3dImplicitSurfaceExtractorBy4DExtension_8cpp_source.html

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<div class="title">3dImplicitSurfaceExtractorBy4DExtension.cpp</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="preprocessor">#include &lt;map&gt;</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="preprocessor">#include &quot;CLI11.hpp&quot;</span></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; </div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;<span class="preprocessor">#include &quot;DGtal/base/Common.h&quot;</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="preprocessor">#include &quot;DGtal/base/CountedPtr.h&quot;</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="preprocessor">#include &quot;DGtal/helpers/StdDefs.h&quot;</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;<span class="preprocessor">#include &quot;DGtal/math/MPolynomial.h&quot;</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="preprocessor">#include &quot;DGtal/io/readers/MPolynomialReader.h&quot;</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;<span class="preprocessor">#include &quot;DGtal/io/DrawWithDisplay3DModifier.h&quot;</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;<span class="preprocessor">#include &quot;DGtal/io/viewers/Viewer3D.h&quot;</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="preprocessor">#include &quot;DGtal/topology/KhalimskySpaceND.h&quot;</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;<span class="preprocessor">#include &quot;DGtal/topology/CubicalComplex.h&quot;</span></div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;<span class="preprocessor">#include &quot;DGtal/topology/CubicalComplexFunctions.h&quot;</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;<span class="preprocessor">#include &quot;DGtal/topology/SetOfSurfels.h&quot;</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;<span class="preprocessor">#include &quot;DGtal/topology/DigitalSurface.h&quot;</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;<span class="preprocessor">#include &quot;DGtal/topology/helpers/Surfaces.h&quot;</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;<span class="preprocessor">#include &quot;DGtal/shapes/GaussDigitizer.h&quot;</span></div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;<span class="preprocessor">#include &quot;DGtal/shapes/Mesh.h&quot;</span></div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;<span class="preprocessor">#include &quot;DGtal/shapes/implicit/ImplicitPolynomial3Shape.h&quot;</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;<span class="keyword">using namespace </span>std;</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;<span class="keyword">using namespace </span><a class="code" href="namespaceDGtal.html">DGtal</a>;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160; </div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> TSpace3, <span class="keyword">typename</span> TSpace4, <span class="keyword">typename</span> TPolynomial3&gt;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="keyword">struct </span>ImplicitSurface4DProductExtension {</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="keyword">typedef</span> TSpace3                          Space3;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="keyword">typedef</span> TSpace4                          Space4;</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  <span class="keyword">typedef</span> TPolynomial3                     Polynomial3;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealPoint       RealPoint3;</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealVector      RealVector3;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::Integer         <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a5d93c6632713d21e2662c93af3a941e6">Integer</a>;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> RealPoint3::Coordinate  Ring;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealPoint       RealPoint4;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealVector      RealVector4;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;  <span class="keyword">typedef</span> RealPoint4                       <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a>;</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  <span class="keyword">typedef</span> RealVector4                      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a>;</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160; </div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;  ImplicitSurface4DProductExtension( <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Clone.html">Clone&lt;Polynomial3&gt;</a> poly )</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    : f( poly )</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  {</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    fx  = derivative&lt;0&gt;( f );</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    fy  = derivative&lt;1&gt;( f );</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    fz  = derivative&lt;2&gt;( f );</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    fxx = derivative&lt;0&gt;( fx );</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    fxy = derivative&lt;0&gt;( fy );</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;    fxz = derivative&lt;0&gt;( fz );</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    fyy = derivative&lt;1&gt;( fy );</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    fyz = derivative&lt;1&gt;( fz );</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    fzz = derivative&lt;2&gt;( fz );</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; </div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  Ring operator()(<span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint)<span class="keyword"> const</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;    Ring x = aPoint[ 0 ];</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;    Ring y = aPoint[ 1 ];</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;    Ring z = aPoint[ 2 ];</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;    Ring t = aPoint[ 3 ];</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;    RealVector3 grad( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z) );</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;    <span class="keywordflow">return</span> f(x)(y)(z) - t * grad.norm();</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  }</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160; </div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;  <span class="keywordtype">bool</span> isInside(<span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint)<span class="keyword"> const</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    <span class="keywordflow">return</span> this-&gt;operator()( aPoint ) &lt;= <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1NumberTraits.html">NumberTraits&lt;Ring&gt;::ZERO</a>;</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 class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41">Orientation</a> orientation(<span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint)<span class="keyword"> const</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    Ring v = this-&gt;operator()( aPoint );</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="keywordflow">if</span> ( v &gt; <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1NumberTraits.html">NumberTraits&lt;Ring&gt;::ZERO</a> )      <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a5f4bdeccc29812b7de1cc0c05b724734">OUTSIDE</a>;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( v &lt; <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1NumberTraits.html">NumberTraits&lt;Ring&gt;::ZERO</a> ) <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a528af0eaf947edc94796219523aa9553">INSIDE</a>;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    <span class="keywordflow">else</span>                                     <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a7671a5416d92f37137f9999ca23dd65e">ON</a>;</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  }</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160; </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="keyword">inline</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a> gradient( <span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint )<span class="keyword"> const</span></div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    Ring x = aPoint[ 0 ];</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;    Ring y = aPoint[ 1 ];</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;    Ring z = aPoint[ 2 ];</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;    Ring t = aPoint[ 3 ];</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;    RealVector3 