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<li><a href="#about" id="toc-about" class="nav-link active" data-scroll-target="#about">About</a></li>
<li><a href="#circles" id="toc-circles" class="nav-link" data-scroll-target="#circles">Circles</a>
<ul>
<li><a href="#converting-from-non-parametric-to-parametric-for-a-unit-circle" id="toc-converting-from-non-parametric-to-parametric-for-a-unit-circle" class="nav-link" data-scroll-target="#converting-from-non-parametric-to-parametric-for-a-unit-circle">Converting from Non-Parametric to Parametric For a Unit Circle</a>
<ul class="collapse">
<li><a href="#creating-the-data" id="toc-creating-the-data" class="nav-link" data-scroll-target="#creating-the-data">Creating the Data</a></li>
</ul></li>
<li><a href="#performing-transformations-on-a-circle" id="toc-performing-transformations-on-a-circle" class="nav-link" data-scroll-target="#performing-transformations-on-a-circle">Performing Transformations on a Circle</a>
<ul class="collapse">
<li><a href="#movement-of-a-circle" id="toc-movement-of-a-circle" class="nav-link" data-scroll-target="#movement-of-a-circle">Movement of a circle</a></li>
<li><a href="#visual-summary" id="toc-visual-summary" class="nav-link" data-scroll-target="#visual-summary">Visual Summary</a></li>
<li><a href="#resizingscaling-a-circle" id="toc-resizingscaling-a-circle" class="nav-link" data-scroll-target="#resizingscaling-a-circle">Resizing/Scaling a Circle</a></li>
<li><a href="#visual-summary-1" id="toc-visual-summary-1" class="nav-link" data-scroll-target="#visual-summary-1">Visual Summary</a></li>
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<div class="quarto-title">
<h1 class="title">Making Shapes Manually in ggplot2</h1>
</div>
<div class="quarto-title-meta">
</div>
</header>
<section id="about" class="level2">
<h2 class="anchored" data-anchor-id="about">About</h2>
<p>I want to make shapes manually…So here’s where I’ll drop processes for that as I learn. This is currently a low–effort work in progress. The hardest part so far has been converting nonparametric equations into parametric equations that will display the shapes as expected on a Cartesian coordinate system.</p>
</section>
<section id="circles" class="level2">
<h2 class="anchored" data-anchor-id="circles">Circles</h2>
<section id="converting-from-non-parametric-to-parametric-for-a-unit-circle" class="level3">
<h3 class="anchored" data-anchor-id="converting-from-non-parametric-to-parametric-for-a-unit-circle">Converting from Non-Parametric to Parametric For a Unit Circle</h3>
<ol type="1">
<li><p><span class="math inline">\(y^2 + x^2 = r^2\)</span> ← Non-Parametric</p></li>
<li><p><span class="math inline">\(\frac{y^2}{r^2} + \frac{x^2}{r^2} = 1\)</span></p></li>
<li><p><span class="math inline">\((\frac{y}{r})^2 + (\frac{x}{r}^2) =1\)</span></p></li>
<li><p><span class="math inline">\(sin^2\theta + cos^2\theta = 1\)</span></p></li>
<li><p><span class="math inline">\(sin \theta = \frac{y}{r}\)</span><br> <span class="math inline">\(cos \theta = \frac{x}{r}\)</span></p></li>
<li><p><span class="math inline">\(x = cos(\theta)\)</span> ← Parametric<br> <span class="math inline">\(y = sin(\theta)\)</span> ← Parametric</p></li>
</ol>
<blockquote class="blockquote">
<p>In order to create the coordinates for a circle, we have to create a system that will generate <code>x</code> and <code>y</code> points that will visually represent a circle when plotted on ggplot2’s carteisan plane.</p>
</blockquote>
<section id="creating-the-data" class="level4">
<h4 class="anchored" data-anchor-id="creating-the-data">Creating the Data</h4>
<ol type="1">
<li>Decide how many angles/points/slices of the circle you wish to calculate. = <code>angle_n</code>.</li>
<li>Create a sequence of angles (thetas aka <span class="math inline">\(\theta\)</span>) based on the amount of angles/points/slices. = <code>theta</code>.</li>
<li>Create a system of coordinates (aka data frame) of calculated <code>x</code> and <code>y</code> points using the <code>theta</code>. = <code>circle_df</code></li>
<li>Plot the dataframe with appropriate aesthetics and geoms desired.</li>
<li>Use <code>coord_equal()</code> for better scaled drawing of circles. (otherwise, it may look like an <a href="https://en.wikipedia.org/wiki/Ellipse">ellipse</a>) <br></li>
</ol>
<p><sub><em>Recall that an angle consists of 360 <span class="math inline">\(\degree\)</span> which in radians (<span class="math inline">\(rad\)</span>) equates to <span class="math inline">\(2pi\)</span></em>.