the following (where the "luma", or brightness component \(\in[0..100]%%\)):
<code c++>// pseudo-code
void brightness(/*array of pixels*/image, int _br){
  for(const & pixel: image){
    pixel.luma = std::clamp(pixel.luma + _br, 0, 100);
  }
}</code>