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<div id="projectbrief">Set of algorithms implemented in C++.</div>
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<div class="title">spirograph Namespace Reference</div> </div>
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplParams" colspan="2">template&lt;std::size_t N&gt; </td></tr>
<tr class="memitem:aeca22dbe4563358960e907a40cd3e1ac"><td class="memTemplItemLeft" align="right" valign="top">void&#160;</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>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; double, double &gt;, N &gt; *points, double l, double k, double rot)</td></tr>
<tr class="separator:aeca22dbe4563358960e907a40cd3e1ac"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="memItemLeft" align="right" valign="top">void&#160;</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">&#160;</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>
<tr class="separator:a8e83a64e8443fff1e5ffdc1c299c1e99"><td class="memSeparator" colspan="2">&#160;</td></tr>
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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>
<a id="aeca22dbe4563358960e907a40cd3e1ac"></a>
<h2 class="memtitle"><span class="permalink"><a href="#aeca22dbe4563358960e907a40cd3e1ac">&#9670;&nbsp;</a></span>spirograph()</h2>
<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;std::size_t N&gt; </div>
<table class="memname">
<tr>
<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>&lt; <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>&lt; double, double &gt;, N &gt; *&#160;</td>
<td class="paramname"><em>points</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">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>. 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="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 \(0&lt;k&lt;1\) </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>&#160; {</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <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>&#160; <span class="keywordtype">double</span> R = 1.f;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <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>&#160; int32_t step = 0;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160;<span class="preprocessor">#ifdef _OPENMP</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160;<span class="preprocessor">#pragma omp for</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">for</span> (step = 0; step &lt; N; step++) {</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="keywordtype">double</span> t = dt * step;</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <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>&#160; <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>&#160; points[0][step].first = first;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; points[0][step].second = second;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; }</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a8e83a64e8443fff1e5ffdc1c299c1e99">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">void spirograph::test </td>
<td>(</td>
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<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>&#160; {</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <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>&#160; <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>&#160; <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>&#160; fname &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/setw.html">std::setw</a>(3) &lt;&lt; <span class="stringliteral">&quot;spirograph_&quot;</span> &lt;&lt; l &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; k &lt;&lt; <span class="stringliteral">&quot;_&quot;</span> &lt;&lt; rot</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; &lt;&lt; <span class="stringliteral">&quot;.csv&quot;</span>;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <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>&#160; <span class="keywordflow">if</span> (!fp.is_open()) {</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <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>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/program/exit.html">exit</a>(EXIT_FAILURE);</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; }</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array&lt;std::pair&lt;double, double&gt;</a>, N&gt; points;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; </div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; <a class="code" href="../../da/dd3/namespacespirograph.html#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a>(&amp;points, l, k, rot);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i &lt; N; i++) {</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; fp &lt;&lt; points[i].first &lt;&lt; <span class="stringliteral">&quot;,&quot;</span> &lt;&lt; points[i].first;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <span class="keywordflow">if</span> (i &lt; N - 1) {</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; fp &lt;&lt; <span class="charliteral">&#39;\n&#39;</span>;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; }</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; fp.close();</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160;}</div>
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