Kristin Stapleton IFDM 210: journal 3/31

Ok, so here is an equation for HSV to RGB. Honestly, the easiest to understand was wikipedia, so that is where I go this.

Given a color with hue H ∈ [0°, 360°), saturation S_HSV ∈ [0, 1], and value V ∈ [0, 1], we first find chroma:

$C = V \times S_{HSV}\,\!$

Then we can find a point (R₁, G₁, B₁) along the bottom three faces of the RGB cube, with the same hue and chroma as our color (using the intermediate value X for the second largest component of this color):

$\begin{align} H^\prime &= \frac{H}{60^\circ} \\ X &= C (1 - |H^\prime \;\bmod 2 - 1|) \end{align}$

$(R_1, G_1, B_1) = \begin{cases} (0, 0, 0) &\mbox{if } H \mbox{ is undefined} \\ (C, X, 0) &\mbox{if } 0 \leq H^\prime < 1 \\ (X, C, 0) &\mbox{if } 1 \leq H^\prime < 2 \\ (0, C, X) &\mbox{if } 2 \leq H^\prime < 3 \\ (0, X, C) &\mbox{if } 3 \leq H^\prime < 4 \\ (X, 0, C) &\mbox{if } 4 \leq H^\prime < 5 \\ (C, 0, X) &\mbox{if } 5 \leq H^\prime < 6 \end{cases}$

Finally, we can find R, G, and B by adding the same amount to each component, to match value:

$\begin{align} &m = V - C \\ &(R, G, B) = (R_1 + m, G_1 + m, B_1 + m) \end{align}$

Kristin Stapleton IFDM 210

Thursday, March 31, 2011

journal 3/31

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