<!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: ImplicitPolynomial3Shape.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  <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&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&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&dn=gpl-2.0.txt GPL-v2 */ $(document).ready(function(){initNavTree('ImplicitPolynomial3Shape_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">ImplicitPolynomial3Shape.ih</div> </div> </div><!--header--> <div class="contents"> <div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> /**</div> <div class="line"><a name="l00002"></a><span class="lineno"> 2</span>  * 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>  * 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>  * published by the Free Software Foundation, either version 3 of the</div> <div class="line"><a name="l00005"></a><span class="lineno"> 5</span>  * License, or (at your option) any later version.</div> <div class="line"><a name="l00006"></a><span class="lineno"> 6</span>  *</div> <div class="line"><a name="l00007"></a><span class="lineno"> 7</span>  * 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>  * but WITHOUT ANY WARRANTY; without even the implied warranty of</div> <div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</div> <div class="line"><a name="l00010"></a><span class="lineno"> 10</span>  * GNU General Public License for more details.</div> <div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  *</div> <div class="line"><a name="l00012"></a><span class="lineno"> 12</span>  * 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>  * along with this program. If not, see <http://www.gnu.org/licenses/>.</div> <div class="line"><a name="l00014"></a><span class="lineno"> 14</span>  *</div> <div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  **/</div> <div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div> <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> /**</div> <div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  * @file ImplicitPolynomial3Shape.ih</div> <div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  * @author Jacques-Olivier Lachaud (\c jacques-olivier.lachaud@univ-savoie.fr )</div> <div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  * Laboratory of Mathematics (CNRS, UMR 5807), University of Savoie, France</div> <div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  *</div> <div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  * @date 2012/02/14</div> <div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  *</div> <div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  * Implementation of inline methods defined in ImplicitPolynomial3Shape.h</div> <div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  *</div> <div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  * This file is part of the DGtal library.</div> <div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  */</div> <div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  </div> <div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  </div> <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> //////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> #include <cstdlib></div> <div class="line"><a name="l00032"></a><span class="lineno"> 32</span> //////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  </div> <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> ///////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> // IMPLEMENTATION of inline methods.</div> <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> ///////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  </div> <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> ///////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00039"></a><span class="lineno"> 39</span> // ----------------------- Standard services ------------------------------</div> <div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  </div> <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> template <typename TSpace></div> <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> inline</div> <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> DGtal::ImplicitPolynomial3Shape<TSpace>::~ImplicitPolynomial3Shape()</div> <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> {</div> <div class="line"><a name="l00046"></a><span class="lineno"> 46</span> }</div> <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00048"></a><span class="lineno"> 48</span> template <typename TSpace></div> <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> inline</div> <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00051"></a><span class="lineno"> 51</span> ImplicitPolynomial3Shape( const Polynomial3 & poly )</div> <div class="line"><a name="l00052"></a><span class="lineno"> 52</span> {</div> <div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  init( poly );</div> <div class="line"><a name="l00054"></a><span class="lineno"> 54</span> }</div> <div class="line"><a name="l00055"></a><span class="lineno"> 55</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00056"></a><span class="lineno"> 56</span> template <typename TSpace></div> <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> inline</div> <div class="line"><a name="l00058"></a><span class="lineno"> 58</span> DGtal::ImplicitPolynomial3Shape<TSpace> &</div> <div class="line"><a name="l00059"></a><span class="lineno"> 59</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00060"></a><span class="lineno"> 60</span> operator=( const ImplicitPolynomial3Shape & other )</div> <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> {</div> <div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  if ( this != &other )</div> <div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  {</div> <div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  myPolynomial = other.myPolynomial;</div> <div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  </div> <div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  myFx= other.myFx;</div> <div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  myFy= other.myFy;</div> <div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  