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<div class="headertitle"><div class="title">3dImplicitSurfaceExtractorBy4DExtension.cpp</div></div>
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<div class="contents">
<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="preprocessor">#include <iostream></span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="preprocessor">#include <sstream></span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="preprocessor">#include <map></span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="preprocessor">#include "CLI11.hpp"</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="preprocessor">#include "DGtal/base/Common.h"</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="preprocessor">#include "DGtal/base/CountedPtr.h"</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="preprocessor">#include "DGtal/helpers/StdDefs.h"</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="preprocessor">#include "DGtal/math/MPolynomial.h"</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="preprocessor">#include "DGtal/io/readers/MPolynomialReader.h"</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="preprocessor">#include "DGtal/io/viewers/PolyscopeViewer.h"</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="preprocessor">#include "DGtal/topology/KhalimskySpaceND.h"</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="preprocessor">#include "DGtal/topology/CubicalComplex.h"</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="preprocessor">#include "DGtal/topology/CubicalComplexFunctions.h"</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="preprocessor">#include "DGtal/topology/SetOfSurfels.h"</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor">#include "DGtal/topology/DigitalSurface.h"</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor">#include "DGtal/topology/helpers/Surfaces.h"</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="preprocessor">#include "DGtal/shapes/GaussDigitizer.h"</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="preprocessor">#include "DGtal/shapes/Mesh.h"</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="preprocessor">#include "DGtal/shapes/implicit/ImplicitPolynomial3Shape.h"</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="keyword">using namespace </span>std;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="keyword">using namespace </span><a class="code hl_namespace" href="namespaceDGtal.html">DGtal</a>;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span><span class="keyword">template</span> <<span class="keyword">typename</span> TSpace3, <span class="keyword">typename</span> TSpace4, <span class="keyword">typename</span> TPolynomial3></div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span><span class="keyword">struct </span>ImplicitSurface4DProductExtension {</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="keyword">typedef</span> TSpace3 Space3;</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keyword">typedef</span> TSpace4 Space4;</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="keyword">typedef</span> TPolynomial3 Polynomial3;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealPoint RealPoint3;</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealVector RealVector3;</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::Integer Integer;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> RealPoint3::Coordinate Ring;</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealPoint RealPoint4;</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealVector RealVector4;</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keyword">typedef</span> RealPoint4 RealPoint;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keyword">typedef</span> RealVector4 RealVector;</div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> </div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> ImplicitSurface4DProductExtension( Clone<Polynomial3> poly )</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> : f( poly )</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> {</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> fx = derivative<0>( f );</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> fy = derivative<1>( f );</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> fz = derivative<2>( f );</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> fxx = derivative<0>( fx );</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> fxy = derivative<0>( fy );</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> fxz = derivative<0>( fz );</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> fyy = derivative<1>( fy );</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> fyz = derivative<1>( fz );</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> fzz = derivative<2>( fz );</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> }</div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> </div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> Ring operator()(<span class="keyword">const</span> RealPoint &aPoint)<span class="keyword"> const</span></div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> Ring x = aPoint[ 0 ];</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> Ring y = aPoint[ 1 ];</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> Ring z = aPoint[ 2 ];</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> Ring t = aPoint[ 3 ];</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> RealVector3 grad( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z) );</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keywordflow">return</span> f(x)(y)(z) - t * grad.norm();</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> }</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keywordtype">bool</span> isInside(<span class="keyword">const</span> RealPoint &aPoint)<span class="keyword"> const</span></div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keywordflow">return</span> this->operator()( aPoint ) <= NumberTraits<Ring>::ZERO;</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> }</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> </div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> Orientation orientation(<span class="keyword">const</span> RealPoint &aPoint)<span class="keyword"> const</span></div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> Ring v = this->operator()( aPoint );</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="keywordflow">if</span> ( v > NumberTraits<Ring>::ZERO ) <span class="keywordflow">return</span> OUTSIDE;</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( v < NumberTraits<Ring>::ZERO ) <span class="keywordflow">return</span> INSIDE;</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <span class="keywordflow">else</span> <span class="keywordflow">return</span> ON;</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> }</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> </div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="keyword">inline</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> RealVector gradient( <span class="keyword">const</span> RealPoint &aPoint )<span class="keyword"> const</span></div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> Ring x = aPoint[ 0 ];</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> Ring y = aPoint[ 1 ];</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> Ring z = aPoint[ 2 ];</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> Ring t = aPoint[ 3 ];</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> RealVector3 grad( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z) );</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> Ring