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POEquation-driven smoothly shaded concentric shapes
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copied!<h2>Background</h2> <p>Looking to create interesting video transitions (in grayscale).</p> <h2>Problem</h2> <p>Given <a href="http://www.wolframalpha.com/input/?i=x%20=%2016%20sin%5E3%20t,%20y%20=%20%2813%20cos%20t%20-%205%20cos%202t%20-%202%20cos%203t%20-%20cos%204t%29" rel="noreferrer">equations</a> that represent a closed, symmetrical shape, plot the outline and concentrically shade the shape towards its centre.</p> <h2>Example</h2> <p>Consider the following equations:</p> <pre><code>x = 16 * sin(t)^3 y = 13 * cos(t) - 5 * cos(2 * t) - 2 * cos(3 * t) - cos(4 * t) t = [0:2 * pi] </code></pre> <p>When plotted:</p> <p><img src="https://i.imgur.com/u0qja.png" /></p> <p>When shaded, it would resemble (not shown completely shaded, but sufficient to show the idea):</p> <p><img src="https://i.imgur.com/oRwFy.png" /></p> <p>Notice that shading is darkest on the outside (e.g., #000000 RGB hex), then lightens as it fills to the centre. The centre would be a white (e.g., #FFFFFF) dot.</p> <h2>Questions</h2> <ol> <li>What would be the most expedient way to produce high-resolution, concentrically shaded grayscale images, such as the shaded heart above?</li> <li>What are such closed, symmetrical shapes formally called?</li> </ol> <p>Thank you!</p> <h2>Ideas</h2> <ul> <li>Use a library such as <a href="http://code.google.com/p/jmathplot/" rel="noreferrer">http://code.google.com/p/jmathplot/</a></li> <li>Use GNUPlot</li> <li>Use R</li> <li>Plot using Wolfram Alpha, use ImageMagick to create smaller concentric versions</li> </ul>

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