myFz= other.myFz;</div> <div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  </div> <div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  myFxx= other.myFxx;</div> <div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  myFxy= other.myFxy;</div> <div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  myFxz= other.myFxz;</div> <div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  </div> <div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  myFyx= other.myFyx;</div> <div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  myFyy= other.myFyy;</div> <div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  myFyz= other.myFyz;</div> <div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  </div> <div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  myFzx= other.myFzx;</div> <div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  myFzy= other.myFzy;</div> <div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  myFzz= other.myFzz;</div> <div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  </div> <div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  myUpPolynome = other.myUpPolynome; </div> <div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  myLowPolynome = other.myLowPolynome;</div> <div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  }</div> <div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  return *this;</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 class="line"><a name="l00088"></a><span class="lineno"> 88</span> template <typename TSpace></div> <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> inline</div> <div class="line"><a name="l00090"></a><span class="lineno"> 90</span> void</div> <div class="line"><a name="l00091"></a><span class="lineno"> 91</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00092"></a><span class="lineno"> 92</span> init( const Polynomial3 & poly )</div> <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>  myPolynomial = poly;</div> <div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  </div> <div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  myFx= derivative<0>( poly );</div> <div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  myFy= derivative<1>( poly );</div> <div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  myFz= derivative<2>( poly );</div> <div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  </div> <div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  myFxx= derivative<0>( myFx );</div> <div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  myFxy= derivative<1>( myFx );</div> <div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  myFxz= derivative<2>( myFx);</div> <div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div> <div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  myFyx= derivative<0>( myFy );</div> <div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  myFyy= derivative<1>( myFy );</div> <div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  myFyz= derivative<2>( myFy );</div> <div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  </div> <div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  myFzx= derivative<0>( myFz );</div> <div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  myFzy= derivative<1>( myFz );</div> <div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  myFzz= derivative<2>( myFz );</div> <div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  </div> <div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  // These two polynomials are used for mean curvature estimation.</div> <div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  myUpPolynome = myFx*(myFx*myFxx+myFy*myFyx+myFz*myFzx)+</div> <div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  myFy*(myFx*myFxy+myFy*myFyy+myFz*myFzy)+</div> <div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  myFz*(myFx*myFxz+myFy*myFyz+myFz*myFzz)-</div> <div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  ( myFx*myFx +myFy*myFy+myFz*myFz )*(myFxx+myFyy+myFzz);</div> <div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  </div> <div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  myLowPolynome = myFx*myFx +myFy*myFy+myFz*myFz;</div> <div class="line"><a name="l00119"></a><span class="lineno"> 119</span> }</div> <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> template <typename TSpace></div> <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> inline</div> <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> double</div> <div class="line"><a name="l00124"></a><span class="lineno"> 124</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00125"></a><span class="lineno"> 125</span> operator()(const RealPoint &aPoint) const</div> <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> {</div> <div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  return myPolynomial( aPoint[ 0 ] )( aPoint[ 1 ] )( aPoint[ 2 ] );</div> <div class="line"><a name="l00128"></a><span class="lineno"> 128</span> }</div> <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00130"></a><span class="lineno"> 130</span> template <typename TSpace></div> <div class="line"><a name="l00131"></a><span class="lineno"> 131</span> inline</div> <div class="line"><a name="l00132"></a><span class="lineno"> 132</span> bool</div> <div class="line"><a name="l00133"></a><span class="lineno"> 133</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00134"></a><span class="lineno"> 134</span> isInside(const RealPoint &aPoint) const</div> <div class="line"><a name="l00135"></a><span class="lineno"> 135</span> {</div> <div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  return orientation( aPoint ) == INSIDE;</div> <div class="line"><a name="l00137"></a><span class="lineno"> 137</span> }</div> <div class="line"><a name="l00138"></a><span class="lineno"> 138</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> template <typename TSpace></div> <div class="line"><a name="l00140"></a><span class="lineno"> 140</span> inline</div> <div class="line"><a name="l00141"></a><span class="lineno"> 141</span> DGtal::Orientation</div> <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> orientation(const RealPoint &aPoint) const</div> <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> {</div> <div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  Ring v = this->operator()(aPoint);</div> <div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  if ( v < (Ring)0 )</div> <div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  return INSIDE;</div> <div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  else if ( v > (Ring)0 )</div> <div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  return OUTSIDE;</div> <div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  else</div> <div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  return ON;</div> <div class="line"><a name="l00152"></a><span class="lineno"> 152</span> }</div> <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> template <typename TSpace></div> <div class="line"><a name="l00155"></a><span class="lineno"> 155</span> inline</div> <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> typename DGtal::ImplicitPolynomial3Shape<TSpace>::RealVector</div> <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> gradient( const RealPoint &aPoint ) const</div> <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> {</div> <div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  // ISO C++ tells that an object created at return time will not be</div> <div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  // copied into the caller context, but will be already defined in</div> <div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  // the correct context.</div> <div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  return RealVector</div> <div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  ( myFx ( aPoint[ 0 ] )( aPoint[ 1 ] )( aPoint[ 2 ] ),</div> <div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  myFy ( aPoint[ 0 ] )( aPoint[ 1 ] )( aPoint[ 2 ] ),</div> <div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  myFz ( aPoint[ 0 ] )( aPoint[ 1 ] )( aPoint[ 2 ] ) );</div> <div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div> <div class="line"><a name="l00168"></a><span class="lineno"> 168</span> }</div> <div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  </div> <div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  </div> <div class="line"><a name="l00171"></a><span class="lineno"> 171</span> // ------------------------------------------------------------ Added by Anis Benyoub</div> <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  </div> <div class="line"><a name="l00174"></a><span class="lineno"> 174</span> /**</div> <div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  * @param aPoint any point in the Euclidean space.</div> <div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  * This computation is based on the hessian formula of the mean curvature</div> <div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  * k=-(∇F ∗ H (F ) ∗ ∇F T − |∇F |^2 *Trace(H (F ))/2|∇F |^3</div> <div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  * we define it as positive for a sphere</div> <div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  * @return the mean curvature value of the polynomial at \a aPoint.</div> <div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  * </div> <div class="line"><a name="l00181"></a><span class="lineno"> 181</span> */</div> <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> template <typename TSpace></div> <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> inline</div> <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> double</div> <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> meanCurvature( const RealPoint &aPoint ) const</div> <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> {</div> <div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  double temp= myLowPolynome( aPoint[ 0 ] )( aPoint[ 1 ] )( aPoint[ 2 ] );</div> <div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  temp = sqrt(temp);</div> <div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  double downValue = 2.0*(temp*temp*temp);</div> <div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  double upValue = myUpPolynome( aPoint[ 0 ] )( aPoint[ 1 ] )( aPoint[ 2 ] );</div> <div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div> <div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  </div> <div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  return -(upValue/downValue);</div> <div class="line"><a name="l00195"></a><span class="lineno"> 195</span> }</div> <div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  </div> <div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  </div> <div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  </div> <div class="line"><a name="l00199"></a><span class="lineno"> 199</span> //-----------------------------------------------------------------------------</div> <div class="line"><a name="l00200"></a><span class="lineno"> 200</span> template <typename TSpace></div> <div class="line"><a name="l00201"></a><span class="lineno"> 201</span> inline</div> <div class="line"><a name="l00202"></a><span class="lineno"> 202</span> double</div> <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> DGtal::ImplicitPolynomial3Shape<TSpace>::</div> <div class="line"><a name="l00204"></a><span class="lineno"> 204</span> gaussianCurvature( const RealPoint &aPoint ) const</div> <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> {</div> <div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  /*</div> <div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  JOL: new Gaussian curvature formula (in sage)</div> <div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  var('Fx','Fy','Fz','Fxx','Fxy','Fxz','Fyy','Fyz','Fzz')</div> <div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  M=Matrix(4,4,[[Fxx,Fxy,Fxz,Fx],[Fxy,Fyy,Fyz,Fy],[Fxz,Fyz,Fzz,Fz],[Fx,Fy,Fz,0]])</div> <div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  det(M)</div> <div class="line"><a name="l00211"></a><span class="lineno"> 211</span> # Fxz^2*Fy^2 - 2*Fx*Fxz*Fy*Fyz + Fx^2*Fyz^2 - 2*Fxy*Fxz*Fy*Fz + 2*Fx*Fxz*Fyy*Fz - 2*Fx*Fxy*Fyz*Fz + 2*Fxx*Fy*Fyz*Fz + Fxy^2*Fz^2 - Fxx*Fyy*Fz^2 + 2*Fx*Fxy*Fy*Fzz - Fxx*Fy^2*Fzz - Fx^2*Fyy*Fzz</div> <div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  