</sub></p>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(ggplot2) <span class="co">#For plotting</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(tibble) <span class="co">#For cleaner df manipulation (base can be used)</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="co">#Step 1====</span></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="co">#Setting 50 points (slices) that lie in a circle#</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a>angle_n <span class="ot"><-</span> <span class="dv">50</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="co">#Step 2====</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="co">#Calculating angle_n angles/points within a circle#</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a>theta <span class="ot"><-</span> <span class="fu">seq</span>(<span class="at">from =</span> <span class="dv">0</span>,</span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a> <span class="at">to =</span> <span class="dv">2</span> <span class="sc">*</span> pi, </span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a> <span class="at">length =</span> angle_n)</span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="co">#Step 3====</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a><span class="co">#Creating a dataframe or corresponding x and y values for the circle using theta</span></span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a>circle_df <span class="ot"><-</span> <span class="fu">tibble</span>(<span class="at">x =</span> <span class="fu">cos</span>(theta),</span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> <span class="fu">sin</span>(theta),</span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a> <span class="at">label =</span> <span class="dv">0</span><span class="sc">:</span>(angle_n<span class="dv">-1</span>))</span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a><span class="co">#Step 4 and 5====</span></span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a><span class="co">#Plotting the circle</span></span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a>circle_df <span class="sc">|></span></span>
<span id="cb1-23"><a href="#cb1-23" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y, <span class="at">label =</span> label)) <span class="sc">+</span></span>
<span id="cb1-24"><a href="#cb1-24" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>() <span class="sc">+</span></span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_label</span>(<span class="at">size =</span> <span class="dv">2</span>) <span class="sc">+</span> <span class="co">#labels added for learning/comparative purposes</span></span>
<span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip1-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
</section>
</section>
<section id="performing-transformations-on-a-circle" class="level3">
<h3 class="anchored" data-anchor-id="performing-transformations-on-a-circle">Performing Transformations on a Circle</h3>
<section id="movement-of-a-circle" class="level4">
<h4 class="anchored" data-anchor-id="movement-of-a-circle">Movement of a circle</h4>
<p>Moving a circle on a plane requires simply adding or subtracting values from the <code>x</code> and <code>y</code> points of the existing system accordingly.</p>
<p><br> <br></p>
<ul>
<li><span style="color:cornflowerblue"><strong>Horizontal</strong></span> movement requires a value added or subtracted to/from the <code>x</code> variable in the system.</li>
</ul>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb2"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(purrr) <span class="co">#For list manipulation</span></span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(dplyr) <span class="co">#for data wrangling</span></span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="co">#Moving the unit circle horizontally by 1 left (subtract) and right (addition)</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>trans_values <span class="ot"><-</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">1</span>,<span class="dv">1</span>)</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a>trans_directions <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"left"</span>, <span class="st">"right"</span>)</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>horizontal_trans <span class="ot"><-</span> <span class="fu">map2_df</span>(trans_values, trans_directions, <span class="sc">~</span>circle_df <span class="sc">|></span></span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">x =</span> x <span class="sc">+</span> .x,</span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> <span class="at">direction =</span> .y)</span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> )</span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a>horizontal_trans <span class="sc">|></span></span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y, <span class="at">group =</span> direction)) <span class="sc">+</span></span>
<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">data =</span> circle_df, <span class="fu">aes</span>(x,y), </span>
<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">3</span>,</span>
<span id="cb2-17"><a href="#cb2-17" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>,</span>
<span id="cb2-18"><a href="#cb2-18" aria-hidden="true" tabindex="-1"></a> <span class="at">inherit.aes =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb2-19"><a href="#cb2-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">color =</span> <span class="st">"cornflowerblue"</span>,</span>
<span id="cb2-20"><a href="#cb2-20" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb2-21"><a href="#cb2-21" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip2-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
<p><br></p>
<ul>
