Astroid2D_8ih_source.html

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>DGtal: Astroid2D.ih Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/x-mathjax-config">
  MathJax.Hub.Config({
    extensions: ["tex2jax.js", "TeX/AMSmath.js", "TeX/AMSsymbols.js"],
    jax: ["input/TeX","output/HTML-CSS"],
});
</script>
<script type="text/javascript" async="async" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/MathJax.js?config=TeX-MML-AM_CHTML/MathJax.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="doxygen-awesome.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname">DGtal
   &#160;<span id="projectnumber">1.4.2</span>
   </div>
  </td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'Search','.html');
/* @license-end */
</script>
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(function() {
  initMenu('',true,false,'search.php','Search');
  $(document).ready(function() { init_search(); });
});
/* @license-end */</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('Astroid2D_8ih_source.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="headertitle">
<div class="title">Astroid2D.ih</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;/**</div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160; *  This program is free software: you can redistribute it and/or modify</div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160; *  it under the terms of the GNU Lesser General Public License as</div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160; *  published by the Free Software Foundation, either version 3 of the</div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160; *  License, or  (at your option) any later version.</div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160; *</div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160; *  This program is distributed in the hope that it will be useful,</div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160; *  but WITHOUT ANY WARRANTY; without even the implied warranty of</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; *  GNU General Public License for more details.</div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160; *</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; *  You should have received a copy of the GNU General Public License</div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160; *  along with this program.  If not, see &lt;http://www.gnu.org/licenses/&gt;.</div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160; *</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; **/</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; /**</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;  * @file Astroid2D.ih</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;  * @author Chouaib Fellah, Adrien Krähenbühl (\c krahenbuhl@unistra.fr )</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;  * Laboratoire des sciences de l&#39;ingénieur, de l&#39;informatique et de l&#39;imagerie - ICube (UMR 7357), France</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  *</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;  * @date 2018/06/12</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  *</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  * Implementation of inline methods defined in Astroid2D.h</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;  *</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  * This file is part of the DGtal library.</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  */</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160; </div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;#include &lt;cstdlib&gt;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;#define ASTROID_3_PI_2 (3. * M_PI_2)</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;#define ASTROID_2_PI   (2. * M_PI)</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;// IMPLEMENTATION of inline methods.</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160; </div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;// ----------------------- Standard services ----------------------------------</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160; </div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;inline</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;DGtal::Astroid2D&lt;T&gt;::Astroid2D( const double x0, const double y0,</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  const double a, const double b ) : myCenter(x0,y0), myA(fabs(a)), myB(fabs(b))</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;{}</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;inline</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;DGtal::Astroid2D&lt;T&gt;::Astroid2D( const RealPoint &amp;aPoint,</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;  const double a, const double b ) : myCenter(aPoint), myA(fabs(a)), myB(fabs(b))</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;{}</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;inline</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;DGtal::Astroid2D&lt;T&gt;::Astroid2D( const Astroid2D&amp; other ) :</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  myCenter(other.myCenter), myA(other.myA), myB(other.myB)</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;{}</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;// ------------- Implementation of &#39;StarShaped&#39; services ----------------------</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;/**</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160; * @param pp any point in the plane.</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; *</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160; * @return the angle parameter between 0 and 2*Pi corresponding to</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; * this point for the shape.</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160; */</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;inline</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;double</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;DGtal::Astroid2D&lt;T&gt;::parameter( const RealPoint &amp; pp ) const</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;{</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  const RealPoint p( pp - myCenter );</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;  double angle = 0.;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  if ( isAlmostEqual(p[0],0.) )</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;      angle = p[1] &gt; 0. ? M_PI_2 : ASTROID_3_PI_2;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  else if ( isAlmostEqual(p[1],0.) )</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;      angle = p[0] &gt; 0. ? 0. : M_PI;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  else if ( ! isAlmostEqual(myB,0.) )</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  {</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;    if( p[1]/p[0] &lt; 0. )</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;      angle = atan(-pow(-(myA*p[1])/(myB*p[0]) , 1/3.))</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;            + (p[0] &gt; 0. ? ASTROID_2_PI : M_PI);</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    else</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      angle = atan(pow(( myA*p[1])/(myB*p[0]) , 1/3.));</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  }</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160; </div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  return angle;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;}</div>