ngrad = grad.norm();</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> grad /= ngrad;</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> RealVector d_gradx( fxx(x)(y)(z), fxy(x)(y)(z),fxz(x)(y)(z) );</div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> RealVector d_grady( fxy(x)(y)(z), fyy(x)(y)(z),fyz(x)(y)(z) );</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> RealVector d_gradz( fxz(x)(y)(z), fyz(x)(y)(z),fzz(x)(y)(z) );</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="keywordflow">return</span> RealVector( grad[ 0 ] - t * d_gradx.dot( grad ),</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> grad[ 1 ] - t * d_grady.dot( grad ),</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> grad[ 2 ] - t * d_gradz.dot( grad ),</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> -ngrad );</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> }</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> </div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> Polynomial3 f;</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> Polynomial3 fx;</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> Polynomial3 fy;</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> Polynomial3 fz;</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> Polynomial3 fxx;</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> Polynomial3 fxy;</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> Polynomial3 fxz;</div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> Polynomial3 fyy;</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> Polynomial3 fyz;</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> Polynomial3 fzz;</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span>};</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> </div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span><span class="keyword">template</span> <<span class="keyword">typename</span> TSpace3, <span class="keyword">typename</span> TSpace4, <span class="keyword">typename</span> TPolynomial3></div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span><span class="keyword">struct </span>ImplicitSurface4DExtension {</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> <span class="keyword">typedef</span> TSpace3 Space3;</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keyword">typedef</span> TSpace4 Space4;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="keyword">typedef</span> TPolynomial3 Polynomial3;</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealPoint RealPoint3;</div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::RealVector RealVector3;</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space3::Integer Integer;</div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> RealPoint3::Coordinate Ring;</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealPoint RealPoint4;</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> Space4::RealVector RealVector4;</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> <span class="keyword">typedef</span> RealPoint4 RealPoint;</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <span class="keyword">typedef</span> RealVector4 RealVector;</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> </div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> ImplicitSurface4DExtension( Clone<Polynomial3> poly )</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> : f( poly )</div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> {</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> fx = derivative<0>( f );</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> fy = derivative<1>( f );</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> fz = derivative<2>( f );</div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> fxx = derivative<0>( fx );</div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> fxy = derivative<0>( fy );</div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span> fxz = derivative<0>( fz );</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> fyy = derivative<1>( fy );</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> fyz = derivative<1>( fz );</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> fzz = derivative<2>( fz );</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> }</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> </div>
<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span> Ring operator()(<span class="keyword">const</span> RealPoint &aPoint)<span class="keyword"> const</span></div>
<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span> Ring x = aPoint[ 0 ];</div>
<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span> Ring y = aPoint[ 1 ];</div>
<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> Ring z = aPoint[ 2 ];</div>
<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> Ring t = aPoint[ 3 ];</div>
<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <span class="comment">// RealVector3 grad( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z) );</span></div>
<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> <span class="keywordflow">return</span> f(x)(y)(z) - t;</div>
<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> }</div>
<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span> </div>
<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keywordtype">bool</span> isInside(<span class="keyword">const</span> RealPoint &aPoint)<span class="keyword"> const</span></div>
<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="keywordflow">return</span> this->operator()( aPoint ) <= NumberTraits<Ring>::ZERO;</div>
<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> }</div>
<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> </div>
<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span> Orientation orientation(<span class="keyword">const</span> RealPoint &aPoint)<span class="keyword"> const</span></div>
<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span> Ring v = this->operator()( aPoint );</div>
<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span> <span class="keywordflow">if</span> ( v > NumberTraits<Ring>::ZERO ) <span class="keywordflow">return</span> OUTSIDE;</div>
<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( v < NumberTraits<Ring>::ZERO ) <span class="keywordflow">return</span> INSIDE;</div>
<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span> <span class="keywordflow">else</span> <span class="keywordflow">return</span> ON;</div>
<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span> }</div>
<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> </div>
<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span> <span class="keyword">inline</span></div>
<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span> RealVector gradient( <span class="keyword">const</span> RealPoint &aPoint )<span class="keyword"> const</span></div>
<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span><span class="keyword"> </span>{</div>
<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span> Ring x = aPoint[ 0 ];</div>
<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span> Ring y = aPoint[ 1 ];</div>
<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span> Ring z = aPoint[ 2 ];</div>
<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span> Ring t = aPoint[ 3 ];</div>
<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span> <span class="keywordflow">return</span> RealVector( fx(x)(y)(z), fy(x)(y)(z), fz(x)(y)(z), -1.0 );</div>
<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span> }</div>
<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span> </div>
<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span><span class="keyword">private</span>:</div>
