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    <p>In HSV, the hue is defined as</p> <pre><code>H = atan2( sqrt(3)*(G-B), 2R-G-B ) </code></pre> <p>(<a href="http://en.wikipedia.org/wiki/HSL_and_HSV#Hue_and_chroma" rel="noreferrer">link</a>). In each of the six sectors (R-Y, Y-G ...), there are equally many hues. Additionally, there are six hues at the boundary between the regions. So, <code>6 + 6 * huesRY</code>.</p> <p>In the red-yellow sector, R > G > B, so both arguments to atan2 are positive.</p> <pre><code> count sqrt(3) * (G-B) / (2R-G-B) =count (G-B) / (2R-G-B) =count (G-B) / ((G-B) + (2R-2G)) </code></pre> <p>since we can apply any linear transformation to the sets of [x,y] and not change the count of its ratios, <code>x / (x+2y) == x / y</code></p> <pre><code>=count (G-B) / (R-G) </code></pre> <p>if we subtract the same value from all R,G,B, the ratio does not change, so assume B=0</p> <pre><code>=count G / (R-G) =count G / R </code></pre> <p>so, there are six times as many hues as there are ratios between two positive integers that are both below 2^8 (assuming 8 bits per channel), and six more. There are as many ratios as there are pairs of coprime positive integers. The number of positive integers below <code>n</code> that are coprime with <code>n</code> is called the Euler's totient function. <a href="http://oeis.org" rel="noreferrer">OEIS</a> <a href="http://oeis.org/A002088/b002088.txt" rel="noreferrer">lists</a> <a href="http://oeis.org/A000010" rel="noreferrer">its</a> <a href="http://oeis.org/A002088" rel="noreferrer">partial sums</a>. There are exactly 19948 pairs of coprime positive integers below 256.</p> <p>6 * 19948 + 6 = 119 694</p> <p><strong>There are exactly 119 694 different hues in the HSV model that correspond to a color in the 8-bit RGB model.</strong> Note that they are not spaced evenly.</p> <p>If 8 bits per channel are used in the HSV model, then there are less colors than in the RGB model with 8 bits per channel simply because some HSV triples map to the same color while every RGB triple defines a different color.</p>
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    1. POIn RGB model how many distinct hues are available?
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    1. USJohn Dvorak
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    1. POIn RGB model how many distinct hues are available?
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    1. COI do not think `sqrt(3)(x)` is a sensible notation. If you mean the cube root, write `root(3)(x)` or `x<sup>1/3</sup>`.
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      1. USPointedEars
    2. CO@PointedEars square root of three multiplied by x. Is it better now?
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