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<div id="projectbrief">Set of algorithms implemented in C.</div>
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<a href="#define-members">Macros</a> &#124;
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<div class="headertitle"><div class="title">spirograph.c File Reference</div></div>
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<p>Implementation of <a href="https://en.wikipedia.org/wiki/Spirograph" target="_blank">Spirograph</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;math.h&gt;</code><br />
<code>#include &lt;stdbool.h&gt;</code><br />
<code>#include &lt;stdio.h&gt;</code><br />
<code>#include &lt;stdlib.h&gt;</code><br />
<code>#include &lt;time.h&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for spirograph.c:</div>
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Macros</h2></td></tr>
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#define&#160;</td><td class="memItemRight" valign="bottom"><b>_USE_MATH_DEFINES</b></td></tr>
<tr class="memdesc:a525335710b53cb064ca56b936120431e"><td class="mdescLeft">&#160;</td><td class="mdescRight">required for MSVC compiler <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:a0daa148091ec953809fc172289f773d3"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d98/spirograph_8c.html#a0daa148091ec953809fc172289f773d3">spirograph</a> (double *x, double *y, double l, double k, size_t N, double rot)</td></tr>
<tr class="memdesc:a0daa148091ec953809fc172289f773d3"><td class="mdescLeft">&#160;</td><td class="mdescRight">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>. <br /></td></tr>
<tr class="separator:a0daa148091ec953809fc172289f773d3"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a708a4c1a4d0c4acc4c447310dd4db27f"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d98/spirograph_8c.html#a708a4c1a4d0c4acc4c447310dd4db27f">test</a> (void)</td></tr>
<tr class="memdesc:a708a4c1a4d0c4acc4c447310dd4db27f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test function to save resulting points to a CSV file. <br /></td></tr>
<tr class="separator:a708a4c1a4d0c4acc4c447310dd4db27f"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d7/d98/spirograph_8c.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a> (int argc, char **argv)</td></tr>
<tr class="memdesc:a3c04138a5bfe5d72780bb7e82a18e627"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
<tr class="separator:a3c04138a5bfe5d72780bb7e82a18e627"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table>
<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" target="_blank">Spirograph</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/kvedala" target="_blank">Krishna Vedala</a> </dd></dl>
<p>Implementation of the program is based on the geometry shown in the figure below:</p>
<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>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a3c04138a5bfe5d72780bb7e82a18e627" name="a3c04138a5bfe5d72780bb7e82a18e627"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a3c04138a5bfe5d72780bb7e82a18e627">&#9670;&#160;</a></span>main()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>argc</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">char **&#160;</td>
<td class="paramname"><em>argv</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Main function. </p>
<div class="fragment"><div class="line"><span class="lineno"> 272</span>{</div>
<div class="line"><span class="lineno"> 273</span> <a class="code hl_function" href="../../d7/d98/spirograph_8c.html#a708a4c1a4d0c4acc4c447310dd4db27f">test</a>();</div>
<div class="line"><span class="lineno"> 274</span> </div>
<div class="line"><span class="lineno"> 275</span><span class="preprocessor">#ifdef USE_GLUT</span></div>
<div class="line"><span class="lineno"> 276</span> glutInit(&amp;argc, argv);</div>
<div class="line"><span class="lineno"> 277</span> glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);</div>
<div class="line"><span class="lineno"> 278</span> glutCreateWindow(<span class="stringliteral">&quot;Spirograph&quot;</span>);</div>
<div class="line"><span class="lineno"> 279</span> glutInitWindowSize(400, 400);</div>
<div class="line"><span class="lineno"> 280</span> <span class="comment">// glutIdleFunc(glutPostRedisplay);</span></div>
<div class="line"><span class="lineno"> 281</span> glutTimerFunc(animation_speed, timer_cb, 0);</div>
<div class="line"><span class="lineno"> 282</span> glutKeyboardFunc(keyboard_cb);</div>