<li><span style="color:tomato"><strong>Vertical</strong></span> movement requires a value added or subtracted to/from the <code>y</code> variable in the system.</li>
</ul>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co">#Moving the unit circle vertically by 1 down (subtract) and up (addition)</span></span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>trans_values <span class="ot"><-</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">1</span>,<span class="dv">1</span>)</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>trans_directions <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"down"</span>, <span class="st">"up"</span>)</span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>vertical_trans <span class="ot"><-</span> <span class="fu">map2_df</span>(trans_values, trans_directions, <span class="sc">~</span>circle_df <span class="sc">|></span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">y =</span> y <span class="sc">+</span> .x,</span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a> <span class="at">direction =</span> .y)</span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a> )</span>
<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a>vertical_trans <span class="sc">|></span></span>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y, <span class="at">group =</span> direction)) <span class="sc">+</span></span>
<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">data =</span> circle_df, <span class="fu">aes</span>(x,y), </span>
<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">3</span>,</span>
<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>,</span>
<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a> <span class="at">inherit.aes =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">color =</span> <span class="st">"tomato"</span>,</span>
<span id="cb3-17"><a href="#cb3-17" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb3-18"><a href="#cb3-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip3-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
<ul>
<li><span style="color:darkmagenta"><strong>Diagonal</strong></span> movement requires a value added or subtracted to/from both the <code>x</code> and <code>y</code> variables in the system.</li>
</ul>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co">#Moving the unit circle diagonally by 1 in all four main quadrants.</span></span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>trans_xvalues <span class="ot"><-</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">1</span>,<span class="dv">1</span>,<span class="sc">-</span><span class="dv">1</span>,<span class="dv">1</span>)</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>trans_yvalues <span class="ot"><-</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">1</span>,<span class="sc">-</span><span class="dv">1</span>)</span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>trans_directions <span class="ot"><-</span> <span class="fu">c</span>(<span class="st">"down-left"</span>, <span class="st">"up-right"</span>, <span class="st">"up-left"</span>, <span class="st">"down-right"</span>)</span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a>circle_options <span class="ot"><-</span> <span class="fu">list</span>(trans_xvalues,</span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a> trans_yvalues,</span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a> trans_directions)</span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a>diagonal_trans <span class="ot"><-</span> <span class="fu">pmap_df</span>(circle_options, <span class="sc">~</span>circle_df <span class="sc">|></span></span>
<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">x =</span> x <span class="sc">+</span> ..<span class="dv">1</span>,</span>
<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> y <span class="sc">+</span> ..<span class="dv">2</span>,</span>
<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a> <span class="at">direction =</span> ..<span class="dv">3</span>)</span>
<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-17"><a href="#cb4-17" aria-hidden="true" tabindex="-1"></a>diagonal_trans <span class="sc">|></span></span>
<span id="cb4-18"><a href="#cb4-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y, <span class="at">group =</span> direction)) <span class="sc">+</span></span>
<span id="cb4-19"><a href="#cb4-19" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">data =</span> circle_df, <span class="fu">aes</span>(x,y), </span>
<span id="cb4-20"><a href="#cb4-20" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">3</span>,</span>
<span id="cb4-21"><a href="#cb4-21" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>,</span>
<span id="cb4-22"><a href="#cb4-22" aria-hidden="true" tabindex="-1"></a> <span class="at">inherit.aes =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb4-23"><a href="#cb4-23" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">color =</span> <span class="st">"darkmagenta"</span>,</span>
<span id="cb4-24"><a href="#cb4-24" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb4-25"><a href="#cb4-25" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip4-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
<p><br></p>
</section>
