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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div class="title">spirograph.cpp File Reference</div> </div>
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<div class="contents">
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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Spirograph">Spirograph</a>
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <array></code><br />
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<code>#include <cmath></code><br />
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<code>#include <cstdlib></code><br />
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<code>#include <ctime></code><br />
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<code>#include <fstream></code><br />
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<code>#include <iomanip></code><br />
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<code>#include <iostream></code><br />
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<code>#include <sstream></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for spirograph.cpp:</div>
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<div class="dyncontent">
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Namespaces</h2></td></tr>
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<tr class="memitem:da/dd3/namespacespirograph"><td class="memItemLeft" align="right" valign="top">  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/namespacespirograph.html">spirograph</a></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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Macros</h2></td></tr>
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<tr class="memitem:a525335710b53cb064ca56b936120431e"><td class="memItemLeft" align="right" valign="top">#define </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d77/spirograph_8cpp.html#a525335710b53cb064ca56b936120431e">_USE_MATH_DEFINES</a></td></tr>
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Functions</h2></td></tr>
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<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplParams" colspan="2">template<std::size_t N> </td></tr>
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<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/dd3/namespacespirograph.html#aeca22dbe4563358960e907a40cd3e1ac">spirograph::spirograph</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< double, double >, N > *points, double l, double k, double rot)</td></tr>
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<tr class="separator:aeca22dbe4563358960e907a40cd3e1ac"><td class="memSeparator" colspan="2"> </td></tr>
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||||
<tr class="memitem:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">spirograph::test</a> ()</td></tr>
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<tr class="memdesc:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="mdescLeft"> </td><td class="mdescRight">Test function to save resulting points to a CSV file. <a href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">More...</a><br /></td></tr>
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<tr class="separator:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/d77/spirograph_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
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<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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||||
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
|
||||
<div class="textblock"><p>Implementation of <a href="https://en.wikipedia.org/wiki/Spirograph">Spirograph</a> </p>
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||||
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala">Krishna Vedala</a></dd></dl>
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<p>Implementation of the program is based on the geometry shown in the figure below:</p>
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||||
<p><a href="https://commons.wikimedia.org/wiki/File:Resonance_Cascade.svg"><img src="https://upload.wikimedia.org/wikipedia/commons/3/39/Resonance_Cascade.svg" alt="Spirograph geometry from Wikipedia" style="pointer-events: none; width: 250px" class="inline"/></a> </p>
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</div><h2 class="groupheader">Macro Definition Documentation</h2>
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<a id="a525335710b53cb064ca56b936120431e"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a525335710b53cb064ca56b936120431e">◆ </a></span>_USE_MATH_DEFINES</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">#define _USE_MATH_DEFINES</td>
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</tr>
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</div><div class="memdoc">
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<p>required for MSVC compiler </p>
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</div>
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</div>
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<h2 class="groupheader">Function Documentation</h2>
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<a id="a3c04138a5bfe5d72780bb7e82a18e627"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">◆ </a></span>main()</h2>
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<div class="memproto">
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<table class="memname">
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>argc</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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</div><div class="memdoc">
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<p>Main function </p>
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||||
<div class="fragment"><div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  {</div>
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<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <a class="code" href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">spirograph::test</a>();</div>
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<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  </div>
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<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> <span class="preprocessor">#ifdef USE_GLUT</span></div>
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<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  glutInit(&argc, argv);</div>