grad( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z) );</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    Ring ngrad = grad.norm();</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;    grad /= ngrad;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;    <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a> d_gradx( fxx(x)(y)(z), fxy(x)(y)(z),fxz(x)(y)(z) );</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a> d_grady( fxy(x)(y)(z), fyy(x)(y)(z),fyz(x)(y)(z) );</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a> d_gradz( fxz(x)(y)(z), fyz(x)(y)(z),fzz(x)(y)(z) );</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a>( grad[ 0 ] - t * d_gradx.dot( grad ),</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;                       grad[ 1 ] - t * d_grady.dot( grad ),</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;                       grad[ 2 ] - t * d_gradz.dot( grad ),</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;                       -ngrad );</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;                      </div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;  }</div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160; </div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;  Polynomial3 f;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;  Polynomial3 fx;</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  Polynomial3 fy;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  Polynomial3 fz;</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  Polynomial3 fxx;</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;  Polynomial3 fxy;</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  Polynomial3 fxz;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  Polynomial3 fyy;</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;  Polynomial3 fyz;</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;  Polynomial3 fzz;</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;};</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160; </div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> TSpace3, <span class="keyword">typename</span> TSpace4, <span class="keyword">typename</span> TPolynomial3&gt;</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;<span class="keyword">struct </span>ImplicitSurface4DExtension {</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  <span class="keyword">typedef</span> TSpace3                          Space3;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  <span class="keyword">typedef</span> TSpace4                          Space4;</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  <span class="keyword">typedef</span> TPolynomial3                     Polynomial3;</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealPoint       RealPoint3;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealVector      RealVector3;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::Integer         <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a5d93c6632713d21e2662c93af3a941e6">Integer</a>;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> RealPoint3::Coordinate  Ring;</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealPoint       RealPoint4;</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealVector      RealVector4;</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;  <span class="keyword">typedef</span> RealPoint4                       <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a>;</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;  <span class="keyword">typedef</span> RealVector4                      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a>;</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160; </div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;  ImplicitSurface4DExtension( <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Clone.html">Clone&lt;Polynomial3&gt;</a> poly )</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;    : f( poly )</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;  {</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;    fx  = derivative&lt;0&gt;( f );</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;    fy  = derivative&lt;1&gt;( f );</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    fz  = derivative&lt;2&gt;( f );</div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    fxx = derivative&lt;0&gt;( fx );</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    fxy = derivative&lt;0&gt;( fy );</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;    fxz = derivative&lt;0&gt;( fz );</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;    fyy = derivative&lt;1&gt;( fy );</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    fyz = derivative&lt;1&gt;( fz );</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;    fzz = derivative&lt;2&gt;( fz );</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  }</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160; </div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;  Ring operator()(<span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint)<span class="keyword"> const</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    Ring x = aPoint[ 0 ];</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    Ring y = aPoint[ 1 ];</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    Ring z = aPoint[ 2 ];</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;    Ring t = aPoint[ 3 ];</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;    <span class="comment">// RealVector3 grad( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z) );</span></div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;    <span class="keywordflow">return</span> f(x)(y)(z) - t;</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;  }</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160; </div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;  <span class="keywordtype">bool</span> isInside(<span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint)<span class="keyword"> const</span></div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    <span class="keywordflow">return</span> this-&gt;operator()( aPoint ) &lt;= <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1NumberTraits.html">NumberTraits&lt;Ring&gt;::ZERO</a>;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;  }</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160; </div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41">Orientation</a> orientation(<span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint)<span class="keyword"> const</span></div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;    Ring v = this-&gt;operator()( aPoint );</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;    <span class="keywordflow">if</span> ( v &gt; <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1NumberTraits.html">NumberTraits&lt;Ring&gt;::ZERO</a> )      <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a5f4bdeccc29812b7de1cc0c05b724734">OUTSIDE</a>;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( v &lt; <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1NumberTraits.html">NumberTraits&lt;Ring&gt;::ZERO</a> ) <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a528af0eaf947edc94796219523aa9553">INSIDE</a>;</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;    <span class="keywordflow">else</span>                                     <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a7671a5416d92f37137f9999ca23dd65e">ON</a>;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  }</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160; </div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="keyword">inline</span></div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a> gradient( <span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> &amp;aPoint )<span class="keyword"> const</span></div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;<span class="keyword">  </span>{</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    Ring x = aPoint[ 0 ];</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    Ring y = aPoint[ 1 ];</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;    Ring z = aPoint[ 2 ];</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    Ring t = aPoint[ 3 ];</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    <span class="keywordflow">return</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a0db3f1b80b0d65707785c1072244befc">RealVector</a>( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z), -1.0 );</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  }</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  Polynomial3 f;</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;  Polynomial3 fx;</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  Polynomial3 fy;</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  Polynomial3 fz;</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;  