<div class="line"><span class="lineno"> 283</span> glutDisplayFunc(<a class="code hl_function" href="../../d6/d76/k__means__clustering_8c.html#a0283886819c7c140a023582b7269e2d0">test2</a>);</div>
<div class="line"><span class="lineno"> 284</span> glutMainLoop();</div>
<div class="line"><span class="lineno"> 285</span><span class="preprocessor">#endif</span></div>
<div class="line"><span class="lineno"> 286</span> </div>
<div class="line"><span class="lineno"> 287</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 288</span>}</div>
<div class="ttc" id="ak__means__clustering_8c_html_a0283886819c7c140a023582b7269e2d0"><div class="ttname"><a href="../../d6/d76/k__means__clustering_8c.html#a0283886819c7c140a023582b7269e2d0">test2</a></div><div class="ttdeci">void test2()</div><div class="ttdef"><b>Definition:</b> k_means_clustering.c:356</div></div>
<div class="ttc" id="aspirograph_8c_html_a708a4c1a4d0c4acc4c447310dd4db27f"><div class="ttname"><a href="../../d7/d98/spirograph_8c.html#a708a4c1a4d0c4acc4c447310dd4db27f">test</a></div><div class="ttdeci">void test(void)</div><div class="ttdoc">Test function to save resulting points to a CSV file.</div><div class="ttdef"><b>Definition:</b> spirograph.c:74</div></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="../../d7/d98/spirograph_8c_a3c04138a5bfe5d72780bb7e82a18e627_cgraph.svg" width="459" height="135"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe>
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<h2 class="memtitle"><span class="permalink"><a href="#a0daa148091ec953809fc172289f773d3">&#9670;&#160;</a></span>spirograph()</h2>
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<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void spirograph </td>
<td>(</td>
<td class="paramtype">double *&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double *&#160;</td>
<td class="paramname"><em>y</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>l</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>k</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">size_t&#160;</td>
<td class="paramname"><em>N</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">double&#160;</td>
<td class="paramname"><em>rot</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<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>. </p>
<p>The generating function is given by: </p><p class="formulaDsp">
\begin{eqnarray*}
x &amp;=&amp; R\left[ (1-k) \cos (t) + l\cdot k\cdot\cos \left(\frac{1-k}{k}t\right)
\right]\\
y &amp;=&amp; 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 \(0&lt;k&lt;1\)</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="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[out]</td><td class="paramname">x</td><td>output array containing absicca of points (must be pre-allocated) </td></tr>
<tr><td class="paramdir">[out]</td><td class="paramname">y</td><td>output array containing ordinates of points (must be pre-allocated) </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 \(0&lt;k&lt;1\) </td></tr>
<tr><td class="paramdir"></td><td class="paramname">N</td><td>number of sample points along the trajectory (higher = better resolution but consumes more time and memory) </td></tr>
<tr><td class="paramdir"></td><td class="paramname">num_rot</td><td>the number of rotations to perform (can be fractional value) </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><span class="lineno"> 58</span>{</div>
<div class="line"><span class="lineno"> 59</span> <span class="keywordtype">double</span> dt = rot * 2.f * M_PI / N;</div>
<div class="line"><span class="lineno"> 60</span> <span class="keywordtype">double</span> t = 0.f, R = 1.f;</div>
<div class="line"><span class="lineno"> 61</span> <span class="keyword">const</span> <span class="keywordtype">double</span> k1 = 1.f - k;</div>
<div class="line"><span class="lineno"> 62</span> </div>
<div class="line"><span class="lineno"> 63</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> dk = 0; dk &lt; N; dk++, t += dt)</div>
<div class="line"><span class="lineno"> 64</span> {</div>
<div class="line"><span class="lineno"> 65</span> x[dk] = R * (k1 * cos(t) + l * k * cos(k1 * t / k));</div>
<div class="line"><span class="lineno"> 66</span> y[dk] = R * (k1 * sin(t) - l * k * sin(k1 * t / k));</div>
<div class="line"><span class="lineno"> 67</span> }</div>
<div class="line"><span class="lineno"> 68</span>}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a708a4c1a4d0c4acc4c447310dd4db27f" name="a708a4c1a4d0c4acc4c447310dd4db27f"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a708a4c1a4d0c4acc4c447310dd4db27f">&#9670;&#160;</a></span>test()</h2>
<div class="memitem">
<div class="memproto">
