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<div class="title">AtlasChart.cpp</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*********************************************************************</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">* Software License Agreement (BSD License)</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">*</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">* Copyright (c) 2014, Rice University</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">* All rights reserved.</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">*</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">* Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">* modification, are permitted provided that the following conditions</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">* are met:</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">*</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">* * Redistributions of source code must retain the above copyright</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">* notice, this list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="comment">* * Redistributions in binary form must reproduce the above</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">* copyright notice, this list of conditions and the following</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">* disclaimer in the documentation and/or other materials provided</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="comment">* with the distribution.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment">* * Neither the name of the Rice University nor the names of its</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment">* contributors may be used to endorse or promote products derived</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="comment">* from this software without specific prior written permission.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="comment">*</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="comment">* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="comment">* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="comment">* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="comment">* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="comment">* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="comment">* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="comment">* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="comment">* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="comment">* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="comment">* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> <span class="comment">* POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="comment">*********************************************************************/</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span> <span class="comment">/* Author: Caleb Voss */</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="preprocessor">#include "ompl/base/spaces/constraint/AtlasChart.h"</span></div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="preprocessor">#include <boost/math/constants/constants.hpp></span></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="preprocessor">#include <Eigen/Dense></span></div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> ompl::base::AtlasChart::Halfspace::Halfspace(<span class="keyword">const</span> AtlasChart *owner, <span class="keyword">const</span> AtlasChart *neighbor) : owner_(owner)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span> {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="comment">// Project neighbor's chart center onto our chart.</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  Eigen::VectorXd u(owner_->k_);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  owner_->psiInverse(*neighbor->getOrigin(), u);</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  </div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="comment">// Compute the halfspace equation, which is the perpendicular bisector</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">// between 0 and u (plus 5% to reduce cracks, see Jaillet et al.).</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  setU(1.05 * u);</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">bool</span> ompl::base::AtlasChart::Halfspace::contains(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &v)<span class="keyword"> const</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="keywordflow">return</span> v.dot(u_) <= rhs_;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> }</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> <span class="keywordtype">void</span> ompl::base::AtlasChart::Halfspace::checkNear(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &v)<span class="keyword"> const</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// Threshold is 10% of the distance from the boundary to the origin.</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">if</span> (distanceToPoint(v) < 1.0 / 20)</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  Eigen::VectorXd x(owner_->n_);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  owner_->psi(v, x);</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  complement_->expandToInclude(x);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  }</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  </div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">bool</span> ompl::base::AtlasChart::Halfspace::circleIntersect(<span class="keyword">const</span> <span class="keywordtype">double</span> r, Eigen::Ref<Eigen::VectorXd> v1,</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  Eigen::Ref<Eigen::VectorXd> v2)<span class="keyword"> const</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">if</span> (owner_->getManifoldDimension() != 2)</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">throw</span> <a class="code" href="classompl_1_1Exception.html">ompl::Exception</a>(<span class="stringliteral">"ompl::base::AtlasChart::Halfspace::circleIntersect() "</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="stringliteral">"Only works on 2D manifolds."</span>);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// Check if there will be no solutions.</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="keywordtype">double</span> discr = 4 * r * r - usqnorm_;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">if</span> (discr < 0)</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  discr = std::sqrt(discr);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">// Compute the 2 solutions (possibly 1 repeated solution).</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordtype">double</span> unorm = std::sqrt(usqnorm_);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  v1[0] = -u_[1] * discr;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  v1[1] = u_[0] * discr;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  v2 = -v1;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  v1 += u_ * unorm;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  v2 += u_ * unorm;</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  v1 /= 2 * unorm;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  v2 /= 2 * unorm;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span> }</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  </div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  </div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="keywordtype">void</span> ompl::base::AtlasChart::Halfspace::intersect(<span class="keyword">const</span> Halfspace &l1, <span class="keyword">const</span> Halfspace &l2,</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  Eigen::Ref<Eigen::VectorXd> out)</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> {</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">if</span> (l1.owner_ != l2.owner_)</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">throw</span> <a class="code" href="classompl_1_1Exception.html">ompl::Exception</a>(<span class="stringliteral">"Cannot intersect linear inequalities on different charts."