Polynomial3 fxx;</div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;  Polynomial3 fxy;</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  Polynomial3 fxz;</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  Polynomial3 fyy;</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  Polynomial3 fyz;</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;  Polynomial3 fzz;</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;};</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160; </div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160; </div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> CellOutputIterator, <span class="keyword">typename</span> DigitalSurface&gt;</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;<span class="keywordtype">void</span></div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;analyzeSurface( CellOutputIterator itSure, CellOutputIterator itUnsure, </div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;                <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html">DigitalSurface</a> surface )</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;{</div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#a9a527561977510dc5ab21cec7438727c">DigitalSurface::KSpace</a>        <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html">KSpace</a>;</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#a022bb4ded759e45963bfe00706ae8214">DigitalSurface::Surfel</a>        Surfel;</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#a40056dd099c93e7ab5dfc5196a56e550">DigitalSurface::ConstIterator</a> ConstIterator;</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#a1e5d3aa778ac2d76c6a5fe1c3986d63b">DigitalSurface::DigitalSurfaceContainer</a> Container;</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#a81da19bd361a25c90f7a0c295e91cfaa">DigitalSurface::DigitalSurfaceTracker</a>   Tracker;</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#a1101d4adbc2a87db33afcb42209b6f04">KSpace::Integer</a>               <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a5d93c6632713d21e2662c93af3a941e6">Integer</a>;</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1KhalimskyCell.html">KSpace::Cell</a>                  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1KhalimskyCell.html">Cell</a>;</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;  <span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> t  = <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#ae2b2dcf34c36a5e3eae4bf13291f1578">KSpace::dimension</a> - 1;</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;  <span class="keyword">const</span> Container&amp; C = surface.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#afd10471a6fb7fb58e5f8744a8b6c1713">container</a>();</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;  <span class="keyword">const</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html">KSpace</a>&amp; K    = surface.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#afd10471a6fb7fb58e5f8744a8b6c1713">container</a>().space();</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;  Surfel s2;</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;  <span class="keywordflow">for</span> ( ConstIterator it = surface.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#a49b0a08eb04ed843d3e2c9ac7112a913">begin</a>(), itE = surface.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html#a00e29d43b6f9d0313c7134aec8c4f4ee">end</a>(); it != itE; ++it )</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    {</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;      Surfel s   = *it;</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1KhalimskyCell.html">Cell</a>   is  = K.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#ab4acf92d6aac9ace694f79c3ecda674d">unsigns</a>( s );</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a5d93c6632713d21e2662c93af3a941e6">Integer</a> s_xt = K.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#a71a96a90f5935efbccfff1d98b874c2d">sKCoord</a>( s, t );</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;      <span class="keywordflow">if</span> ( s_xt == 0 )         *itUnsure++ = is;</div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( s_xt == -1 ) </div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;        {</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;          <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1CountedPtr.html">CountedPtr&lt;Tracker&gt;</a> tracker( C.newTracker( s ) );</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;          <span class="keywordflow">if</span> ( tracker-&gt;adjacent( s2, t, <span class="keyword">true</span> ) != 0 )</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;            {</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;              <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a5d93c6632713d21e2662c93af3a941e6">Integer</a> s2_xt = K.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#a71a96a90f5935efbccfff1d98b874c2d">sKCoord</a>( s2, t );</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;              <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1KhalimskyCell.html">Cell</a> ic = K.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#ab9ccd18c393b7bfd31289391a0a99b8d">uIncident</a>( is, t, <span class="keyword">true</span> ); </div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;              <span class="keywordflow">if</span> ( s2_xt &gt; 0 ) *itSure++   = ic;</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;              <span class="keywordflow">else</span>             *itUnsure++ = ic;</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;            }</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;        }</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( s_xt == 1 )</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;        {</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;          <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1CountedPtr.html">CountedPtr&lt;Tracker&gt;</a> tracker( C.newTracker( s ) );</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;          <span class="keywordflow">if</span> ( tracker-&gt;adjacent( s2, t, <span class="keyword">false</span> ) != 0 )</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;            {</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;              <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a5d93c6632713d21e2662c93af3a941e6">Integer</a> s2_xt = K.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#a71a96a90f5935efbccfff1d98b874c2d">sKCoord</a>( s2, t );</div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;              <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1KhalimskyCell.html">Cell</a> ic = K.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#ab9ccd18c393b7bfd31289391a0a99b8d">uIncident</a>( is, t, <span class="keyword">false</span> ); </div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;              <span class="keywordflow">if</span> ( s2_xt &lt; 0 ) *itSure++   = ic;</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;              <span class="keywordflow">else</span>             *itUnsure++ = ic;</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;            }</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;        }</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;      <span class="keywordflow">else</span> cout &lt;&lt; <span class="stringliteral">&quot; &quot;</span> &lt;&lt; s_xt;</div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;    }</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;}</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160; </div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> ImplicitSurface, <span class="keyword">typename</span> RealPo<span class="keywordtype">int</span>&gt;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> projectNewton( <span class="keyword">const</span> ImplicitSurface &amp; is, </div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;                         <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> x, </div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;                         <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html#a6409a51203e0edc907d523fb19ed7e41">RealPoint::Coordinate</a> epsilon,</div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;                         <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> max_iter )</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;{</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html#a6409a51203e0edc907d523fb19ed7e41">RealPoint::Coordinate</a> Scalar;</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html">RealPoint</a> gx;</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;  Scalar f, g2;</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;  Scalar eps2 = epsilon * epsilon;</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;  <span class="keywordflow">while</span> ( max_iter-- != 0 )</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;    {</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;      f = is( x );</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;      <span class="keywordflow">if</span> ( <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1functions.html#af95dcf36f806f7fc15626ca6b1c27d22">abs</a>( f ) &lt; epsilon ) <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;      gx = is.gradient( x );</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;      g2 = gx.