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<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);</div>
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<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  glutCreateWindow(<span class="stringliteral">"Spirograph"</span>);</div>
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<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  glutInitWindowSize(400, 400);</div>
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<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="comment">// glutIdleFunc(glutPostRedisplay);</span></div>
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<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  glutTimerFunc(spirograph::animation_speed, spirograph::timer_cb, 0);</div>
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<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  glutKeyboardFunc(spirograph::keyboard_cb);</div>
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<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  glutDisplayFunc(<a class="code" href="../../d7/db9/hill__cipher_8cpp.html#a04391124480d2a49f2dec900237b0712">spirograph::test2</a>);</div>
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||||
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  glutMainLoop();</div>
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<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  </div>
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<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> }</div>
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</div><!-- fragment --><div class="dynheader">
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Here is the call graph for this function:</div>
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<div class="ttc" id="ahill__cipher_8cpp_html_a04391124480d2a49f2dec900237b0712"><div class="ttname"><a href="../../d7/db9/hill__cipher_8cpp.html#a04391124480d2a49f2dec900237b0712">test2</a></div><div class="ttdeci">void test2(const std::string &text)</div><div class="ttdoc">Self test 2 - using 8x8 randomly generated key.</div><div class="ttdef"><b>Definition:</b> hill_cipher.cpp:505</div></div>
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<div class="ttc" id="anamespacespirograph_html_a8e83a64e8443fff1e5ffdc1c299c1e99"><div class="ttname"><a href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">spirograph::test</a></div><div class="ttdeci">void test()</div><div class="ttdoc">Test function to save resulting points to a CSV file.</div><div class="ttdef"><b>Definition:</b> spirograph.cpp:93</div></div>
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da/d77/spirograph_8cpp.js
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<div class="title">spirograph Namespace Reference</div> </div>
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Functions</h2></td></tr>
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<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplParams" colspan="2">template<std::size_t N> </td></tr>
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<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="../../da/dd3/namespacespirograph.html#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< double, double >, N > *points, double l, double k, double rot)</td></tr>
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<tr class="separator:aeca22dbe4563358960e907a40cd3e1ac"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">test</a> ()</td></tr>
|
||||
<tr class="memdesc:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="mdescLeft"> </td><td class="mdescRight">Test function to save resulting points to a CSV file. <a href="../../da/dd3/namespacespirograph.html#a8e83a64e8443fff1e5ffdc1c299c1e99">More...</a><br /></td></tr>
|
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<tr class="separator:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
|
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
|
||||
<div class="textblock"><p>Functions related to <a class="el" href="../../da/d77/spirograph_8cpp.html" title="Implementation of Spirograph">spirograph.cpp</a> </p>
|
||||
</div><h2 class="groupheader">Function Documentation</h2>
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<a id="aeca22dbe4563358960e907a40cd3e1ac"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#aeca22dbe4563358960e907a40cd3e1ac">◆ </a></span>spirograph()</h2>
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||||
<div class="memitem">
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<div class="memproto">
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<div class="memtemplate">
|
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template<std::size_t N> </div>
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<table class="memname">
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<tr>
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||||
<td class="memname">void spirograph::spirograph </td>
|
||||
<td>(</td>
|
||||
<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< double, double >, N > * </td>
|
||||
<td class="paramname"><em>points</em>, </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="paramkey"></td>
|
||||
<td></td>
|
||||
<td class="paramtype">double </td>
|
||||
<td class="paramname"><em>l</em>, </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="paramkey"></td>
|
||||
<td></td>
|
||||
<td class="paramtype">double </td>
|
||||
<td class="paramname"><em>k</em>, </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="paramkey"></td>
|
||||
<td></td>
|
||||
<td class="paramtype">double </td>
|
||||
<td class="paramname"><em>rot</em> </td>
|
||||
</tr>
|
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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<p>Generate spirograph curve into arrays <code>x</code> and <code>y</code> such that the i^th point in 2D is represented by <code>(x[i],y[i])</code>. The generating function is given by: </p><p class="formulaDsp">
|
||||
\begin{eqnarray*} x &=& R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right) \right]\\ y &=& R\left[ (1-k) \sin (t) - l\cdot k\cdot\sin \left(\frac{1-k}{k}t\right) \right] \end{eqnarray*}
|
||||
</p>
|
||||
<p> where</p><ul>
|
||||
<li>\(R\) is the scaling parameter that we will consider \(=1\)</li>
|
||||
<li>\(l=\frac{\rho}{r}\) is the relative distance of marker from the centre of inner circle and \(0\le l\le1\)</li>
|
||||
<li>\(\rho\) is physical distance of marker from centre of inner circle</li>
|
||||