</span>);</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">if</span> (l1.owner_->getManifoldDimension() != 2)</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">throw</span> <a class="code" href="classompl_1_1Exception.html">ompl::Exception</a>(<span class="stringliteral">"AtlasChart::Halfspace::intersect() only works on 2D manifolds."</span>);</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">// Computer the intersection point of these lines.</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  Eigen::MatrixXd A(2, 2);</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  A.row(0) = l1.u_.transpose();</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  A.row(1) = l2.u_.transpose();</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  out[0] = l1.u_.squaredNorm();</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  out[1] = l2.u_.squaredNorm();</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  out = 0.5 * A.inverse() * out;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> }</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> <span class="keywordtype">void</span> ompl::base::AtlasChart::Halfspace::setU(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &u)</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> {</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  u_ = u;</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">// Precompute the squared norm of u.</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  usqnorm_ = u_.squaredNorm();</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">// Precompute the right-hand side of the linear inequality.</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  rhs_ = usqnorm_ / 2;</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span> }</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  </div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> <span class="keywordtype">double</span> ompl::base::AtlasChart::Halfspace::distanceToPoint(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &v)<span class="keyword"> const</span></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="comment">// Result is a scalar factor of u_.</span></div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordflow">return</span> (0.5 - v.dot(u_)) / usqnorm_;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span> }</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> <span class="keywordtype">void</span> ompl::base::AtlasChart::Halfspace::expandToInclude(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &x)</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span> {</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="comment">// Compute how far v = psiInverse(x) lies past the boundary, if at all.</span></div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  Eigen::VectorXd v(owner_->k_);</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  owner_->psiInverse(x, v);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> t = -distanceToPoint(v);</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// Move u_ further out by twice that much.</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">if</span> (t > 0)</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  setU((1 + 2 * t) * u_);</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span> }</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  </div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  </div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  </div>
<div class="line"><a name="l00152"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a5a6ce37aa4aad64612026ee371a3bc04"> 152</a></span> ompl::base::AtlasChart::AtlasChart(<span class="keyword">const</span> <a class="code" href="classompl_1_1base_1_1AtlasStateSpace.html">AtlasStateSpace</a> *atlas, <span class="keyword">const</span> <a class="code" href="classompl_1_1base_1_1AtlasStateSpace_1_1StateType.html">AtlasStateSpace::StateType</a> *state)</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  : constraint_(atlas->getConstraint().get())</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  , n_(atlas->getAmbientDimension())</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  , k_(atlas->getManifoldDimension())</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  , state_(state)</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  , bigPhi_([&]() -> const Eigen::MatrixXd {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  Eigen::MatrixXd j(n_ - k_, n_);</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <a class="code" href="classompl_1_1base_1_1AtlasChart.html#aa47b5b21a44f6df48a3fc582a71c8e0b">constraint_</a>-><a class="code" href="classompl_1_1base_1_1Constraint.html#a7f15239c4bbc8b1b8a36e7579d47346c">jacobian</a>(*state_, j);</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  Eigen::FullPivLU<Eigen::MatrixXd> decomp = j.fullPivLu();</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">if</span> (!decomp.isSurjective())</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordflow">throw</span> <a class="code" href="classompl_1_1Exception.html">ompl::Exception</a>(<span class="stringliteral">"Cannot compute full-rank tangent space."</span>);</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  </div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="comment">// Compute the null space and orthonormalize, which is a basis for the tangent space.</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">return</span> decomp.kernel().householderQr().householderQ() * Eigen::MatrixXd::Identity(n_, k_);</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  }())</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  , radius_(atlas->getRho_s())</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span> {</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span> }</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  </div>
<div class="line"><a name="l00172"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a788555d0c062181c6a3b104bd8c4d585"> 172</a></span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a788555d0c062181c6a3b104bd8c4d585">ompl::base::AtlasChart::~AtlasChart</a>()</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  clear();</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> }</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  </div>
<div class="line"><a name="l00177"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a1c95639fbf7570db68cd26c17780b3ca"> 177</a></span> <span class="keywordtype">void</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a1c95639fbf7570db68cd26c17780b3ca">ompl::base::AtlasChart::clear</a>()</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span> {</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keywordflow">for</span> (<span class="keyword">auto</span> h : polytope_)</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  <span class="keyword">delete</span> h;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  polytope_.clear();</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span> }</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  </div>
<div class="line"><a name="l00185"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#af3a07a6b5b871980e26c0bfda1b4ceb1"> 185</a></span> <span class="keywordtype">void</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#af3a07a6b5b871980e26c0bfda1b4ceb1">ompl::base::AtlasChart::phi</a>(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &u, Eigen::Ref<Eigen::VectorXd> out)<span class="keyword"> const</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  out = *state_ + bigPhi_ * u;</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> }</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  </div>