<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;/**</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; * @param t any angle between 0 and 2*Pi.</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160; *</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; * @return the vector (x(t),y(t)) which is the position on the</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160; * shape boundary.</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; */</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;inline</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;typename DGtal::Astroid2D&lt;T&gt;::RealPoint</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;DGtal::Astroid2D&lt;T&gt;::x( const double t ) const</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;  return RealPoint( myA*pow(cos(t),3), myB*pow(sin(t),3) ) + myCenter;</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; </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;/**</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; * @param t any angle between 0 and 2*Pi.</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160; *</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; * @return the vector (x&#39;(t),y&#39;(t)) which is the tangent to the</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160; * shape boundary.</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;template &lt;typename T&gt;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;inline</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;typename DGtal::Astroid2D&lt;T&gt;::RealVector</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;DGtal::Astroid2D&lt;T&gt;::xp( const double t ) const</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;{</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160; </div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  return RealVector( myA * 3*(-sin(t))*pow(cos(t),2),</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                     myB * 3*cos(t)*pow(sin(t),2) );</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;}</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;inline</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;typename DGtal::Astroid2D&lt;T&gt;::RealVector</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;DGtal::Astroid2D&lt;T&gt;::xpp( const double t ) const</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;{</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  return RealVector( -myA * 3*pow(cos(t),3) + 6*pow(sin(t),2)*cos(t),</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                      myB * (6*pow(cos(t),2)*sin(t) - 3*pow(sin(t),3)) );</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;}</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160; </div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;// Interface - public :</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160; </div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;/**</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; * Writes/Displays the object on an output stream.</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160; * @param out the output stream where the object is written.</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160; */</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;inline</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;void</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;DGtal::Astroid2D&lt;T&gt;::selfDisplay ( std::ostream &amp; out ) const</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;{</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  out &lt;&lt; &quot;[Astroid2D] center= &quot; &lt;&lt; myCenter</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;      &lt;&lt; &quot; a=&quot; &lt;&lt; myA</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;      &lt;&lt; &quot; b=&quot; &lt;&lt; myB;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;}</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;/**</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160; * Checks the validity/consistency of the object.</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160; * @return &#39;true&#39; if the object is valid, &#39;false&#39; otherwise.</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; */</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;inline</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;bool</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;DGtal::Astroid2D&lt;T&gt;::isValid() const</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;{</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    return true;</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;}</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160; </div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;// Implementation of inline functions                                        //</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160; </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;template &lt;typename T&gt;</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;inline</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;std::ostream&amp;</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;DGtal::operator&lt;&lt; ( std::ostream &amp; out,</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;      const Astroid2D&lt;T&gt; &amp; object )</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;{</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;  object.selfDisplay( out );</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  return out;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;}</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160; </div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;//                                                                           //</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;///////////////////////////////////////////////////////////////////////////////</div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
  <ul>
    <li class="navelem"><a class="el" href="dir_68267d1309a1af8e8297ef4c3efbcdba.html">src</a></li><li class="navelem"><a class="el" href="dir_f2cd1aeea1cfa982bb13a5f95fa4218c.html">DGtal</a></li><li class="navelem"><a class="el" href="dir_b5cedd3610db960cb0235f10a76b8ff0.html">shapes</a></li><li class="navelem"><a class="el" href="dir_399699993fff7c2f4ed171da804e88fb.html">parametric</a></li><li class="navelem"><b>Astroid2D.ih</b></li>
    <li class="footer">Generated on Mon Dec 23 2024 13:18:27 for DGtal by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.1 </li>
  </ul>
</div>
</body>
</html>