<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span> Polynomial3 f;</div>
<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> Polynomial3 fx;</div>
<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> Polynomial3 fy;</div>
<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> Polynomial3 fz;</div>
<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> Polynomial3 fxx;</div>
<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> Polynomial3 fxy;</div>
<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> Polynomial3 fxz;</div>
<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> Polynomial3 fyy;</div>
<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> Polynomial3 fyz;</div>
<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> Polynomial3 fzz;</div>
<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span>};</div>
<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> </div>
<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> </div>
<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span><span class="keyword">template</span> <<span class="keyword">typename</span> CellOutputIterator, <span class="keyword">typename</span> DigitalSurface></div>
<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span><span class="keywordtype">void</span></div>
<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span>analyzeSurface( CellOutputIterator itSure, CellOutputIterator itUnsure, </div>
<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> DigitalSurface surface )</div>
<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span>{</div>
<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> DigitalSurface::KSpace KSpace;</div>
<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> DigitalSurface::Surfel Surfel;</div>
<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> DigitalSurface::ConstIterator ConstIterator;</div>
<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> DigitalSurface::DigitalSurfaceContainer Container;</div>
<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> DigitalSurface::DigitalSurfaceTracker Tracker;</div>
<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> KSpace::Integer Integer;</div>
<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> KSpace::Cell Cell;</div>
<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> <span class="keyword">const</span> Dimension t = KSpace::dimension - 1;</div>
<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> <span class="keyword">const</span> Container& C = surface.container();</div>
<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span> <span class="keyword">const</span> KSpace& K = surface.container().space();</div>
<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> Surfel s2;</div>
<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span> <span class="keywordflow">for</span> ( ConstIterator it = surface.begin(), itE = surface.end(); it != itE; ++it )</div>
<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> {</div>
<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> Surfel s = *it;</div>
<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> Cell is = K.unsigns( s );</div>
<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> Integer s_xt = K.sKCoord( s, t );</div>
<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <span class="keywordflow">if</span> ( s_xt == 0 ) *itUnsure++ = is;</div>
<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( s_xt == -1 ) </div>
<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> {</div>
<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> CountedPtr<Tracker> tracker( C.newTracker( s ) );</div>
<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> <span class="keywordflow">if</span> ( tracker->adjacent( s2, t, <span class="keyword">true</span> ) != 0 )</div>
<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> {</div>
<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> Integer s2_xt = K.sKCoord( s2, t );</div>
<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> Cell ic = K.uIncident( is, t, <span class="keyword">true</span> ); </div>
<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <span class="keywordflow">if</span> ( s2_xt > 0 ) *itSure++ = ic;</div>
<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <span class="keywordflow">else</span> *itUnsure++ = ic;</div>
<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> }</div>
<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> }</div>
<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( s_xt == 1 )</div>
<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> {</div>
<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> CountedPtr<Tracker> tracker( C.newTracker( s ) );</div>
<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="keywordflow">if</span> ( tracker->adjacent( s2, t, <span class="keyword">false</span> ) != 0 )</div>
<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span> {</div>
<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> Integer s2_xt = K.sKCoord( s2, t );</div>
<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span> Cell ic = K.uIncident( is, t, <span class="keyword">false</span> ); </div>
<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> <span class="keywordflow">if</span> ( s2_xt < 0 ) *itSure++ = ic;</div>
<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="keywordflow">else</span> *itUnsure++ = ic;</div>
<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> }</div>
<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> }</div>
<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> <span class="keywordflow">else</span> cout << <span class="stringliteral">" "</span> << s_xt;</div>
<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> }</div>
<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span>}</div>
<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> </div>
<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span><span class="keyword">template</span> <<span class="keyword">typename</span> ImplicitSurface, <span class="keyword">typename</span> RealPo<span class="keywordtype">int</span>></div>
<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span>RealPoint projectNewton( <span class="keyword">const</span> ImplicitSurface & is, </div>
<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> RealPoint x, </div>
<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> <span class="keyword">typename</span> RealPoint::Coordinate epsilon,</div>
<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> max_iter )</div>
<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span>{</div>
<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> RealPoint::Coordinate Scalar;</div>
<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> RealPoint gx;</div>
<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> Scalar f, g2;</div>
<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> Scalar eps2 = epsilon * epsilon;</div>
<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> <span class="keywordflow">while</span> ( max_iter-- != 0 )</div>
<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> {</div>
<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> f = is( x );</div>
<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> <span class="keywordflow">if</span> ( abs( f ) < epsilon ) <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> gx = is.gradient( x );</div>
<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> g2 = gx.dot( gx );</div>
<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="keywordflow">if</span> ( g2 < eps2 ) <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> x -= (f/g2) * gx;</div>