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1PointVector.html#aa0bb99ecab1fcb8a34f94dde061f6eac">dot</a>( gx );</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;      <span class="keywordflow">if</span> ( g2 &lt; eps2 ) <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;      x -= (f/g2) * gx;</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    }</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;  <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;}</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160; </div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160; </div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> CubicalComplex4, <span class="keyword">typename</span> ImplicitShape4, </div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;          <span class="keyword">typename</span> ImplicitDigitalShape4, <span class="keyword">typename</span> ImplicitShape3&gt;</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;<span class="keywordtype">void</span> projectComplex( std::vector&lt; typename ImplicitShape3::RealPoint &gt;&amp; points,</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;                     <span class="keyword">const</span> CubicalComplex4&amp; complex4,</div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;                     <span class="keyword">const</span> ImplicitShape4&amp; shape,</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;                     <span class="keyword">const</span> ImplicitDigitalShape4&amp; dshape,</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;                     <span class="keyword">const</span> ImplicitShape3&amp; shape3,</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;                     <span class="keywordtype">double</span> epsilon,</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;                     <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> max_iter )</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;{</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Cell     Cell4;</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Point    Point4;</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::CellMapConstIterator CellMapConstIterator;</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::RealPoint RealPoint4;</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::Ring      Ring;</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape3::RealPoint RealPoint3;</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;  points.clear();</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;  <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 0 ), itE = complex4.end( 0 ); it != itE; ++it )</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;    {</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;      Cell4 cell    = it-&gt;first;</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;      Point4 dp     = complex4.space().uCoords( cell );</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;      RealPoint4 p  = dshape-&gt;embed( dp );</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;      RealPoint3 p3 = RealPoint3( p[ 0 ], p[ 1 ], p[ 2 ] );</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;      RealPoint3 q  = projectNewton( shape3, p3, epsilon, max_iter );</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;      points.push_back( q );</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    }</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;}</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160; </div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> CubicalComplex4, <span class="keyword">typename</span> ImplicitShape4, </div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;          <span class="keyword">typename</span> ImplicitDigitalShape4, <span class="keyword">typename</span> ImplicitShape3&gt;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;<span class="keywordtype">void</span> doNotProjectComplex( std::vector&lt; typename ImplicitShape3::RealPoint &gt;&amp; points,</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;                          <span class="keyword">const</span> CubicalComplex4&amp; complex4,</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160;                          <span class="keyword">const</span> ImplicitShape4&amp; shape,</div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;                          <span class="keyword">const</span> ImplicitDigitalShape4&amp; dshape,</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;                          <span class="keyword">const</span> ImplicitShape3&amp; shape3 )</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;{</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Cell     Cell4;</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Point    Point4;</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::CellMapConstIterator CellMapConstIterator;</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::RealPoint RealPoint4;</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::Ring      Ring;</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape3::RealPoint RealPoint3;</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;  <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 0 ), itE = complex4.end( 0 ); it != itE; ++it )</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    {</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;      Cell4 cell    = it-&gt;first;</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;      Point4 dp     = complex4.space().uCoords( cell );</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;      RealPoint4 p  = dshape-&gt;embed( dp );</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;      RealPoint3 p3 = RealPoint3( p[ 0 ], p[ 1 ], p[ 2 ] );</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;      points.push_back( p3 );</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    }</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;}</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    </div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160; </div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;<span class="keywordtype">int</span> <a class="code" href="3dHeightMapViewer_8cpp.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a>( <span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv )</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;{</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;  <span class="keyword">typedef</span> <span class="keywordtype">int</span>                               <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z2i.html#a5d93c6632713d21e2662c93af3a941e6">Integer</a>;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1SpaceND.html">SpaceND&lt;3,Integer&gt;</a>                Space3;</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html">KhalimskySpaceND&lt;3,Integer&gt;</a>       KSpace3;</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;  <span class="keyword">typedef</span> KSpace3::Cell                     Cell3;</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  <span class="keyword">typedef</span> std::map&lt;Cell3, CubicalCellData&gt;  Map3;</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1CubicalComplex.html">CubicalComplex&lt; KSpace3, Map3 &gt;</a>   CC3;</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;  <span class="keyword">typedef</span> Space3::Point                     Point3;</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;  <span class="keyword">typedef</span> Space3::RealPoint                 RealPoint3;</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;  <span class="keyword">typedef</span> RealPoint3::Coordinate            Ring;</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;  <span class="keyword">typedef</span> Ring                              Scalar;</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1MPolynomial.html">MPolynomial&lt;3, Ring&gt;</a>              Polynomial3;</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1MPolynomialReader.html">MPolynomialReader&lt;3, Ring&gt;</a>        Polynomial3Reader;</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1ImplicitPolynomial3Shape.html">ImplicitPolynomial3Shape&lt;Space3&gt;</a>  