G = -det(M) / ( Fx^2 + Fy^2 + Fz^2 )^2</div> <div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  */</div> <div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  const double x = aPoint[ 0 ];</div> <div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  const double y = aPoint[ 1 ];</div> <div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  const double z = aPoint[ 2 ];</div> <div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  const double Fx = myFx( x )( y )( z );</div> <div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  const double Fy = myFy( x )( y )( z );</div> <div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  const double Fz = myFz( x )( y )( z );</div> <div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  const double Fx2 = Fx * Fx;</div> <div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  const double Fy2 = Fy * Fy;</div> <div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  const double Fz2 = Fz * Fz;</div> <div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  const double G2 = Fx2 + Fy2 + Fz2;</div> <div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  const double Fxx = myFxx( x )( y )( z );</div> <div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  const double Fxy = myFxy( x )( y )( z );</div> <div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  const double Fxz = myFxz( x )( y )( z );</div> <div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  const double Fyy = myFyy( x )( y )( z );</div> <div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  const double Fyz = myFyz( x )( y )( z );</div> <div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  const double Fzz = myFzz( x )( y )( z );</div> <div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  const double Ax2 = ( Fyz * Fyz - Fyy * Fzz ) * Fx2;</div> <div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  const double Ay2 = ( Fxz * Fxz - Fxx * Fzz ) * Fy2; </div> <div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  const double Az2 = ( Fxy * Fxy - Fxx * Fyy ) * Fz2;</div> <div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  const double Axy = ( Fxy * Fzz - Fxz * Fyz ) * Fx * Fy;</div> <div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  const double Axz = ( Fxz * Fyy - Fxy * Fyz ) * Fx * Fz;</div> <div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  const double Ayz = ( Fxx * Fyz - Fxy * Fxz ) * Fy * Fz;</div> <div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  const double det = Ax2 + Ay2 + Az2 + 2 * ( Axy + Axz + Ayz );</div> <div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  return - det / ( G2*G2 );</div> <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> }</div> <div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  </div> <div class="line"><a name="l00240"></a><span class="lineno"> 240</span> template< typename TSpace ></div> <div class="line"><a name="l00241"></a><span class="lineno"> 241</span> inline</div> <div class="line"><a name="l00242"></a><span class="lineno"> 242</span> void</div> <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> DGtal::ImplicitPolynomial3Shape<TSpace>::principalCurvatures</div> <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> ( const RealPoint & aPoint,</div> <div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  double & k1,</div> <div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  double & k2 ) const</div> <div class="line"><a name="l00247"></a><span class="lineno"> 247</span> {</div> <div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  double H = meanCurvature( aPoint );</div> <div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  double G = gaussianCurvature( aPoint );</div> <div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  double tmp = std::sqrt( fabs( H * H - G ));</div> <div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  k2 = H + tmp;</div> <div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  k1 = H - tmp;</div> <div class="line"><a name="l00253"></a><span class="lineno"> 253</span> }</div> <div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  </div> <div class="line"><a name="l00255"></a><span class="lineno"> 255</span> template< typename TSpace ></div> <div class="line"><a name="l00256"></a><span class="lineno"> 256</span> inline</div> <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> void</div> <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> DGtal::ImplicitPolynomial3Shape<TSpace>::principalDirections</div> <div class="line"><a name="l00259"></a><span class="lineno"> 259</span> ( const RealPoint & aPoint,</div> <div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  RealVector & d1,</div> <div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  RealVector & d2 ) const</div> <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> {</div> <div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  const RealVector grad_F = gradient( aPoint );</div> <div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  const auto Fn = grad_F.norm();</div> <div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  if ( Fn < 1e-8 )</div> <div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  {</div> <div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  d1 = d2 = RealVector();</div> <div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  return;</div> <div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  }</div> <div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  RealVector u, v;</div> <div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  const RealVector n = grad_F / Fn;</div> <div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  u = RealVector( 1.0, 0.0, 0.0 ).crossProduct( n );</div> <div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  auto u_norm = u.norm();</div> <div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  if ( u_norm < 1e-8 )</div> <div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  {</div> <div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  u = RealVector( 0.0, 1.0, 0.0 ).crossProduct( n );</div> <div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  u_norm = u.norm();</div> <div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  }</div> <div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  u /= u_norm;</div> <div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  v = n.crossProduct( u );</div> <div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  double k_min, k_max;</div> <div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  principalCurvatures( aPoint, k_min, k_max );</div> <div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  const double x = aPoint[ 0 ];</div> <div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  const double y = aPoint[ 1 ];</div> <div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  const double z = aPoint[ 2 ];</div> <div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  // Computing Hessian matrix</div> <div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  const double Fxx = myFxx( x )( y )( z );</div> <div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  const double Fxy = myFxy( x )( y )( z );</div> <div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  const double Fxz = myFxz( x )( y )( z );</div> <div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  const double Fyy = myFyy( x )( y )( z );</div> <div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  const double Fyz = myFyz( x )( y )( z );</div> <div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  const double Fzz = myFzz( x )( y )( z );</div> <div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  const RealVector HessF_u = { Fxx * u[ 0 ] + Fxy * u[ 1 ] + Fxz * u[ 2 ],</div> <div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  Fxy * u[ 0 ] + Fyy * u[ 1 ] + Fyz * u[ 2 ],</div> <div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  Fxz * u[ 0 ] + Fyz * u[ 1 ] + Fzz * u[ 2 ] };</div> <div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  const RealVector HessF_v = { Fxx * v[ 0 ] + Fxy * v[ 1 ] + Fxz * v[ 2 ],</div> <div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  Fxy * v[ 0 ] + Fyy * v[ 1 ] + Fyz * v[ 2 ],</div> <div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  Fxz * v[ 0 ] + Fyz * v[ 1 ] + Fzz * v[ 2 ] };</div> <div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  const double Fuu = u.dot( HessF_u );</div> <div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  const double Fuv = u.dot( HessF_v );</div> <div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  const double Fvv = v.dot( HessF_v );</div> <div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  if ( fabs( k_min * Fn - Fuu ) >= fabs( k_min * Fn - Fvv ) )</div> <div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  {</div> <div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  // Choose k1 = k_min and k2 = k_max,</div> <div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  // to avoid null k1*Fn - Fuu = -(k2*Fn - Fvv) = 0</div> <div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  double k1 = k_min;</div> <div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  double k2 = k_max;</div> <div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  d1 = RealVector( ( k1 * Fn - Fuu ) * v[ 0 ] + Fuv * u[ 0 ],</div> <div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  ( k1 * Fn - Fuu ) * v[ 1 ] + Fuv * u[ 1 ],</div> <div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  ( k1 * Fn - Fuu ) * v[ 2 ] + Fuv * u[ 2 ] );</div> <div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  d2 = -1.0 * RealVector( ( k2 * Fn - Fvv ) * u[ 0 ] + Fuv * v[ 0 ],</div> <div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  ( k2 * Fn - Fvv ) * u[ 1 ] + Fuv * v[ 1 ],</div> <div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  ( k2 * Fn - Fvv ) * u[ 2 ] + Fuv * v[ 2 ] );</div> <div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  }</div> <div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  else</div> <div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  {</div> <div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  // Choose k2 = k_min and k1 = k_max,</div> <div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  // then | k_max*Fn - Fuu | >= | k_max*Fn - Fvv | >= 0</div> <div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  double k1 = k_max;</div> <div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  double k2 = k_min;</div> <div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  d2 = RealVector( ( k1 * Fn - Fuu ) * v[ 0 ] + Fuv * u[ 0 ],</div> <div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  ( k1 * Fn - Fuu ) * v[ 1 ] + Fuv * u[ 1 ],</div> <div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  ( k1 * Fn - Fuu ) * v[ 2 ] + Fuv * u[ 2 ] );</div> <div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  d1 = -1.0 * RealVector( ( k2 * Fn - Fvv ) * u[ 0 ] + Fuv * v[ 0 ],</div> <div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  ( k2 * Fn - Fvv ) * u[ 1 ] + Fuv * v[ 1 ],</div> <div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  ( k2 * Fn - Fvv ) * u[ 2 ] + Fuv * v[ 2 ] );</div> <div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  }</div> <div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  d1 /= d1.norm();</div> <div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  d2 /= d2.norm();</div> <div class="line"><a name="l00330"></a><span class="lineno"> 330</span> }</div> <div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  </div> <div class="line"><a name="l00332"></a><span class="lineno"> 332</span> /**</div> <div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  *@param aPoint any point in the Euclidean space.</div> <div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  *@param accuracy refers to the precision </div> <div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  *@param maxIter refers to the maximum iterations the fonction user authorises</div> <div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  *@param gamma refers to the step</div> <div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  *@return the nearest point on the surface to the one given in parameter.