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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>
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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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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>Functions related to <a class="el" href="../../da/d77/spirograph_8cpp.html" title="Implementation of Spirograph">spirograph.cpp</a> </p>
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</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>
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<td>(</td>
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<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>
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<td class="paramname"><em>points</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>l</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>k</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">double </td>
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<td class="paramname"><em>rot</em> </td>
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</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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</table>
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</div><div class="memdoc">
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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">
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\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*}
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</p>
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<p> where</p><ul>
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<li>\(R\) is the scaling parameter that we will consider \(=1\)</li>
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<li>\(l=\frac{\rho}{r}\) is the relative distance of marker from the centre of inner circle and \(0\le l\le1\)</li>
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<li>\(\rho\) is physical distance of marker from centre of inner circle</li>
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<li>\(r\) is the radius of inner circle</li>
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<li>\(k=\frac{r}{R}\) is the ratio of radius of inner circle to outer circle and \(0<k<1\)</li>
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<li>\(R\) is the radius of outer circle</li>
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<li>\(t\) is the angle of rotation of the point i.e., represents the time parameter</li>
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</ul>
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<p>Since we are considering ratios, the actual values of \(r\) and \(R\) are immaterial.</p>
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<dl class="tparams"><dt>Template Parameters</dt><dd>
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<table class="tparams">
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<tr><td class="paramname">N</td><td>number of points = size of array </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<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>
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<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>
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<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>
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<tr><td class="paramdir"></td><td class="paramname">rot</td><td>the number of rotations to perform (can be fractional value) </td></tr>
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</table>
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</dd>
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</dl>
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<div class="fragment"><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  {</div>
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<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>
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<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keywordtype">double</span> R = 1.f;</div>
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<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>
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<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  int32_t step = 0;</div>
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<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div>
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<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="preprocessor">#ifdef _OPENMP</span></div>
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<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="preprocessor">#pragma omp for</span></div>
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<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="preprocessor">#endif</span></div>
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<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordflow">for</span> (step = 0; step < N; step++) {</div>
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<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordtype">double</span> t = dt * step;</div>
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<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>
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<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>
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<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  points[0][step].first = first;</div>
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<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  points[0][step].second = second;</div>
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<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  }</div>
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<div class="line"><a name="l00087"></a><span class="lineno"> 87</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="dyncontent">
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<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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<a id="a8e83a64e8443fff1e5ffdc1c299c1e99"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a8e83a64e8443fff1e5ffdc1c299c1e99">◆ </a></span>test()</h2>
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<div class="memproto">
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<tr>
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<td class="memname">void spirograph::test </td>
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<td>(</td>
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<td class="paramname"></td><td>)</td>
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<td></td>
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</tr>
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</div><div class="memdoc">
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<p>Test function to save resulting points to a CSV file. </p>
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<div class="fragment"><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  {</div>
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<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>
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<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>
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<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>
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<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>
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<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  << <span class="stringliteral">".csv"</span>;</div>
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<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>
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<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">if</span> (!fp.is_open()) {</div>
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<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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<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  }</div>
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<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  </div>
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<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/array.html">std::array<std::pair<double, double></a>, N> points;</div>
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<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  </div>
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<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <a class="code" href="../../da/dd3/namespacespirograph.html#aeca22dbe4563358960e907a40cd3e1ac">spirograph</a>(&points, l, k, rot);</div>
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<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  </div>
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<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">for</span> (<span class="keywordtype">size_t</span> i = 0; i < N; i++) {</div>
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<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  fp << points[i].first << <span class="stringliteral">","</span> << points[i].first;</div>
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<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordflow">if</span> (i < N - 1) {</div>
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<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  fp << <span class="charliteral">'\n'</span>;</div>
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<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  }</div>
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<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  }</div>
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<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  </div>
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<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  fp.close();</div>
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<div class="line"><a name="l00117"></a><span class="lineno"> 117</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>
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