<div class="line"><a name="l00190"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a593871dafb4eded9ba4152375636f6b1"> 190</a></span> <span class="keywordtype">bool</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a593871dafb4eded9ba4152375636f6b1">ompl::base::AtlasChart::psi</a>(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &u, Eigen::Ref<Eigen::VectorXd> out)<span class="keyword"> const</span></div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  <span class="comment">// Initial guess for Newton's method</span></div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  Eigen::VectorXd x0(n_);</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  phi(u, x0);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">// Newton-Raphson to solve Ax = b</span></div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> iter = 0;</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordtype">double</span> norm = 0;</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  Eigen::MatrixXd A(n_, n_);</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  Eigen::VectorXd b(n_);</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  </div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> tolerance = constraint_->getTolerance();</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> squaredTolerance = tolerance * tolerance;</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  </div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="comment">// Initialize output to initial guess</span></div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  out = x0;</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  </div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="comment">// Initialize A with orthonormal basis (constant)</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  A.block(n_ - k_, 0, k_, n_) = bigPhi_.transpose();</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="comment">// Initialize b with initial f(out) = b</span></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  constraint_->function(out, b.head(n_ - k_));</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  b.tail(k_).setZero();</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">while</span> ((norm = b.squaredNorm()) > squaredTolerance && iter++ < constraint_->getMaxIterations())</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  {</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="comment">// Recompute the Jacobian at the new guess.</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  constraint_->jacobian(out, A.block(0, 0, n_ - k_, n_));</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  </div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="comment">// Move in the direction that decreases F(out) and is perpendicular to</span></div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// the chart.</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  out -= A.partialPivLu().solve(b);</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  </div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  <span class="comment">// Recompute b with new guess.</span></div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  constraint_->function(out, b.head(n_ - k_));</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  b.tail(k_) = bigPhi_.transpose() * (out - x0);</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  }</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  </div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keywordflow">return</span> norm < squaredTolerance;</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span> }</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  </div>
<div class="line"><a name="l00232"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#ad85f550b77dadee97c78cf4fdf90b03f"> 232</a></span> <span class="keywordtype">void</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#ad85f550b77dadee97c78cf4fdf90b03f">ompl::base::AtlasChart::psiInverse</a>(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &x,</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  Eigen::Ref<Eigen::VectorXd> out)<span class="keyword"> const</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  out = bigPhi_.transpose() * (x - *state_);</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span> }</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  </div>
<div class="line"><a name="l00238"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a05629a40e81a141f70084c186d0e8b1e"> 238</a></span> <span class="keywordtype">bool</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a05629a40e81a141f70084c186d0e8b1e">ompl::base::AtlasChart::inPolytope</a>(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &u, <span class="keyword">const</span> Halfspace *<span class="keyword">const</span> ignore1,</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keyword">const</span> Halfspace *<span class="keyword">const</span> ignore2)<span class="keyword"> const</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keywordflow">if</span> (u.norm() > radius_)</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  </div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keywordflow">for</span> (Halfspace *h : polytope_)</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  {</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <span class="keywordflow">if</span> (h == ignore1 || h == ignore2)</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordflow">continue</span>;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  </div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">if</span> (!h->contains(u))</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  }</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  </div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> }</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  </div>
<div class="line"><a name="l00256"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a87c309b951f651df5b9f999c289a6d46"> 256</a></span> <span class="keywordtype">void</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a87c309b951f651df5b9f999c289a6d46">ompl::base::AtlasChart::borderCheck</a>(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &v)<span class="keyword"> const</span></div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <span class="keywordflow">for</span> (Halfspace *h : polytope_)</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  h->checkNear(v);</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> }</div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  </div>
<div class="line"><a name="l00262"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#af8b404d3158c034b027be68d5f9ba903"> 262</a></span> <span class="keyword">const</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html">ompl::base::AtlasChart</a> *<a class="code" href="classompl_1_1base_1_1AtlasChart.html#af8b404d3158c034b027be68d5f9ba903">ompl::base::AtlasChart::owningNeighbor</a>(<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &x)<span class="keyword"> const</span></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  Eigen::VectorXd projx(n_), proju(k_);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keywordflow">for</span> (Halfspace *h : polytope_)</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  {</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="comment">// Project onto the neighboring chart.</span></div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keyword">const</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html">AtlasChart</a> *c = h->getComplement()->getOwner();</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  c->psiInverse(x, proju);</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  c->phi(proju, projx);</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="comment">// Check if it's within the validity region and polytope boundary.</span></div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="keyword">const</span> <span class="keywordtype">bool</span> withinTolerance = (projx - x).norm();</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keyword">const</span> <span class="keywordtype">bool</span> inPolytope = c->inPolytope(proju);</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  </div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">if</span> (withinTolerance && inPolytope)</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keywordflow">return</span> c;</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  }</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  </div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keywordflow">return</span> <span class="keyword">nullptr</span>;</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> }</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  </div>