<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> }</div>
<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span>}</div>
<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> </div>
<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> </div>
<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span><span class="keyword">template</span> <<span class="keyword">typename</span> CubicalComplex4, <span class="keyword">typename</span> ImplicitShape4, </div>
<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="keyword">typename</span> ImplicitDigitalShape4, <span class="keyword">typename</span> ImplicitShape3></div>
<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span><span class="keywordtype">void</span> projectComplex( std::vector< typename ImplicitShape3::RealPoint >& points,</div>
<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="keyword">const</span> CubicalComplex4& complex4,</div>
<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> <span class="keyword">const</span> ImplicitShape4& shape,</div>
<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> <span class="keyword">const</span> ImplicitDigitalShape4& dshape,</div>
<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> <span class="keyword">const</span> ImplicitShape3& shape3,</div>
<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> <span class="keywordtype">double</span> epsilon,</div>
<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> max_iter )</div>
<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span>{</div>
<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Cell Cell4;</div>
<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Point Point4;</div>
<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::CellMapConstIterator CellMapConstIterator;</div>
<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::RealPoint RealPoint4;</div>
<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::Ring Ring;</div>
<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape3::RealPoint RealPoint3;</div>
<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> points.clear();</div>
<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 0 ), itE = complex4.end( 0 ); it != itE; ++it )</div>
<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> {</div>
<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> Cell4 cell = it->first;</div>
<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> Point4 dp = complex4.space().uCoords( cell );</div>
<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span> RealPoint4 p = dshape->embed( dp );</div>
<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> RealPoint3 p3 = RealPoint3( p[ 0 ], p[ 1 ], p[ 2 ] );</div>
<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span> RealPoint3 q = projectNewton( shape3, p3, epsilon, max_iter );</div>
<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> points.push_back( q );</div>
<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> }</div>
<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span>}</div>
<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> </div>
<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span><span class="keyword">template</span> <<span class="keyword">typename</span> CubicalComplex4, <span class="keyword">typename</span> ImplicitShape4, </div>
<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="keyword">typename</span> ImplicitDigitalShape4, <span class="keyword">typename</span> ImplicitShape3></div>
<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span><span class="keywordtype">void</span> doNotProjectComplex( std::vector< typename ImplicitShape3::RealPoint >& points,</div>
<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <span class="keyword">const</span> CubicalComplex4& complex4,</div>
<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> <span class="keyword">const</span> ImplicitShape4& shape,</div>
<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> <span class="keyword">const</span> ImplicitDigitalShape4& dshape,</div>
<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> <span class="keyword">const</span> ImplicitShape3& shape3 )</div>
<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span>{</div>
<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Cell Cell4;</div>
<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::Point Point4;</div>
<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> CubicalComplex4::CellMapConstIterator CellMapConstIterator;</div>
<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::RealPoint RealPoint4;</div>
<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape4::Ring Ring;</div>
<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> ImplicitShape3::RealPoint RealPoint3;</div>
<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 0 ), itE = complex4.end( 0 ); it != itE; ++it )</div>
<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> {</div>
<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> Cell4 cell = it->first;</div>
<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> Point4 dp = complex4.space().uCoords( cell );</div>
<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> RealPoint4 p = dshape->embed( dp );</div>
<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> RealPoint3 p3 = RealPoint3( p[ 0 ], p[ 1 ], p[ 2 ] );</div>
<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> points.push_back( p3 );</div>
<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> }</div>
<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span>}</div>
<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> </div>
<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> </div>
<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span><span class="keywordtype">int</span> main( <span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv )</div>
<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span>{</div>
<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> <span class="keyword">typedef</span> <span class="keywordtype">int</span> Integer;</div>
<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="keyword">typedef</span> SpaceND<3,Integer> Space3;</div>
<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> <span class="keyword">typedef</span> KhalimskySpaceND<3,Integer> KSpace3;</div>
<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> <span class="keyword">typedef</span> KSpace3::Cell Cell3;</div>
<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <span class="keyword">typedef</span> std::map<Cell3, CubicalCellData> Map3;</div>
<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> <span class="keyword">typedef</span> CubicalComplex< KSpace3, Map3 > CC3;</div>
<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <span class="keyword">typedef</span> Space3::Point Point3;</div>
<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> <span class="keyword">typedef</span> Space3::RealPoint RealPoint3;</div>
<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> <span class="keyword">typedef</span> RealPoint3::Coordinate Ring;</div>
<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> <span class="keyword">typedef</span> Ring Scalar;</div>
<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> <span class="keyword">typedef</span> MPolynomial<3, Ring> Polynomial3;</div>
<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> <span class="keyword">typedef</span> MPolynomialReader<3, Ring> Polynomial3Reader;</div>
<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <span class="keyword">typedef</span> ImplicitPolynomial3Shape<Space3> ImplicitShape3;</div>
<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> <span class="keyword">typedef</span> SpaceND<4,Integer> Space4;</div>