</div> <div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  */</div> <div class="line"><a name="l00339"></a><span class="lineno"> 339</span> template <typename TSpace></div> <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> inline</div> <div class="line"><a name="l00341"></a><span class="lineno"> 341</span> typename DGtal::ImplicitPolynomial3Shape<TSpace>::RealPoint </div> <div class="line"><a name="l00342"></a><span class="lineno"> 342</span> DGtal::ImplicitPolynomial3Shape<TSpace>::nearestPoint</div> <div class="line"><a name="l00343"></a><span class="lineno"> 343</span> ( const RealPoint &aPoint, const double accuracy, </div> <div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  const int maxIter, const double gamma ) const</div> <div class="line"><a name="l00345"></a><span class="lineno"> 345</span> {</div> <div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  RealPoint X = aPoint;</div> <div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  for ( int numberIter = 0; numberIter < maxIter; numberIter++ )</div> <div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  {</div> <div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  double val_X = (*this)( X );</div> <div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  if ( fabs( val_X ) < accuracy ) break;</div> <div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  RealVector grad_X = (*this).gradient( X );</div> <div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  double n2_grad_X = grad_X.dot( grad_X );</div> <div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  if ( n2_grad_X > 0.000001 ) grad_X /= n2_grad_X;</div> <div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  X -= val_X * gamma * grad_X ;</div> <div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  }</div> <div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  return X;</div> <div class="line"><a name="l00357"></a><span class="lineno"> 357</span> }</div> <div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  </div> <div class="line"><a name="l00359"></a><span class="lineno"> 359</span> ///////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00360"></a><span class="lineno"> 360</span> // Interface - public :</div> <div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  </div> <div class="line"><a name="l00362"></a><span class="lineno"> 362</span> /**</div> <div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  * Writes/Displays the object on an output stream.</div> <div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  * @param out the output stream where the object is written.</div> <div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  */</div> <div class="line"><a name="l00366"></a><span class="lineno"> 366</span> template <typename TSpace></div> <div class="line"><a name="l00367"></a><span class="lineno"> 367</span> inline</div> <div class="line"><a name="l00368"></a><span class="lineno"> 368</span> void</div> <div class="line"><a name="l00369"></a><span class="lineno"> 369</span> DGtal::ImplicitPolynomial3Shape<TSpace>::selfDisplay ( std::ostream & out ) const</div> <div class="line"><a name="l00370"></a><span class="lineno"> 370</span> {</div> <div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  out << "[ImplicitPolynomial3Shape] P(x,y,z) = " << myPolynomial;</div> <div class="line"><a name="l00372"></a><span class="lineno"> 372</span> }</div> <div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  </div> <div class="line"><a name="l00374"></a><span class="lineno"> 374</span> /**</div> <div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  * Checks the validity/consistency of the object.</div> <div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  * @return 'true' if the object is valid, 'false' otherwise.</div> <div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  */</div> <div class="line"><a name="l00378"></a><span class="lineno"> 378</span> template <typename TSpace></div> <div class="line"><a name="l00379"></a><span class="lineno"> 379</span> inline</div> <div class="line"><a name="l00380"></a><span class="lineno"> 380</span> bool</div> <div class="line"><a name="l00381"></a><span class="lineno"> 381</span> DGtal::ImplicitPolynomial3Shape<TSpace>::isValid() const</div> <div class="line"><a name="l00382"></a><span class="lineno"> 382</span> {</div> <div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  return true;</div> <div class="line"><a name="l00384"></a><span class="lineno"> 384</span> }</div> <div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  </div> <div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  </div> <div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  </div> <div class="line"><a name="l00388"></a><span class="lineno"> 388</span> ///////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00389"></a><span class="lineno"> 389</span> // Implementation of inline functions //</div> <div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  </div> <div class="line"><a name="l00391"></a><span class="lineno"> 391</span> template <typename TSpace></div> <div class="line"><a name="l00392"></a><span class="lineno"> 392</span> inline</div> <div class="line"><a name="l00393"></a><span class="lineno"> 393</span> std::ostream&</div> <div class="line"><a name="l00394"></a><span class="lineno"> 394</span> DGtal::operator<< ( std::ostream & out,</div> <div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  const ImplicitPolynomial3Shape<TSpace> & object )</div> <div class="line"><a name="l00396"></a><span class="lineno"> 396</span> {</div> <div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  object.selfDisplay( out );</div> <div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  return out;</div> <div class="line"><a name="l00399"></a><span class="lineno"> 399</span> }</div> <div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  </div> <div class="line"><a name="l00401"></a><span class="lineno"> 401</span> // //</div> <div class="line"><a name="l00402"></a><span class="lineno"> 402</span> ///////////////////////////////////////////////////////////////////////////////</div> <div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  </div> <div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  </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" 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