ImplicitShape3;</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1SpaceND.html">SpaceND&lt;4,Integer&gt;</a>                Space4;</div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html">KhalimskySpaceND&lt;4,Integer&gt;</a>       KSpace4;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;  <span class="keyword">typedef</span> KSpace4::Cell                     Cell4;</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  <span class="keyword">typedef</span> KSpace4::Cells                    Cells4;</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="keyword">typedef</span> KSpace4::SCell                    SCell4;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  <span class="keyword">typedef</span> Space4::Point                     Point4;</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;  <span class="keyword">typedef</span> Space4::RealPoint                 RealPoint4;</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;  <span class="keyword">typedef</span> Space4::RealVector                RealVector4;</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160;  <span class="keyword">typedef</span> ImplicitSurface4DProductExtension&lt;Space3,Space4,Polynomial3&gt;</div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;                                            ImplicitShape4;</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1GaussDigitizer.html">GaussDigitizer&lt; Space4, ImplicitShape4 &gt;</a> </div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;                                            ImplicitDigitalShape4;</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;  <span class="keyword">typedef</span> ImplicitDigitalShape4::Domain     Domain4;</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;  <span class="keyword">typedef</span> std::map&lt;Cell4, CubicalCellData&gt;  Map4;</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1CubicalComplex.html">CubicalComplex&lt; KSpace4, Map4 &gt;</a>   CC4;</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;  <span class="keyword">typedef</span> CC4::CellMapIterator              CellMapIterator;</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;  <span class="keyword">typedef</span> CC4::CellMapConstIterator         CellMapConstIterator;</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;  <span class="keyword">typedef</span> CC4::Cells                        Cells4;</div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160; </div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;  </div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;  <span class="comment">// parse command line using CLI ----------------------------------------------</span></div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;  CLI::App app;</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;  <span class="keywordtype">string</span> poly_str;</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;  std::string outputFileName {<span class="stringliteral">&quot;result.raw&quot;</span>};</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a1c09e3f63904ff371f1b99f45069fc63">DGtal::int64_t</a> rescaleInputMin {0};</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a1c09e3f63904ff371f1b99f45069fc63">DGtal::int64_t</a> rescaleInputMax {255};</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;  Ring min_x {-10.0};</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160;  Ring max_x {10.0};</div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;  Ring h {1.0};</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160;  Ring t {0.000001};</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160; </div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;  std::string project {<span class="stringliteral">&quot;Newton&quot;</span>};</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  <span class="keywordtype">double</span> epsilon {1e-6};</div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> max_iter {500};</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;  std::string view {<span class="stringliteral">&quot;Normal&quot;</span>};</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;    app.description( <span class="stringliteral">&quot;Computes the zero level set of the given polynomial. Usage:  3dImplicitSurfaceExtractorBy4DExtension -p &lt;polynomial&gt; [options]\n Example:\n 3dImplicitSurfaceExtractorBy4DExtension  -p \&quot;-0.9*(y^2+z^2-1)^2-(x^2+y^2-1)^3\&quot; -g 0.06125 -a -2 -A 2 -v Singular -t 0.02 \n - whitney  : x^2-y*z^2 \n - 4lines   : x*y*(y-x)*(y-z*x) \n - cone     : z^2-x^2-y^2 \n - simonU   : x^2-z*y^2+x^4+y^4 \n - cayley3  : 4*(x^2 + y^2 + z^2) + 16*x*y*z - 1 \n - crixxi   : -0.9*(y^2+z^2-1)^2-(x^2+y^2-1)^3 \n Some other examples (more difficult): \n 3dImplicitSurfaceExtractorBy4DExtension -a -2 -A 2 -p \&quot;((y^2+z^2-1)^2-(x^2+y^2-1)^3)*(y*(x-1)^2-z*(x+1))^2\&quot; -g 0.025 -e 1e-6 -n 50000 -v Singular -t 0.5 -P Newton \n 3dImplicitSurfaceExtractorBy4DExtension -a -2 -A 2 -p \&quot;(x^5-4*z^3*y^2)*((x+y)^2-(z-x)^3)\&quot; -g 0.025 -e 1e-6 -n 50000 -v Singular -t 0.05 -P Newton &quot;</span>);</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;  app.add_option(<span class="stringliteral">&quot;-p,--polynomial,1&quot;</span>, poly_str, <span class="stringliteral">&quot;the implicit polynomial whose zero-level defines the shape of interest.&quot;</span> )</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  -&gt;required();</div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  app.add_option(<span class="stringliteral">&quot;--minAABB,-a&quot;</span>,min_x, <span class="stringliteral">&quot;the min value of the AABB bounding box (domain)&quot;</span> , <span class="keyword">true</span>);</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;  app.add_option(<span class="stringliteral">&quot;--maxAABB,-A&quot;</span>,max_x, <span class="stringliteral">&quot;the max value of the AABB bounding box (domain)&quot;</span> , <span class="keyword">true</span>);</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;  app.add_option(<span class="stringliteral">&quot;--gridstep,-g&quot;</span>, h, <span class="stringliteral">&quot;the gridstep that defines the digitization in the 4th dimension (small is generally a good idea, default is 1e-6). &quot;</span>, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;  app.add_option(<span class="stringliteral">&quot;--timestep,-t&quot;</span>,t, <span class="stringliteral">&quot;the thickening parameter for the implicit surface.&quot;</span> , <span class="keyword">true</span>);</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;  app.add_option(<span class="stringliteral">&quot;--project,-P&quot;</span>, project, <span class="stringliteral">&quot;defines the projection: either No or Newton.&quot;</span>, <span class="keyword">true</span>)</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;   -&gt; check(CLI::IsMember({<span class="stringliteral">&quot;No&quot;</span>, <span class="stringliteral">&quot;Newton&quot;</span>}));</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  app.add_option(<span class="stringliteral">&quot;--epsilon,-e&quot;</span>, epsilon, <span class="stringliteral">&quot;the maximum precision relative to the implicit surface in the Newton approximation of F=0.&quot;</span>, <span class="keyword">true</span>);</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  app.add_option(<span class="stringliteral">&quot;--max_iter,-n&quot;</span>, max_iter, <span class="stringliteral">&quot;the maximum number of iteration in the Newton approximation of F=0.&quot;</span>, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  app.add_option(<span class="stringliteral">&quot;--view,-v&quot;</span>, view, <span class="stringliteral">&quot;specifies if the surface is viewed as is (Normal) or if places close to singularities are highlighted (Singular), or if unsure places should not be displayed (Hide).