<section id="visual-summary" class="level4">
<h4 class="anchored" data-anchor-id="visual-summary">Visual Summary</h4>
<ul>
<li><span style="color:cornflowerblue">Horizontal</span> (<code>x</code> variable operations)</li>
<li><span style="color:tomato">Vertical</span> (<code>y</code> variable operations)</li>
<li><span style="color:darkmagenta">Diagonal</span> (<code>x</code> and <code>y</code> variable operations)</li>
</ul>
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip4-2-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
</section>
<section id="resizingscaling-a-circle" class="level4">
<h4 class="anchored" data-anchor-id="resizingscaling-a-circle">Resizing/Scaling a Circle</h4>
<p>Scaling/resizing a circle on a plane requires multiplying or dividing values from the <code>x</code> and <code>y</code> points of the existing system accordingly.</p>
<p><span style="color:orange">Multiplying</span> both the <code>x</code> and <code>y</code> variables will <strong>increase</strong> the scale of the circle (<em>size it up/make it larger</em> by the value)</p>
<p><br></p>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb5"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co">#Increasing the size of the circle by 5 units on both the x and y axis - multiplying.</span></span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>trans_value <span class="ot"><-</span> <span class="dv">5</span></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>multi_trans <span class="ot"><-</span> <span class="fu">map_df</span>(trans_value, <span class="sc">~</span>circle_df <span class="sc">|></span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">x =</span> x <span class="sc">*</span> .x,</span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> y <span class="sc">*</span> .x)</span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a>multi_trans <span class="sc">|></span></span>
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y)) <span class="sc">+</span></span>
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">data =</span> circle_df, <span class="fu">aes</span>(x,y), </span>
<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">3</span>,</span>
<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>,</span>
<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a> <span class="at">inherit.aes =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb5-16"><a href="#cb5-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">color =</span> <span class="st">"orange"</span>,</span>
<span id="cb5-17"><a href="#cb5-17" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb5-18"><a href="#cb5-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip5-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
<p><br></p>
<p><span style="color:limegreen">Dividing</span> both the <code>x</code> and <code>y</code> variables will <strong>decrease</strong> the scale of the circle (<em>size it down/make it smaller</em> by the inverse of the value)</p>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co">#Decreasing the size of the circle by 1/2 units on both the x and y axis - dividing.</span></span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>trans_value <span class="ot"><-</span> <span class="dv">2</span></span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>div_trans <span class="ot"><-</span> <span class="fu">map_df</span>(trans_value, <span class="sc">~</span>circle_df <span class="sc">|></span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">x =</span> x <span class="sc">/</span> .x,</span>
<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> y <span class="sc">/</span> .x)</span>
<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a>div_trans <span class="sc">|></span></span>
<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y)) <span class="sc">+</span></span>
<span id="cb6-12"><a href="#cb6-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">data =</span> circle_df, <span class="fu">aes</span>(x,y), </span>
<span id="cb6-13"><a href="#cb6-13" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">3</span>,</span>
<span id="cb6-14"><a href="#cb6-14" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>,</span>
<span id="cb6-15"><a href="#cb6-15" aria-hidden="true" tabindex="-1"></a> <span class="at">inherit.aes =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb6-16"><a href="#cb6-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">color =</span> <span class="st">"limegreen"</span>,</span>
<span id="cb6-17"><a href="#cb6-17" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb6-18"><a href="#cb6-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip6-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
<p><br></p>