<table class="memname">
<tr>
<td class="memname">void test </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Test function to save resulting points to a CSV file. </p>
<div class="fragment"><div class="line"><span class="lineno"> 75</span>{</div>
<div class="line"><span class="lineno"> 76</span> <span class="keywordtype">size_t</span> N = 500;</div>
<div class="line"><span class="lineno"> 77</span> <span class="keywordtype">double</span> l = 0.3, k = 0.75, rot = 10.;</div>
<div class="line"><span class="lineno"> 78</span> <span class="keywordtype">char</span> fname[50];</div>
<div class="line"><span class="lineno"> 79</span> snprintf(fname, 50, <span class="stringliteral">&quot;spirograph_%.2f_%.2f_%.2f.csv&quot;</span>, l, k, rot);</div>
<div class="line"><span class="lineno"> 80</span> FILE *fp = fopen(fname, <span class="stringliteral">&quot;wt&quot;</span>);</div>
<div class="line"><span class="lineno"> 81</span> <span class="keywordflow">if</span> (!fp)</div>
<div class="line"><span class="lineno"> 82</span> {</div>
<div class="line"><span class="lineno"> 83</span> perror(fname);</div>
<div class="line"><span class="lineno"> 84</span> exit(EXIT_FAILURE);</div>
<div class="line"><span class="lineno"> 85</span> }</div>
<div class="line"><span class="lineno"> 86</span> </div>
<div class="line"><span class="lineno"> 87</span> <span class="keywordtype">double</span> *x = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(N * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><span class="lineno"> 88</span> <span class="keywordtype">double</span> *y = (<span class="keywordtype">double</span> *)<a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a>(N * <span class="keyword">sizeof</span>(<span class="keywordtype">double</span>));</div>
<div class="line"><span class="lineno"> 89</span> </div>
<div class="line"><span class="lineno"> 90</span> <a class="code hl_function" href="../../d7/d98/spirograph_8c.html#a0daa148091ec953809fc172289f773d3">spirograph</a>(x, y, l, k, N, rot);</div>
<div class="line"><span class="lineno"> 91</span> </div>
<div class="line"><span class="lineno"> 92</span> <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++)</div>
<div class="line"><span class="lineno"> 93</span> {</div>
<div class="line"><span class="lineno"> 94</span> fprintf(fp, <span class="stringliteral">&quot;%.5g, %.5g&quot;</span>, x[i], y[i]);</div>
<div class="line"><span class="lineno"> 95</span> <span class="keywordflow">if</span> (i &lt; N - 1)</div>
<div class="line"><span class="lineno"> 96</span> {</div>
<div class="line"><span class="lineno"> 97</span> fputc(<span class="charliteral">&#39;\n&#39;</span>, fp);</div>
<div class="line"><span class="lineno"> 98</span> }</div>
<div class="line"><span class="lineno"> 99</span> }</div>
<div class="line"><span class="lineno"> 100</span> </div>
<div class="line"><span class="lineno"> 101</span> fclose(fp);</div>
<div class="line"><span class="lineno"> 102</span> </div>
<div class="line"><span class="lineno"> 103</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(x);</div>
<div class="line"><span class="lineno"> 104</span> <a class="code hl_define" href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a>(y);</div>
<div class="line"><span class="lineno"> 105</span>}</div>
<div class="ttc" id="amalloc__dbg_8h_html_a725f50ecaf1959d96de79b36b4788fee"><div class="ttname"><a href="../../d2/ddd/malloc__dbg_8h.html#a725f50ecaf1959d96de79b36b4788fee">malloc</a></div><div class="ttdeci">#define malloc(bytes)</div><div class="ttdoc">This macro replace the standard malloc function with malloc_dbg.</div><div class="ttdef"><b>Definition:</b> malloc_dbg.h:18</div></div>
<div class="ttc" id="amalloc__dbg_8h_html_a9cc854374299a1dd933bf62029761768"><div class="ttname"><a href="../../d2/ddd/malloc__dbg_8h.html#a9cc854374299a1dd933bf62029761768">free</a></div><div class="ttdeci">#define free(ptr)</div><div class="ttdoc">This macro replace the standard free function with free_dbg.</div><div class="ttdef"><b>Definition:</b> malloc_dbg.h:26</div></div>
<div class="ttc" id="aspirograph_8c_html_a0daa148091ec953809fc172289f773d3"><div class="ttname"><a href="../../d7/d98/spirograph_8c.html#a0daa148091ec953809fc172289f773d3">spirograph</a></div><div class="ttdeci">void spirograph(double *x, double *y, double l, double k, size_t N, double rot)</div><div class="ttdoc">Generate spirograph curve into arrays x and y such that the i^th point in 2D is represented by (x[i],...</div><div class="ttdef"><b>Definition:</b> spirograph.c:57</div></div>
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