&quot;</span>,<span class="keyword">true</span> )</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160;   -&gt; check(CLI::IsMember({<span class="stringliteral">&quot;Singular&quot;</span>, <span class="stringliteral">&quot;Normal&quot;</span>, <span class="stringliteral">&quot;Hide&quot;</span>}));</div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  </div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  app.get_formatter()-&gt;column_width(40);</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  CLI11_PARSE(app, argc, argv);</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;  <span class="comment">// END parse command line using CLI ----------------------------------------------</span></div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160; </div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;   </div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;  <span class="comment">//-------------- read polynomial and creating 4d implicit fct -----------------</span></div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Reading polynomial and creating 4D implicit function&quot;</span> );</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;  Polynomial3 poly;</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;  Polynomial3Reader reader;</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;  string::const_iterator iter = reader.read( poly, poly_str.begin(), poly_str.end() );</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;  <span class="keywordflow">if</span> ( iter != poly_str.end() )</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;    {</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160;      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a1e786a1f3b1047e92b73c82f67e3c295">error</a>() &lt;&lt; <span class="stringliteral">&quot;ERROR reading polynomial: I read only &lt;&quot;</span> &lt;&lt; poly_str.substr( 0, iter - poly_str.begin() )</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;                    &lt;&lt; <span class="stringliteral">&quot;&gt;, and I built P=&quot;</span> &lt;&lt; poly &lt;&lt; std::endl;</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;      <span class="keywordflow">return</span> 2;</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;    }</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;  <span class="comment">// Creating implicit shape and storing it with smart pointer for automatic deallocation.</span></div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  ImplicitShape3 shape3( poly );</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1CountedPtr.html">CountedPtr&lt;ImplicitShape4&gt;</a> shape( <span class="keyword">new</span> ImplicitShape4( poly ) ); </div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160; </div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;  </div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  RealPoint4 p1( min_x, min_x, min_x, -t*h );</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;  RealPoint4 p2( max_x, max_x, max_x,  0 );</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;  <span class="comment">// Creating digitized shape and storing it with smart pointer for automatic deallocation.</span></div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1CountedPtr.html">CountedPtr&lt;ImplicitDigitalShape4&gt;</a> dshape( <span class="keyword">new</span> ImplicitDigitalShape4() );</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;  dshape-&gt;attach( *shape );</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;  dshape-&gt;init( p1, p2, RealVector4( h, h, h, t ) );</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;  Domain4 domain4 = dshape-&gt;getDomain();</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;  KSpace4 K4;</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;  K4.init( domain4.lowerBound(), domain4.upperBound(), <span class="keyword">true</span> );</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- domain is &quot;</span> &lt;&lt; domain4 &lt;&lt; std::endl;</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160; </div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;  <span class="comment">//-------------- read polynomial and creating 4d implicit fct -----------------</span></div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Extracting isosurface 0 of 4D polynomial. &quot;</span> );</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;  CC4 complex4( K4 );</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;  std::vector&lt;SCell4&gt; surface_cells;</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;  std::back_insert_iterator&lt; std::vector&lt;SCell4&gt; &gt; outItSurface( surface_cells );</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Surfaces.html">Surfaces&lt;KSpace4&gt;::sWriteBoundary</a>( outItSurface,</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;                                     K4, *dshape, domain4.lowerBound(), domain4.upperBound() );</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- 4D surface has &quot;</span> &lt;&lt; surface_cells.size() &lt;&lt; <span class="stringliteral">&quot; 3-cells.&quot;</span> &lt;&lt; endl;</div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;  <span class="keyword">typedef</span> <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1SetOfSurfels.html">SetOfSurfels&lt;KSpace4&gt;</a> SurfaceContainer;</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;  SurfaceContainer* ptrF0 = <span class="keyword">new</span> SurfaceContainer( K4, <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1SurfelAdjacency.html">SurfelAdjacency&lt; KSpace4::dimension &gt;</a>( <span class="keyword">false</span> ) );</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;  ptrF0-&gt;surfelSet().insert( surface_cells.begin(), surface_cells.end() );</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1DigitalSurface.html">DigitalSurface&lt;SurfaceContainer&gt;</a> surface( ptrF0 );</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;  std::vector&lt;Cell4&gt; sure_cells;</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;  std::vector&lt;Cell4&gt; unsure_cells;</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;  analyzeSurface( std::back_inserter( sure_cells ), std::back_inserter( unsure_cells ),</div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;                  surface );</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- sure cells   = &quot;</span> &lt;&lt; sure_cells.size() &lt;&lt; endl;</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- unsure cells = &quot;</span> &lt;&lt; unsure_cells.size() &lt;&lt; endl;</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1CubicalCellData.html">CubicalCellData</a> unsure_data( 0 );</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1CubicalCellData.html">CubicalCellData</a> sure_data( CC4::FIXED );</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;  complex4.insertCells( sure_cells.begin(), sure_cells.end(), sure_data );</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;  complex4.insertCells( unsure_cells.begin(), unsure_cells.end(), unsure_data );</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160;  surface_cells.clear();</div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160; </div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;  <span class="comment">//-------------- Get boundary and inner cells  --------------------------------</span></div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Get boundary and inner cells. &quot;</span> );</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  std::vector&lt;Cell4&gt; inner;</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;  std::vector&lt;Cell4&gt; bdry;</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;  complex4.close();</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- K=&quot;</span> &lt;&lt; complex4 &lt;&lt; endl;</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;  functions::filterCellsWithinBounds</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;    ( complex4, K4.uKCoords( K4.lowerCell() ), K4.uKCoords( K4.upperCell() ),</div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;      std::back_inserter( bdry ), std::back_inserter( inner ) );</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- there are &quot;</span> &lt;&lt; inner.size() &lt;&lt; <span class="stringliteral">&quot; inner cells.&quot;</span> &lt;&lt; endl;</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- there are &quot;</span> &lt;&lt; bdry.size() &lt;&lt; <span class="stringliteral">&quot; boundary cells.&quot;</span> &lt;&lt; endl;</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160; </div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;  <span class="comment">//-------------- Compute priority function  -----------------------------------</span></div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Compute priority function. &quot;</span> );</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> d = complex4.dim();</div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;  <span class="keywordflow">for</span> ( <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> i = 0; i &lt;= d; ++i )</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;    {</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;      <span class="keywordflow">for</span> ( CellMapIterator it = complex4.begin( i ), itE = complex4.end( i ); it != itE; ++it )</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;        {</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;          Cell4 cell   = it-&gt;first;</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;          Point4 dp    = K4.uCoords( cell );</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;          RealPoint4 p = dshape-&gt;embed( dp );</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;          Ring v       = (*shape)( p );</div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;          v = <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1functions.html#af95dcf36f806f7fc15626ca6b1c27d22">abs</a>( 