<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> <span class="keyword">typedef</span> KhalimskySpaceND<4,Integer> KSpace4;</div>
<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> <span class="keyword">typedef</span> KSpace4::Cell Cell4;</div>
<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> <span class="keyword">typedef</span> KSpace4::Cells Cells4;</div>
<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> <span class="keyword">typedef</span> KSpace4::SCell SCell4;</div>
<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> <span class="keyword">typedef</span> Space4::Point Point4;</div>
<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> <span class="keyword">typedef</span> Space4::RealPoint RealPoint4;</div>
<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> <span class="keyword">typedef</span> Space4::RealVector RealVector4;</div>
<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> <span class="keyword">typedef</span> ImplicitSurface4DProductExtension<Space3,Space4,Polynomial3></div>
<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span> ImplicitShape4;</div>
<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> <span class="keyword">typedef</span> GaussDigitizer< Space4, ImplicitShape4 > </div>
<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span> ImplicitDigitalShape4;</div>
<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span> <span class="keyword">typedef</span> ImplicitDigitalShape4::Domain Domain4;</div>
<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span> <span class="keyword">typedef</span> std::map<Cell4, CubicalCellData> Map4;</div>
<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span> <span class="keyword">typedef</span> CubicalComplex< KSpace4, Map4 > CC4;</div>
<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span> <span class="keyword">typedef</span> CC4::CellMapIterator CellMapIterator;</div>
<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span> <span class="keyword">typedef</span> CC4::CellMapConstIterator CellMapConstIterator;</div>
<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span> <span class="keyword">typedef</span> CC4::Cells Cells4;</div>
<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span> </div>
<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span> </div>
<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span> <span class="comment">// parse command line using CLI ----------------------------------------------</span></div>
<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span> CLI::App app;</div>
<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span> <span class="keywordtype">string</span> poly_str;</div>
<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span> std::string outputFileName {<span class="stringliteral">"result.raw"</span>};</div>
<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span> DGtal::int64_t rescaleInputMin {0};</div>
<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span> DGtal::int64_t rescaleInputMax {255};</div>
<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span> Ring min_x {-10.0};</div>
<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> Ring max_x {10.0};</div>
<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> Ring h {1.0};</div>
<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> Ring t {0.000001};</div>
<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> </div>
<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> std::string project {<span class="stringliteral">"Newton"</span>};</div>
<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> <span class="keywordtype">double</span> epsilon {1e-6};</div>
<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> max_iter {500};</div>
<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> std::string view {<span class="stringliteral">"Normal"</span>};</div>
<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> app.description( <span class="stringliteral">"Computes the zero level set of the given polynomial. Usage: 3dImplicitSurfaceExtractorBy4DExtension -p <polynomial> [options]\n Example:\n 3dImplicitSurfaceExtractorBy4DExtension -p \"-0.9*(y^2+z^2-1)^2-(x^2+y^2-1)^3\" -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 \"((y^2+z^2-1)^2-(x^2+y^2-1)^3)*(y*(x-1)^2-z*(x+1))^2\" -g 0.025 -e 1e-6 -n 50000 -v Singular -t 0.5 -P Newton \n 3dImplicitSurfaceExtractorBy4DExtension -a -2 -A 2 -p \"(x^5-4*z^3*y^2)*((x+y)^2-(z-x)^3)\" -g 0.025 -e 1e-6 -n 50000 -v Singular -t 0.05 -P Newton "</span>);</div>
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> app.add_option(<span class="stringliteral">"-p,--polynomial,1"</span>, poly_str, <span class="stringliteral">"the implicit polynomial whose zero-level defines the shape of interest."</span> )</div>
<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> ->required();</div>
<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> app.add_option(<span class="stringliteral">"--minAABB,-a"</span>,min_x, <span class="stringliteral">"the min value of the AABB bounding box (domain)"</span> );</div>
<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> app.add_option(<span class="stringliteral">"--maxAABB,-A"</span>,max_x, <span class="stringliteral">"the max value of the AABB bounding box (domain)"</span> );</div>
<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> app.add_option(<span class="stringliteral">"--gridstep,-g"</span>, h, <span class="stringliteral">"the gridstep that defines the digitization in the 4th dimension (small is generally a good idea, default is 1e-6). "</span>);</div>
<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> app.add_option(<span class="stringliteral">"--timestep,-t"</span>,t, <span class="stringliteral">"the thickening parameter for the implicit surface."</span> );</div>
<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> app.add_option(<span class="stringliteral">"--project,-P"</span>, project, <span class="stringliteral">"defines the projection: either No or Newton."</span>)</div>
<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> -> check(CLI::IsMember({<span class="stringliteral">"No"</span>, <span class="stringliteral">"Newton"</span>}));</div>
<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> app.add_option(<span class="stringliteral">"--epsilon,-e"</span>, epsilon, <span class="stringliteral">"the maximum precision relative to the implicit surface in the Newton approximation of F=0."</span>);</div>
<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> app.add_option(<span class="stringliteral">"--max_iter,-n"</span>, max_iter, <span class="stringliteral">"the maximum number of iteration in the Newton approximation of F=0."</span>);</div>
<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> app.add_option(<span class="stringliteral">"--view,-v"</span>, view, <span class="stringliteral">"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)."</span>)</div>
<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> -> check(CLI::IsMember({<span class="stringliteral">"Singular"</span>, <span class="stringliteral">"Normal"</span>, <span class="stringliteral">"Hide"</span>}));</div>
<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> </div>
<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> app.get_formatter()->column_width(40);</div>
<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> CLI11_PARSE(app, argc, argv);</div>
<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> <span class="comment">// END parse command line using CLI ----------------------------------------------</span></div>
<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> </div>
<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> </div>