<p><span style="color:brown">Dividing and Multiplying</span> the <code>x</code> and <code>y</code> variables will <strong>increase</strong> and <strong>decrease</strong> the scale of the circle based on which variable receives which operation. In the following example, the <code>x</code> variable is multiplied so increases by 2 along the <code>x axis</code>. The <code>y</code> variable is divided by 2 so is decreased by that inverse (1/2). This will result in an ellipse most of the time.</p>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb7"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="co">#Decreasing the size of the circle by 1/2 units on both the x and y axis - dividing.</span></span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>trans_value <span class="ot"><-</span> <span class="dv">2</span></span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>combo_trans1 <span class="ot"><-</span> <span class="fu">map_df</span>(trans_value, <span class="sc">~</span>circle_df <span class="sc">|></span></span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">x =</span> x <span class="sc">*</span> .x,</span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> y <span class="sc">/</span> .x)</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>combo_trans1 <span class="sc">|></span></span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y)) <span class="sc">+</span></span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">data =</span> circle_df, <span class="fu">aes</span>(x,y), </span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">3</span>,</span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>,</span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a> <span class="at">inherit.aes =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">color =</span> <span class="st">"brown"</span>,</span>
<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip7-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
<p><span style="color:magenta">Dividing and Multiplying with different values</span> for the <code>x</code> and <code>y</code> variables will <strong>increase</strong> and <strong>decrease</strong> the scale of the circle based on which variable receives which operation. In the following example, the <code>x</code> variable is multiplied so increases by 2 along the <code>x axis</code>. The <code>y</code> variable is divided by 6 so is decreased by that inverse (1/6 ≈ .1666). This will result in an ellipse most of the time.</p>
<div class="cell" data-layout-align="center">
<div class="sourceCode cell-code" id="cb8"><pre class="sourceCode r code-with-copy"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co">#Increasing the size of the circle by 2 on the x axis (multiplying)</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="co">#Decreasing the size of the circle by 1/6 units on the y axis - dividing.</span></span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>trans_valuex <span class="ot"><-</span> <span class="dv">2</span></span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>trans_valuey <span class="ot"><-</span> <span class="dv">6</span></span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a>combo_trans2 <span class="ot"><-</span> <span class="fu">map2_df</span>(trans_valuex, trans_valuey, <span class="sc">~</span>circle_df <span class="sc">|></span></span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a> <span class="fu">mutate</span>(<span class="at">x =</span> x <span class="sc">*</span> .x,</span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a> <span class="at">y =</span> y <span class="sc">/</span> .y)</span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a>combo_trans2 <span class="sc">|></span></span>
<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a> <span class="fu">ggplot</span>(<span class="fu">aes</span>(x,y)) <span class="sc">+</span></span>
<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">data =</span> circle_df, <span class="fu">aes</span>(x,y), </span>
<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a> <span class="at">linetype =</span> <span class="dv">3</span>,</span>
<span id="cb8-16"><a href="#cb8-16" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>,</span>
<span id="cb8-17"><a href="#cb8-17" aria-hidden="true" tabindex="-1"></a> <span class="at">inherit.aes =</span> <span class="cn">FALSE</span>) <span class="sc">+</span></span>
<span id="cb8-18"><a href="#cb8-18" aria-hidden="true" tabindex="-1"></a> <span class="fu">geom_path</span>(<span class="at">color =</span> <span class="st">"magenta"</span>,</span>
<span id="cb8-19"><a href="#cb8-19" aria-hidden="true" tabindex="-1"></a> <span class="at">linewidth =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb8-20"><a href="#cb8-20" aria-hidden="true" tabindex="-1"></a> <span class="fu">coord_equal</span>()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip8-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
</div>
</section>
<section id="visual-summary-1" class="level4">
<h4 class="anchored" data-anchor-id="visual-summary-1">Visual Summary</h4>
<ul>
<li><span style="color:orange">Multiplying</span></li>
<li><span style="color:limegreen">Dividing</span></li>
<li><span style="color:brown">Dividing and Multiplying</span></li>
<li><span style="color:magenta">Dividing and Multiplying with different values</span></li>
</ul>
<div class="cell" data-layout-align="center">
<div class="cell-output-display">
<div class="quarto-figure quarto-figure-center">
<figure class="figure">
<p><img src="manual_shapes_files/figure-html/circlesnip9-1.png" class="img-fluid figure-img" width="672"></p>
</figure>
</div>
</div>
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