1000.0*v );</div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;          <span class="keywordflow">if</span> ( v &gt; 1000000.0 ) v = 1000000.0;</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;          it-&gt;second.data &amp;= ~CC4::VALUE;</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;          it-&gt;second.data |= (<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a27c59126488e9c545120667959d2fc4e">DGtal::uint32_t</a>) floor( v );</div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;          <span class="comment">// std::cout &lt;&lt; &quot; &quot; &lt;&lt; it-&gt;second.data;</span></div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;        }</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;    }</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160; </div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  <span class="comment">//-------------- Collapse boundary -------------------------------------------</span></div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Collapse boundary. &quot;</span> );</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  <span class="keyword">typename</span> CC4::DefaultCellMapIteratorPriority priority;</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  CC4 bdry_complex4( K4 );</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;  <span class="keywordflow">for</span> ( std::vector&lt;Cell4&gt;::const_iterator it = bdry.begin(), itE = bdry.end(); it != itE; ++it )</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;    {</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160;      Cell4 cell = *it;</div>
<div class="line"><a name="l00622"></a><span class="lineno">  622</span>&#160;      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> d = K4.uDim( cell );</div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;      CellMapConstIterator cmIt = complex4.findCell( d, cell );</div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;      bdry_complex4.insertCell( d, cell, cmIt-&gt;second );</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;    }</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;  <span class="comment">//bdry_complex4.insertCells( bdry.begin(), bdry.end() );</span></div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- [before collapse] K_bdry =&quot;</span> &lt;&lt; bdry_complex4 &lt;&lt; endl;</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;  functions::collapse( bdry_complex4, bdry.begin(), bdry.end(), priority, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- [after collapse]  K_bdry =&quot;</span> &lt;&lt; bdry_complex4 &lt;&lt; endl;</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;  <span class="keywordflow">for</span> ( std::vector&lt;Cell4&gt;::const_iterator it = bdry.begin(), itE = bdry.end(); it != itE; ++it )</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;    {</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160;      Cell4 cell  = *it;</div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">Dimension</a> d = K4.uDim( cell );</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;      CellMapConstIterator cmIt = bdry_complex4.findCell( d, cell );</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;      <span class="keywordflow">if</span> ( cmIt != bdry_complex4.end( d ) ) {</div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;        CellMapIterator cmIt2 = complex4.findCell( d, cell );</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;        cmIt2-&gt;second = sure_data;</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;      }</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;    }</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160; </div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;  <span class="comment">//-------------- Collapse all -------------------------------------------</span></div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Collapse all. &quot;</span> );</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;  std::copy( bdry.begin(), bdry.end(), std::back_inserter( inner ) );</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;  <span class="comment">//typename CC4::DefaultCellMapIteratorPriority priority;</span></div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;  functions::collapse( complex4, inner.begin(), inner.end(), priority, <span class="keyword">true</span>, <span class="keyword">true</span>, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#ad054990834d2763627166540087a2980">info</a>() &lt;&lt; <span class="stringliteral">&quot;- K=&quot;</span> &lt;&lt; complex4 &lt;&lt; endl;</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160; </div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;  <span class="comment">//-------------- Project complex onto surface --------------------------------</span></div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Project complex onto surface. &quot;</span> );</div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;  std::vector&lt;RealPoint3&gt; points;</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;  <span class="keywordflow">if</span> ( project == <span class="stringliteral">&quot;Newton&quot;</span> )</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;    projectComplex( points, complex4, *shape, dshape, shape3, epsilon, max_iter );</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;    doNotProjectComplex( points, complex4, *shape, dshape, shape3 );</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160; </div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;  <span class="comment">//-------------- Create Mesh -------------------------------------------</span></div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#a352b7160bf722e2f0bcbee5d0bad6ef3">beginBlock</a>( <span class="stringliteral">&quot;Create Mesh. &quot;</span> );</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160;  <span class="keywordtype">bool</span> highlight = ( view == <span class="stringliteral">&quot;Singular&quot;</span> );</div>
<div class="line"><a name="l00662"></a><span class="lineno">  662</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Mesh.html">Mesh&lt;RealPoint3&gt;</a> mesh( <span class="keyword">true</span> );</div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;  std::map&lt;Cell4,unsigned int&gt; indices;</div>
<div class="line"><a name="l00664"></a><span class="lineno">  664</span>&#160;  <span class="keywordtype">int</span> idx = 0;</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;  <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 0 ), itE = complex4.end( 0 ); it != itE; ++it, ++idx )</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;    {</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;      Cell4 cell = it-&gt;first;</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;      indices[ cell ] = idx;</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;      mesh.addVertex( points[ idx ] );</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;    }</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160;  <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 2 ), itE = complex4.end( 2 ); it != itE; ++it, ++idx )</div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;    {</div>
<div class="line"><a name="l00673"></a><span class="lineno">  673</span>&#160;      Cell4 cell = it-&gt;first;</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;      <span class="keywordtype">bool</span> fixed = it-&gt;second.data &amp; CC4::FIXED;</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;      Cells4 bdry = complex4.cellBoundary( cell, <span class="keyword">true</span> );</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;      std::vector&lt;unsigned int&gt; face_idx;</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;      <span class="keywordflow">for</span> ( Cells4::const_iterator itC = bdry.begin(), itCE = bdry.end(); itC != itCE; ++itC )</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;        {</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;          <span class="keywordflow">if</span> ( complex4.dim( *itC ) == 0 )</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;            face_idx.push_back( indices[ *itC ] );</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;        }</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;      <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Color.html">Color</a> color = highlight</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;        ? ( fixed ? Color::White : <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Color.html">Color</a>(128,255,128)  )</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160;        : Color::White;</div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;      mesh.addQuadFace( face_idx[ 0 ], face_idx[ 1 ], face_idx[ 3 ], face_idx[ 2 ], color );</div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;     }</div>