<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> <span class="comment">//-------------- read polynomial and creating 4d implicit fct -----------------</span></div>
<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> trace.beginBlock( <span class="stringliteral">"Reading polynomial and creating 4D implicit function"</span> );</div>
<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> Polynomial3 poly;</div>
<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> Polynomial3Reader reader;</div>
<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> string::const_iterator iter = reader.read( poly, poly_str.begin(), poly_str.end() );</div>
<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span> <span class="keywordflow">if</span> ( iter != poly_str.end() )</div>
<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> {</div>
<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span> trace.error() << <span class="stringliteral">"ERROR reading polynomial: I read only <"</span> << poly_str.substr( 0, iter - poly_str.begin() )</div>
<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span> << <span class="stringliteral">">, and I built P="</span> << poly << std::endl;</div>
<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span> <span class="keywordflow">return</span> 2;</div>
<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span> }</div>
<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span> <span class="comment">// Creating implicit shape and storing it with smart pointer for automatic deallocation.</span></div>
<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span> ImplicitShape3 shape3( poly );</div>
<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span> CountedPtr<ImplicitShape4> shape( <span class="keyword">new</span> ImplicitShape4( poly ) ); </div>
<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span> </div>
<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span> </div>
<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span> RealPoint4 p1( min_x, min_x, min_x, -t*h );</div>
<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span> RealPoint4 p2( max_x, max_x, max_x, 0 );</div>
<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span> <span class="comment">// Creating digitized shape and storing it with smart pointer for automatic deallocation.</span></div>
<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span> CountedPtr<ImplicitDigitalShape4> dshape( <span class="keyword">new</span> ImplicitDigitalShape4() );</div>
<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span> dshape->attach( *shape );</div>
<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span> dshape->init( p1, p2, RealVector4( h, h, h, t ) );</div>
<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span> Domain4 domain4 = dshape->getDomain();</div>
<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span> KSpace4 K4;</div>
<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> K4.init( domain4.lowerBound(), domain4.upperBound(), <span class="keyword">true</span> );</div>
<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> trace.info() << <span class="stringliteral">"- domain is "</span> << domain4 << std::endl;</div>
<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> trace.endBlock();</div>
<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> </div>
<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> <span class="comment">//-------------- read polynomial and creating 4d implicit fct -----------------</span></div>
<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> trace.beginBlock( <span class="stringliteral">"Extracting isosurface 0 of 4D polynomial. "</span> );</div>
<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> CC4 complex4( K4 );</div>
<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> std::vector<SCell4> surface_cells;</div>
<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> std::back_insert_iterator< std::vector<SCell4> > outItSurface( surface_cells );</div>
<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> Surfaces<KSpace4>::sWriteBoundary( outItSurface,</div>
<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span> K4, *dshape, domain4.lowerBound(), domain4.upperBound() );</div>
<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> trace.info() << <span class="stringliteral">"- 4D surface has "</span> << surface_cells.size() << <span class="stringliteral">" 3-cells."</span> << endl;</div>
<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> <span class="keyword">typedef</span> SetOfSurfels<KSpace4> SurfaceContainer;</div>
<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> SurfaceContainer* ptrF0 = <span class="keyword">new</span> SurfaceContainer( K4, SurfelAdjacency< KSpace4::dimension >( <span class="keyword">false</span> ) );</div>
<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> ptrF0->surfelSet().insert( surface_cells.begin(), surface_cells.end() );</div>
<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> DigitalSurface<SurfaceContainer> surface( ptrF0 );</div>
<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> std::vector<Cell4> sure_cells;</div>
<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> std::vector<Cell4> unsure_cells;</div>
<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> analyzeSurface( std::back_inserter( sure_cells ), std::back_inserter( unsure_cells ),</div>
<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> surface );</div>
<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> trace.info() << <span class="stringliteral">"- sure cells = "</span> << sure_cells.size() << endl;</div>
<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> trace.info() << <span class="stringliteral">"- unsure cells = "</span> << unsure_cells.size() << endl;</div>
<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> CubicalCellData unsure_data( 0 );</div>
<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> CubicalCellData sure_data( CC4::FIXED );</div>
<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> complex4.insertCells( sure_cells.begin(), sure_cells.end(), sure_data );</div>
<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> complex4.insertCells( unsure_cells.begin(), unsure_cells.end(), unsure_data );</div>
<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> surface_cells.clear();</div>
<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> trace.endBlock();</div>
<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span> </div>
<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> <span class="comment">//-------------- Get boundary and inner cells --------------------------------</span></div>
<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span> trace.beginBlock( <span class="stringliteral">"Get boundary and inner cells. "</span> );</div>
<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> std::vector<Cell4> inner;</div>
<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> std::vector<Cell4> bdry;</div>
<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> complex4.close();</div>
<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> trace.info() << <span class="stringliteral">"- K="</span> << complex4 << endl;</div>
<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> functions::filterCellsWithinBounds</div>
<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> ( complex4, K4.uKCoords( K4.lowerCell() ), K4.uKCoords( K4.upperCell() ),</div>
<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> std::back_inserter( bdry ), std::back_inserter( inner ) );</div>
<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> trace.info() << <span class="stringliteral">"- there are "</span> << inner.size() << <span class="stringliteral">" inner cells."</span> << endl;</div>