<li>\(r\) is the radius of inner circle</li>
|
||||
<li>\(k=\frac{r}{R}\) is the ratio of radius of inner circle to outer circle and \(0<k<1\)</li>
|
||||
<li>\(R\) is the radius of outer circle</li>
|
||||
<li>\(t\) is the angle of rotation of the point i.e., represents the time parameter</li>
|
||||
</ul>
|
||||
<p>Since we are considering ratios, the actual values of \(r\) and \(R\) are immaterial.</p>
|
||||
<dl class="tparams"><dt>Template Parameters</dt><dd>
|
||||
<table class="tparams">
|
||||
<tr><td class="paramname">N</td><td>number of points = size of array </td></tr>
|
||||
</table>
|
||||
</dd>
|
||||
</dl>
|
||||
<dl class="params"><dt>Parameters</dt><dd>
|
||||
<table class="params">
|
||||
<tr><td class="paramdir">[out]</td><td class="paramname">points</td><td>Array of 2D points represented as <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a> </td></tr>
|
||||
<tr><td class="paramdir"></td><td class="paramname">l</td><td>the relative distance of marker from the centre of inner circle and \(0\le l\le1\) </td></tr>
|
||||
<tr><td class="paramdir"></td><td class="paramname">k</td><td>the ratio of radius of inner circle to outer circle and \(0<k<1\) </td></tr>
|
||||
<tr><td class="paramdir"></td><td class="paramname">rot</td><td>the number of rotations to perform (can be fractional value) </td></tr>
|
||||
</table>
|
||||
</dd>
|
||||
</dl>
|
||||
<div class="fragment"><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  {</div>
|
||||
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordtype">double</span> dt = rot * 2.f * M_PI / N;</div>
|
||||
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordtype">double</span> R = 1.f;</div>
|
||||
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> k1 = 1.f - k;</div>
|
||||
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  int32_t step = 0;</div>
|
||||
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div>
|
||||
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
|
||||
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="preprocessor">#pragma omp for</span></div>
|
||||
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="preprocessor">#endif</span></div>
|
||||
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">for</span> (step = 0; step < N; step++) {</div>
|
||||
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordtype">double</span> t = dt * step;</div>
|
||||
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordtype">double</span> first = R * (k1 * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(t) + l * k * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/cos.html">std::cos</a>(k1 * t / k));</div>
|
||||
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordtype">double</span> second = R * (k1 * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(t) - l * k * <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/math/sin.html">std::sin</a>(k1 * t / k));</div>
|
||||
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  points[0][step].first = first;</div>
|
||||
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  points[0][step].second = second;</div>
|
||||
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  }</div>
|
||||
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> }</div>
|
||||
</div><!-- fragment --><div class="dynheader">
|
||||
Here is the call graph for this function:</div>
|
||||
<div class="dyncontent">
|
||||
<div class="center"><iframe scrolling="no" frameborder="0" src="../../da/dd3/namespacespirograph_aeca22dbe4563358960e907a40cd3e1ac_cgraph.svg" width="279" height="88"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
|
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</div>
|
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</div>
|
||||
|
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</div>
|
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</div>
|
||||
<a id="a8e83a64e8443fff1e5ffdc1c299c1e99"></a>
|
||||
<h2 class="memtitle"><span class="permalink"><a href="#a8e83a64e8443fff1e5ffdc1c299c1e99">◆ </a></span>test()</h2>
|
||||
|
||||
<div class="memitem">
|
||||
<div class="memproto">
|
||||
<table class="memname">
|
||||
<tr>
|
||||
<td class="memname">void spirograph::test </td>
|
||||
<td>(</td>
|
||||
<td class="paramname"></td><td>)</td>
|
||||
<td></td>
|
||||
</tr>
|
||||
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|
||||
</div><div class="memdoc">
|
||||
|
||||
<p>Test function to save resulting points to a CSV file. </p>
|
||||
<div class="fragment"><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  {</div>
|
||||
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keyword">const</span> <span class="keywordtype">size_t</span> N = 500;</div>
|
||||
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordtype">double</span> l = 0.3, k = 0.75, rot = 10.;</div>
|
||||
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream.html">std::stringstream</a> fname;</div>
|
||||
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  fname << <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(3) << <span class="stringliteral">"spirograph_"</span> << l << <span class="stringliteral">"_"</span> << k << <span class="stringliteral">"_"</span> << rot</div>
|
||||
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  << <span class="stringliteral">".csv"</span>;</div>
|
||||
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ofstream.html">std::ofstream</a> fp(fname.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>());</div>
|
||||
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">if</span> (!fp.is_open()) {</div>
|
||||
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/c/perror.html">perror</a>(fname.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_stringstream/str.html">str</a>().c_str());</div>
|
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<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">exit</a>(EXIT_FAILURE);</div>
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|
||||
<g id="edge2" class="edge">
|
||||
<title>Node1->Node3</title>
|
||||
<path fill="none" stroke="midnightblue" d="M113.02,-19.95C122.35,-18.42 131.78,-16.89 140.34,-15.49"/>
|
||||
<polygon fill="midnightblue" stroke="midnightblue" points="140.98,-18.93 150.28,-13.87 139.85,-12.02 140.98,-18.93"/>
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||||
</g>
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</g>
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||||
</svg>
|
||||
|
After Width: | Height: | Size: 2.4 KiB |
Reference in New Issue
Block a user