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<!DOCTYPE html>
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   Chuck Orde — I can't drive 55
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       <a href="/i-cant-drive-55.html">
        Jun.01.2014
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       By
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        Chuck Orde
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        Data Visualization
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        I can't drive 55
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           It's Sunday and all I have is boredom, so I'll recreate and plot the goofy speed limit sign I made for my garage.
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          In [11]:
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            <pre><span></span><span class="n">figsize</span><span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mf">11.5</span><span class="p">)</span>
<span class="n">xticks</span><span class="p">([])</span>
<span class="n">yticks</span><span class="p">([])</span>
<span class="n">text</span><span class="p">(</span><span class="o">.</span><span class="mi">5</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="s1">'''</span>
<span class="s1">SPEED</span><span class="se">\n</span><span class="s1">LIMIT</span>
<span class="s1">$\int^</span><span class="si">{28}</span><span class="s1">_</span><span class="si">{27}</span><span class="s1">\!f(2x)\mathrm</span><span class="si">{d}</span><span class="s1">x$</span>
<span class="s1">'''</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">90</span><span class="p">,</span>
     <span class="n">name</span><span class="o">=</span><span class="s1">'Arial Black'</span><span class="p">,</span>
     <span class="n">horizontalalignment</span><span class="o">=</span><span class="s1">'center'</span><span class="p">)</span>

<span class="n">text</span><span class="p">(</span><span class="o">.</span><span class="mi">4</span><span class="p">,</span><span class="mf">0.45</span><span class="p">,</span><span class="s1">' - 2'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="n">text</span><span class="p">(</span><span class="o">.</span><span class="mi">33</span><span class="p">,</span><span class="mf">0.13</span><span class="p">,</span><span class="s1">' - 3'</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">50</span><span class="p">)</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">()</span>
<span class="n">x</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">],[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]]</span>
<span class="n">y</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">],[</span><span class="mi">1</span><span class="p">,</span><span class="mi">0</span><span class="p">]]</span>
<span class="n">p</span> <span class="o">=</span> <span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s1">'k'</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">25</span><span class="p">)</span>
</pre>
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          <p>
           I should round the corners to make it more like a speed limit sign, but I'll just be lazy and pretend that this is the way that they really look.
          </p>
          <p>
           Now we can create the $y$ function, plug in the limits, and compute the area under the "curve".  This is a stupid example that makes me laugh (motorcycles and math!) so it's a pretty trivial equation.
          </p>
          <p>
           We know the answer is $b^2 - a^2$, so we'll plot it to understand why.
          </p>
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            <pre><span></span><span class="kn">from</span> <span class="nn">matplotlib.patches</span> <span class="k">import</span> <span class="n">Polygon</span>

<span class="k">def</span> <span class="nf">func</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
    <span class="k">return</span> <span class="mi">2</span><span class="o">*</span><span class="n">x</span>

<span class="k">def</span> <span class="nf">integrate</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">,</span><span class="n">ax</span><span class="p">,</span> <span class="n">title</span><span class="o">=</span><span class="s1">''</span><span class="p">):</span>
    <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">50</span><span class="p">,</span><span class="o">.</span><span class="mi">1</span><span class="p">)</span>
    <span class="n">y</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">y</span><span class="p">,</span> <span class="n">lw</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
    <span class="n">ix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">,</span> <span class="o">.</span><span class="mi">01</span><span class="p">)</span>
    <span class="n">iy</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">ix</span><span class="p">)</span>
    <span class="n">verts</span> <span class="o">=</span> <span class="p">[(</span><span class="n">a</span><span class="p">,</span><span class="mi">0</span><span class="p">)]</span> <span class="o">+</span> <span class="nb">list</span><span class="p">(</span><span class="nb">zip</span><span class="p">(</span><span class="n">ix</span><span class="p">,</span><span class="n">iy</span><span class="p">))</span> <span class="o">+</span> <span class="p">[(</span><span class="n">b</span><span class="p">,</span><span class="mi">0</span><span class="p">)]</span>
    <span class="n">poly</span> <span class="o">=</span> <span class="n">Polygon</span><span class="p">(</span><span class="n">verts</span><span class="p">,</span> <span class="n">facecolor</span><span class="o">=</span><span class="s1">'.8'</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">yaxis</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">xaxis</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">add_patch</span><span class="p">(</span><span class="n">poly</span><span class="p">)</span>

    <span class="n">ax</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">68</span><span class="p">,</span><span class="s2">"$\int_{</span><span class="si">%d</span><span class="s2">}^{</span><span class="si">%d</span><span class="s2">}\!f(2x)\mathrm</span><span class="si">{d}</span><span class="s2">x = </span><span class="si">%d</span><span class="s2">$"</span>
            <span class="o">%</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="n">b</span><span class="p">,</span> <span class="n">b</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">32</span><span class="p">)</span>
    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">title</span><span class="p">,</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">14</span><span class="p">)</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">suptitle</span><span class="p">(</span><span class="s1">'Integral of $\!f(2x)$'</span><span class="p">,</span><span class="n">fontsize</span><span class="o">=</span><span class="mi">18</span><span class="p">)</span>

<span class="n">figsize</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span><span class="mi">8</span><span class="p">)</span>
<span class="n">ax1</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">121</span><span class="p">)</span>
<span class="n">ax2</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span>

<span class="n">integrate</span><span class="p">(</span><span class="mi">27</span><span class="p">,</span> <span class="mi">28</span><span class="p">,</span> <span class="n">ax1</span><span class="p">,</span> <span class="s1">'with limits $27$ and $28$'</span><span class="p">)</span>
<span class="n">integrate</span><span class="p">(</span><span class="mi">27</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">28</span><span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="n">ax2</span><span class="p">,</span> <span class="s1">'with limits $27-3$ and $28-2$'</span><span class="p">)</span>
</pre>
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