<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> trace.info() << <span class="stringliteral">"- there are "</span> << bdry.size() << <span class="stringliteral">" boundary cells."</span> << endl;</div>
<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> trace.endBlock();</div>
<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> </div>
<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> <span class="comment">//-------------- Compute priority function -----------------------------------</span></div>
<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> trace.beginBlock( <span class="stringliteral">"Compute priority function. "</span> );</div>
<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> Dimension d = complex4.dim();</div>
<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> <span class="keywordflow">for</span> ( Dimension i = 0; i <= d; ++i )</div>
<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> {</div>
<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> <span class="keywordflow">for</span> ( CellMapIterator it = complex4.begin( i ), itE = complex4.end( i ); it != itE; ++it )</div>
<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> {</div>
<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> Cell4 cell = it->first;</div>
<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> Point4 dp = K4.uCoords( cell );</div>
<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> RealPoint4 p = dshape->embed( dp );</div>
<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> Ring v = (*shape)( p );</div>
<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> v = abs( 1000.0*v );</div>
<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span> <span class="keywordflow">if</span> ( v > 1000000.0 ) v = 1000000.0;</div>
<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> it->second.data &= ~CC4::VALUE;</div>
<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span> it->second.data |= (DGtal::uint32_t) floor( v );</div>
<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> <span class="comment">// std::cout << " " << it->second.data;</span></div>
<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span> }</div>
<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span> }</div>
<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span> trace.endBlock();</div>
<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> </div>
<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> <span class="comment">//-------------- Collapse boundary -------------------------------------------</span></div>
<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> trace.beginBlock( <span class="stringliteral">"Collapse boundary. "</span> );</div>
<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> <span class="keyword">typename</span> CC4::DefaultCellMapIteratorPriority priority;</div>
<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> CC4 bdry_complex4( K4 );</div>
<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> <span class="keywordflow">for</span> ( std::vector<Cell4>::const_iterator it = bdry.begin(), itE = bdry.end(); it != itE; ++it )</div>
<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> {</div>
<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> Cell4 cell = *it;</div>
<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> Dimension d = K4.uDim( cell );</div>
<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> CellMapConstIterator cmIt = complex4.findCell( d, cell );</div>
<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> bdry_complex4.insertCell( d, cell, cmIt->second );</div>
<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span> }</div>
<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> <span class="comment">//bdry_complex4.insertCells( bdry.begin(), bdry.end() );</span></div>
<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> trace.info() << <span class="stringliteral">"- [before collapse] K_bdry ="</span> << bdry_complex4 << endl;</div>
<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> 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 id="l00630" name="l00630"></a><span class="lineno"> 630</span> trace.info() << <span class="stringliteral">"- [after collapse] K_bdry ="</span> << bdry_complex4 << endl;</div>
<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> <span class="keywordflow">for</span> ( std::vector<Cell4>::const_iterator it = bdry.begin(), itE = bdry.end(); it != itE; ++it )</div>
<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span> {</div>
<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> Cell4 cell = *it;</div>
<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> Dimension d = K4.uDim( cell );</div>
<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span> CellMapConstIterator cmIt = bdry_complex4.findCell( d, cell );</div>
<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> <span class="keywordflow">if</span> ( cmIt != bdry_complex4.end( d ) ) {</div>
<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> CellMapIterator cmIt2 = complex4.findCell( d, cell );</div>
<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> cmIt2->second = sure_data;</div>
<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> }</div>
<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> }</div>
<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> trace.endBlock();</div>
<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span> </div>
<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> <span class="comment">//-------------- Collapse all -------------------------------------------</span></div>
<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> trace.beginBlock( <span class="stringliteral">"Collapse all. "</span> );</div>
<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> std::copy( bdry.begin(), bdry.end(), std::back_inserter( inner ) );</div>
<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> <span class="comment">//typename CC4::DefaultCellMapIteratorPriority priority;</span></div>
<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span> 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 id="l00648" name="l00648"></a><span class="lineno"> 648</span> trace.info() << <span class="stringliteral">"- K="</span> << complex4 << endl;</div>
<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span> trace.endBlock();</div>
<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span> </div>
<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span> <span class="comment">//-------------- Project complex onto surface --------------------------------</span></div>
<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span> trace.beginBlock( <span class="stringliteral">"Project complex onto surface. "</span> );</div>
<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> std::vector<RealPoint3> points;</div>
<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span> <span class="keywordflow">if</span> ( project == <span class="stringliteral">"Newton"</span> )</div>
<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> projectComplex( points, complex4, *shape, dshape, shape3, epsilon, max_iter );</div>
<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> <span class="keywordflow">else</span></div>
<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> doNotProjectComplex( points, complex4, *shape, dshape, shape3 );</div>
<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span> trace.endBlock();</div>
<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> </div>
<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> <span class="comment">//-------------- Create Mesh -------------------------------------------</span></div>
