Convert RGB to HSL

Hue Calculation

To calculate the hue, ( h ):

$$h=\{\begin{array}{ll}\frac{g-b}{\Delta }+(g<b?6:0),& \text{if }\max =r\\ \frac{b-r}{\Delta }+2,& \text{if }\max =g\\ \frac{r-g}{\Delta }+4,& \text{if }\max =b\end{array}$$ $$\Delta =\max -\min$$

and (\max) and (\min) are the maximum and minimum RGB values, respectively. The result is normalized:

$$h=\frac{h}{6}$$

Saturation Calculation

To calculate the saturation, ( s ):

$$s=\{\begin{array}{ll}0,& \text{if }\max =\min \\ \frac{\Delta }{2-\max -\min },& \text{if }l>0.5\\ \frac{\Delta }{\max +\min },& \text{otherwise}\end{array}$$

where

$$l=\frac{\max +\min }{2}$$

is the lightness.

Lightness Calculation

To calculate the lightness, ( l ):

$$l=\frac{\max +\min }{2}$$

Pseudocode Algorithm

\begin{algorithm}
\caption{RGBtoHSL}
\begin{algorithmic}
  \Procedure{RGBtoHSL}{$r, g, b$}
    \State Normalize $r, g, b$ by dividing each by $255$
    \State $maxVal \gets \max(r, g, b)$
    \State $minVal \gets \min(r, g, b)$
    \State $l \gets (maxVal + minVal) / 2$
    \If{$maxVal = minVal$}
      \State $s \gets 0$
      \State $h \gets 0$
    \Else
      \State $delta \gets maxVal - minVal$
      \If{$l > 0.5$}
        \State $s \gets delta / (2 - maxVal - minVal)$
      \Else
        \State $s \gets delta / (maxVal + minVal)$
      \EndIf
      \If{$maxVal = r$}
        \State $h \gets (g - b) / delta + (g < b \ ? 6 \ : 0)$
      \ElsIf{$maxVal = g$}
        \State $h \gets (b - r) / delta + 2$
      \ElsIf{$maxVal = b$}
        \State $h \gets (r - g) / delta + 4$
      \EndIf
      \State $h \gets h / 6$
    \EndIf
    \State \Return $h, s, l$
  \EndProcedure
\end{algorithmic}
\end{algorithm}