<div class="line"><a name="l00687"></a><span class="lineno">  687</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">trace</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">endBlock</a>();</div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160; </div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;  <span class="comment">//-------------- View surface -------------------------------------------</span></div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;  QApplication application(argc,argv);</div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;  Point4 low4 = K4.lowerBound();</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;  Point4 up4  = K4.upperBound();</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160;  KSpace3 <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z3i.html#a4b7ee43018f9144683fab486eef6f205">K3</a>;</div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1Z3i.html#a4b7ee43018f9144683fab486eef6f205">K3</a>.<a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#a15dcbcaae831dd1c36090e6336c177d4">init</a>( Point3( low4[ 0 ], low4[ 1 ], low4[ 2 ] ),</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;           Point3( up4 [ 0 ], up4 [ 1 ], up4 [ 2 ] ), <span class="keyword">true</span> );</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;  <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Viewer3D.html">Viewer3D&lt;Space3,KSpace3&gt;</a> viewer( K3 );</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;  viewer.setWindowTitle(<span class="stringliteral">&quot;Implicit surface viewer by 4d extension&quot;</span>);</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;  viewer.show();</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160;  viewer &lt;&lt; mesh;</div>
<div class="line"><a name="l00700"></a><span class="lineno">  700</span>&#160;  viewer.setLineColor( highlight ? Color::Red : <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Color.html">Color</a>( 120, 120, 120 ) );</div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;  <span class="comment">// Drawing lines</span></div>
<div class="line"><a name="l00702"></a><span class="lineno">  702</span>&#160;  <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 1 ), itE = complex4.end( 1 ); it != itE; ++it )</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;    {</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;      Cell4 cell = it-&gt;first;</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;      std::vector&lt;Cell4&gt; dummy;</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;      std::back_insert_iterator&lt; std::vector&lt;Cell4&gt; &gt; outIt1( dummy );</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;      complex4.directCoFaces( outIt1, cell );</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;      <span class="keywordflow">if</span> ( ! dummy.empty() ) <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;      Cells4 <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceboost.html#a9b4917fc7850f916bcbfec9ab2572fe9">vertices</a> = complex4.cellBoundary( cell );</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;      ASSERT( <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceboost.html#a9b4917fc7850f916bcbfec9ab2572fe9">vertices</a>.size() == 2 );</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;      RealPoint3 p1 = points[ indices[ <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceboost.html#a9b4917fc7850f916bcbfec9ab2572fe9">vertices</a>.front() ] ];</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;      RealPoint3 p2 = points[ indices[ <a class="codeRef" href="https://dgtal-team.github.io/doc-nightly/namespaceboost.html#a9b4917fc7850f916bcbfec9ab2572fe9">vertices</a>.back()  ] ];</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;      viewer.addLine( p1, p2, 0.05 );</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160;    }</div>
<div class="line"><a name="l00715"></a><span class="lineno">  715</span>&#160;  viewer &lt;&lt; Viewer3D&lt;Space3,KSpace3&gt;::updateDisplay;</div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;  <span class="keywordflow">return</span> application.exec();</div>
<div class="line"><a name="l00717"></a><span class="lineno">  717</span>&#160;}</div>
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<div class="ttc" id="aclassDGtal_1_1KhalimskySpaceND_html_a1101d4adbc2a87db33afcb42209b6f04"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1KhalimskySpaceND.html#a1101d4adbc2a87db33afcb42209b6f04">DGtal::KhalimskySpaceND::Integer</a></div><div class="ttdeci">TInteger Integer</div></div>
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<div class="ttc" id="aclassDGtal_1_1SurfelAdjacency_html"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1SurfelAdjacency.html">DGtal::SurfelAdjacency</a></div></div>
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<div class="ttc" id="aclassDGtal_1_1Trace_html_afa3a2874289734884107b1ce68ccb93d"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Trace.html#afa3a2874289734884107b1ce68ccb93d">DGtal::Trace::endBlock</a></div><div class="ttdeci">double endBlock()</div></div>
<div class="ttc" id="aclassDGtal_1_1Viewer3D_html"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/classDGtal_1_1Viewer3D.html">DGtal::Viewer3D</a></div></div>
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<div class="ttc" id="anamespaceDGtal_1_1functions_html_af95dcf36f806f7fc15626ca6b1c27d22"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal_1_1functions.html#af95dcf36f806f7fc15626ca6b1c27d22">DGtal::functions::abs</a></div><div class="ttdeci">T abs(const T &amp;a)</div></div>
<div class="ttc" id="anamespaceDGtal_html"><div class="ttname"><a href="namespaceDGtal.html">DGtal</a></div></div>
<div class="ttc" id="anamespaceDGtal_html_a1c09e3f63904ff371f1b99f45069fc63"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a1c09e3f63904ff371f1b99f45069fc63">DGtal::int64_t</a></div><div class="ttdeci">boost::int64_t int64_t</div></div>
<div class="ttc" id="anamespaceDGtal_html_a27c59126488e9c545120667959d2fc4e"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a27c59126488e9c545120667959d2fc4e">DGtal::uint32_t</a></div><div class="ttdeci">boost::uint32_t uint32_t</div></div>
<div class="ttc" id="anamespaceDGtal_html_a604c07ec391ad12a1f3fb6479993f112"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a604c07ec391ad12a1f3fb6479993f112">DGtal::trace</a></div><div class="ttdeci">Trace trace(traceWriterTerm)</div></div>
<div class="ttc" id="anamespaceDGtal_html_a8fbe8c8d47ca5c36ced14284ac62613d"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a8fbe8c8d47ca5c36ced14284ac62613d">DGtal::Dimension</a></div><div class="ttdeci">DGtal::uint32_t Dimension</div></div>
<div class="ttc" id="anamespaceDGtal_html_a9f6cc75dc44e45506a66cd233e0deb41"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41">DGtal::Orientation</a></div><div class="ttdeci">Orientation</div></div>
<div class="ttc" id="anamespaceDGtal_html_a9f6cc75dc44e45506a66cd233e0deb41a528af0eaf947edc94796219523aa9553"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a528af0eaf947edc94796219523aa9553">DGtal::INSIDE</a></div><div class="ttdeci">INSIDE</div></div>
<div class="ttc" id="anamespaceDGtal_html_a9f6cc75dc44e45506a66cd233e0deb41a5f4bdeccc29812b7de1cc0c05b724734"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a5f4bdeccc29812b7de1cc0c05b724734">DGtal::OUTSIDE</a></div><div class="ttdeci">OUTSIDE</div></div>
<div class="ttc" id="anamespaceDGtal_html_a9f6cc75dc44e45506a66cd233e0deb41a7671a5416d92f37137f9999ca23dd65e"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceDGtal.html#a9f6cc75dc44e45506a66cd233e0deb41a7671a5416d92f37137f9999ca23dd65e">DGtal::ON</a></div><div class="ttdeci">ON</div></div>
<div class="ttc" id="anamespaceboost_html_a9b4917fc7850f916bcbfec9ab2572fe9"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/namespaceboost.html#a9b4917fc7850f916bcbfec9ab2572fe9">boost::vertices</a></div><div class="ttdeci">std::pair&lt; typename graph_traits&lt; DGtal::DigitalSurface&lt; TDigitalSurfaceContainer &gt; &gt;::vertex_iterator, typename graph_traits&lt; DGtal::DigitalSurface&lt; TDigitalSurfaceContainer &gt; &gt;::vertex_iterator &gt; vertices(const DGtal::DigitalSurface&lt; TDigitalSurfaceContainer &gt; &amp;digSurf)</div></div>
<div class="ttc" id="astructDGtal_1_1CubicalCellData_html"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1CubicalCellData.html">DGtal::CubicalCellData</a></div></div>
<div class="ttc" id="astructDGtal_1_1KhalimskyCell_html"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1KhalimskyCell.html">KhalimskyCell&lt; dim, Integer &gt;</a></div></div>
<div class="ttc" id="astructDGtal_1_1NumberTraits_html"><div class="ttname"><a href="https://dgtal-team.github.io/doc-nightly/structDGtal_1_1NumberTraits.html">DGtal::NumberTraits</a></div></div>
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