<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> trace.beginBlock( <span class="stringliteral">"Create Mesh. "</span> );</div>
<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> <span class="keywordtype">bool</span> highlight = ( view == <span class="stringliteral">"Singular"</span> );</div>
<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> Mesh<RealPoint3> mesh( <span class="keyword">true</span> );</div>
<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> std::map<Cell4,unsigned int> indices;</div>
<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> <span class="keywordtype">int</span> idx = 0;</div>
<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 0 ), itE = complex4.end( 0 ); it != itE; ++it, ++idx )</div>
<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> {</div>
<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span> Cell4 cell = it->first;</div>
<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span> indices[ cell ] = idx;</div>
<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> mesh.addVertex( points[ idx ] );</div>
<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"> 671</span> }</div>
<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 2 ), itE = complex4.end( 2 ); it != itE; ++it, ++idx )</div>
<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> {</div>
<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> Cell4 cell = it->first;</div>
<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> <span class="keywordtype">bool</span> fixed = it->second.data & CC4::FIXED;</div>
<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> Cells4 bdry = complex4.cellBoundary( cell, <span class="keyword">true</span> );</div>
<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> std::vector<unsigned int> face_idx;</div>
<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span> <span class="keywordflow">for</span> ( Cells4::const_iterator itC = bdry.begin(), itCE = bdry.end(); itC != itCE; ++itC )</div>
<div class="line"><a id="l00679" name="l00679"></a><span class="lineno"> 679</span> {</div>
<div class="line"><a id="l00680" name="l00680"></a><span class="lineno"> 680</span> <span class="keywordflow">if</span> ( complex4.dim( *itC ) == 0 )</div>
<div class="line"><a id="l00681" name="l00681"></a><span class="lineno"> 681</span> face_idx.push_back( indices[ *itC ] );</div>
<div class="line"><a id="l00682" name="l00682"></a><span class="lineno"> 682</span> }</div>
<div class="line"><a id="l00683" name="l00683"></a><span class="lineno"> 683</span> Color color = highlight</div>
<div class="line"><a id="l00684" name="l00684"></a><span class="lineno"> 684</span> ? ( fixed ? Color::White : Color(128,255,128) )</div>
<div class="line"><a id="l00685" name="l00685"></a><span class="lineno"> 685</span> : Color::White;</div>
<div class="line"><a id="l00686" name="l00686"></a><span class="lineno"> 686</span> mesh.addQuadFace( face_idx[ 0 ], face_idx[ 1 ], face_idx[ 3 ], face_idx[ 2 ], color );</div>
<div class="line"><a id="l00687" name="l00687"></a><span class="lineno"> 687</span> }</div>
<div class="line"><a id="l00688" name="l00688"></a><span class="lineno"> 688</span> trace.endBlock();</div>
<div class="line"><a id="l00689" name="l00689"></a><span class="lineno"> 689</span> </div>
<div class="line"><a id="l00690" name="l00690"></a><span class="lineno"> 690</span> <span class="comment">//-------------- View surface -------------------------------------------</span></div>
<div class="line"><a id="l00691" name="l00691"></a><span class="lineno"> 691</span> Point4 low4 = K4.lowerBound();</div>
<div class="line"><a id="l00692" name="l00692"></a><span class="lineno"> 692</span> Point4 up4 = K4.upperBound();</div>
<div class="line"><a id="l00693" name="l00693"></a><span class="lineno"> 693</span> KSpace3 K3;</div>
<div class="line"><a id="l00694" name="l00694"></a><span class="lineno"> 694</span> K3.init( Point3( low4[ 0 ], low4[ 1 ], low4[ 2 ] ),</div>
<div class="line"><a id="l00695" name="l00695"></a><span class="lineno"> 695</span> Point3( up4 [ 0 ], up4 [ 1 ], up4 [ 2 ] ), <span class="keyword">true</span> );</div>
<div class="line"><a id="l00696" name="l00696"></a><span class="lineno"> 696</span> stringstream s;</div>
<div class="line"><a id="l00697" name="l00697"></a><span class="lineno"> 697</span> s << <span class="stringliteral">"3dImplicitSurfaceExtractorBy4DExtension - DGtalTools"</span>;</div>
<div class="line"><a id="l00698" name="l00698"></a><span class="lineno"> 698</span> </div>
<div class="line"><a id="l00699" name="l00699"></a><span class="lineno"> 699</span> polyscope::options::programName = s.str();</div>
<div class="line"><a id="l00700" name="l00700"></a><span class="lineno"> 700</span> polyscope::view::setNavigateStyle(polyscope::NavigateStyle::Free);</div>
<div class="line"><a id="l00701" name="l00701"></a><span class="lineno"> 701</span> </div>
<div class="line"><a id="l00702" name="l00702"></a><span class="lineno"> 702</span> PolyscopeViewer<Space3,KSpace3> viewer( K3 );</div>
<div class="line"><a id="l00703" name="l00703"></a><span class="lineno"> 703</span> viewer << mesh;</div>
<div class="line"><a id="l00704" name="l00704"></a><span class="lineno"> 704</span> viewer.drawColor( highlight ? Color::Red : Color( 120, 120, 120 ) );</div>
<div class="line"><a id="l00705" name="l00705"></a><span class="lineno"> 705</span> <span class="comment">// Drawing lines</span></div>
<div class="line"><a id="l00706" name="l00706"></a><span class="lineno"> 706</span> <span class="keywordflow">for</span> ( CellMapConstIterator it = complex4.begin( 1 ), itE = complex4.end( 1 ); it != itE; ++it )</div>
<div class="line"><a id="l00707" name="l00707"></a><span class="lineno"> 707</span> {</div>
<div class="line"><a id="l00708" name="l00708"></a><span class="lineno"> 708</span> Cell4 cell = it->first;</div>
<div class="line"><a id="l00709" name="l00709"></a><span class="lineno"> 709</span> std::vector<Cell4> dummy;</div>
<div class="line"><a id="l00710" name="l00710"></a><span class="lineno"> 710</span> std::back_insert_iterator< std::vector<Cell4> > outIt1( dummy );</div>
<div class="line"><a id="l00711" name="l00711"></a><span class="lineno"> 711</span> complex4.directCoFaces( outIt1, cell );</div>
<div class="line"><a id="l00712" name="l00712"></a><span class="lineno"> 712</span> <span class="keywordflow">if</span> ( ! dummy.empty() ) <span class="keywordflow">continue</span>;</div>
<div class="line"><a id="l00713" name="l00713"></a><span class="lineno"> 713</span> Cells4 vertices = complex4.cellBoundary( cell );</div>
<div class="line"><a id="l00714" name="l00714"></a><span class="lineno"> 714</span> ASSERT( vertices.size() == 2 );</div>
<div class="line"><a id="l00715" name="l00715"></a><span class="lineno"> 715</span> RealPoint3 p1 = points[ indices[ vertices.front() ] ];</div>
<div class="line"><a id="l00716" name="l00716"></a><span class="lineno"> 716</span> RealPoint3 p2 = points[ indices[ vertices.back() ] ];</div>
<div class="line"><a id="l00717" name="l00717"></a><span class="lineno"> 717</span> viewer.drawLine( p1, p2 );</div>
<div class="line"><a id="l00718" name="l00718"></a><span class="lineno"> 718</span> } </div>
<div class="line"><a id="l00719" name="l00719"></a><span class="lineno"> 719</span> viewer.show();</div>
<div class="line"><a id="l00720" name="l00720"></a><span class="lineno"> 720</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00721" name="l00721"></a><span class="lineno"> 721</span>}</div>
<div class="ttc" id="anamespaceDGtal_html"><div class="ttname"><a href="namespaceDGtal.html">DGtal</a></div><div class="ttdef"><b>Definition</b> <a href="ATu0v1_8h_source.html#l00056">ATu0v1.h:57</a></div></div>
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