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<header id="title-block-header">
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<h1 class="title">1.6 Application: Representing Colour</h1>
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</header>
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<section>
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<p>The physics behind how we perceive colour is incredibly interesting, but also complex. Humans have developed a broad range of names of colours to identify categories like “red” in everyday language.<label for="sn-0" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn-0" class="margin-toggle"/><span class="sidenote"> Although the names we use for colours vary widely from language to language!</span> Yet these categories can be fairly broad and imprecise; useful for everyday communication, but not for computer graphics and design. So in this section, we’ll learn about how computers represent colour data.</p>
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<p><img src="https://images.unsplash.com/photo-1534872471805-7a1c5a014651?ixlib=rb-1.2.1&ixid=eyJhcHBfaWQiOjEyMDd9&auto=format&fit=crop&w=1052&q=80" alt="color image" /><br />
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</p>
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<p>Mathematics can help us represent colours by a combination of numbers; the rules for how numbers map to colours is called a <em>colour model</em>. Many colour models exist, but one of the most common is the <em>RGB colour model</em>. At some point in your youth, you may have discovered that mixing two colours together (i.e., with paint, crayons, etc.) produces a different colour. The RGB colour model is based on the same idea: each colour is represented by three numbers, one for the “amount” of red, green, and blue to be mixed together.</p>
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<p>A common form of the RGB colour model in a computer is called the <strong>RGB24</strong> colour model, and allows for each of the red, green, and blue amounts to be a number between 0 and 255, inclusive.<label for="sn-1" class="margin-toggle sidenote-number"></label><input type="checkbox" id="sn-1" class="margin-toggle"/><span class="sidenote"> Though RGB24 is quite common, software like Photoshop allow for a larger range of numbers, enabling more granularity it their colour representations. You can look up the term <em>deep colour</em> to find out more about more sophisticated colour models</span> Formally, we can define the set <span class="math inline">\(S = \{0, 1, \dots, 255\}\)</span> and <span class="math inline">\(\mathcal{C}\)</span> to be the set of all possible colours in the universe. Then the RGB colour model is a function <span class="math inline">\(RGB_{24}: S \times S \times S \to \mathcal{C}\)</span> that takes in red, green, and blue values from <span class="math inline">\(S\)</span> and returns a colour. This <span class="math inline">\(RGB_{24}\)</span> function is <em>one-to-one</em>, as every combination of (red, green, blue) values produces a different colour.</p>
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<tr class="header">
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<th>RGB Value</th>
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<th>Colour</th>
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</tr>
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<td>(0, 0, 0)</td>
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<td><div height="10px" style="background-color: rgb(0,0,0)">
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</div></td>
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<td>(255, 0, 0)</td>
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<td><div height="10px" style="background-color: rgb(255,0,0)">
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</div></td>
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<td>(0, 255, 0)</td>
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</div></td>
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<td>(0, 0, 255)</td>
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<td><div height="10px" style="background-color: rgb(0,0,255)">
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</div></td>
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<td>(181, 57, 173)</td>
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<td><div height="10px" style="background-color: rgb(181,57,173)">
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</div></td>
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<tr class="even">
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<td>(255, 255, 255)</td>
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<td><div height="10px" style="background-color: rgb(255,255,255)">
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</div></td>
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<h3 id="colours-in-python">Colours in Python</h3>
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<p>The RGB24 colour model translates naturally to Python: we represent a colour value as a tuple of three integers, where each integer is between 0 and 255, inclusive. For example, we can use <code>(0, 0, 0)</code> to represent a pure black, and <code>(181, 57, 173)</code> to represent a shade of purple. Of course, just representing these values as tuples doesn’t automatically make them colours:</p>
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<div class="sourceCode" id="cb1"><pre class="sourceCode python"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1"></a><span class="op">>>></span> (<span class="dv">181</span>, <span class="dv">57</span>, <span class="dv">173</span>) <span class="co"># This tuple evaluates to... itself</span></span>
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<span id="cb1-2"><a href="#cb1-2"></a>(<span class="dv">181</span>, <span class="dv">57</span>, <span class="dv">173</span>)</span></code></pre></div>
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<p>But as you’ll see in your first tutorial this year, we can pass these tuples to operations that expect colour values, and get remarkable results.</p>
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<p><img src="images/colour_gradient.png" alt="Pygame demo of colour gradient" /><br />
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</p>
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<h2 id="references">References</h2>
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<ul>
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<li><a href="https://www.mathsisfun.com/hexadecimal-decimal-colors.html">Hexadecimal Colors</a></li>
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<li><a href="http://learn.colorotate.org/color-models/">Color Theory</a></li>
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</ul>
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</section>
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<footer>
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<a href="https://www.teach.cs.toronto.edu/~csc110y/fall/notes/">CSC110 Course Notes Home</a>
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</footer>
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