<div class="line"><a name="l00283"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a95f3c07160e1628ccf0dee0cc33179dd"> 283</a></span> <span class="keywordtype">bool</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a95f3c07160e1628ccf0dee0cc33179dd">ompl::base::AtlasChart::toPolygon</a>(std::vector<Eigen::VectorXd> &vertices)<span class="keyword"> const</span></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keywordflow">if</span> (k_ != 2)</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keywordflow">throw</span> <a class="code" href="classompl_1_1Exception.html">ompl::Exception</a>(<span class="stringliteral">"AtlasChart::toPolygon() only works on 2D manifold/charts."</span>);</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  </div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">// Compile a list of all the vertices in P and all the times the border</span></div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  <span class="comment">// intersects the circle.</span></div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  Eigen::VectorXd v(2);</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  Eigen::VectorXd intersection(n_);</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  vertices.clear();</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordflow">for</span> (std::size_t i = 0; i < polytope_.size(); i++)</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  {</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keywordflow">for</span> (std::size_t j = i + 1; j < polytope_.size(); j++)</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  {</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  <span class="comment">// Check if intersection of the lines is a part of the boundary and</span></div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  <span class="comment">// within the circle.</span></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  Halfspace::intersect(*polytope_[i], *polytope_[j], v);</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  phi(v, intersection);</div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">if</span> (inPolytope(v, polytope_[i], polytope_[j]))</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  vertices.push_back(intersection);</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  }</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="comment">// Check if intersection with circle is part of the boundary.</span></div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  Eigen::VectorXd v1(2), v2(2);</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">if</span> ((polytope_[i])->circleIntersect(radius_, v1, v2))</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordflow">if</span> (inPolytope(v1, polytope_[i]))</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  {</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  phi(v1, intersection);</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  vertices.push_back(intersection);</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  }</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordflow">if</span> (inPolytope(v2, polytope_[i]))</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  {</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  phi(v2, intersection);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  vertices.push_back(intersection);</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  }</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  }</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  }</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  </div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="comment">// Include points approximating the circle, if they're inside the polytope.</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <span class="keywordtype">bool</span> is_frontier = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  Eigen::VectorXd v0(2);</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  v0 << radius_, 0;</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> step = boost::math::constants::pi<double>() / 32.;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keywordflow">for</span> (<span class="keywordtype">double</span> a = 0.; a < 2. * boost::math::constants::pi<double>(); a += step)</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  {</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  <span class="keyword">const</span> Eigen::VectorXd vn = Eigen::Rotation2Dd(a) * v0;</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  </div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keywordflow">if</span> (inPolytope(vn))</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  {</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  is_frontier = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  phi(vn, intersection);</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  vertices.push_back(intersection);</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  }</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  }</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  </div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="comment">// Put all the points in order.</span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  std::sort(vertices.begin(), vertices.end(),</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  [&](<span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &x1, <span class="keyword">const</span> Eigen::Ref<const Eigen::VectorXd> &x2) -> <span class="keywordtype">bool</span> {</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="comment">// Check the angles to see who should come first.</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  Eigen::VectorXd v1(2), v2(2);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  psiInverse(x1, v1);</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  psiInverse(x2, v2);</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  return std::atan2(v1[1], v1[0]) < std::atan2(v2[1], v2[0]);</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  });</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  </div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">return</span> is_frontier;</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span> }</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  </div>
<div class="line"><a name="l00352"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a1363834e31fd5c979046ace59608630f"> 352</a></span> <span class="keywordtype">bool</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a1363834e31fd5c979046ace59608630f">ompl::base::AtlasChart::estimateIsFrontier</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  <a class="code" href="classompl_1_1RNG.html">RNG</a> rng;</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  Eigen::VectorXd ru(k_);</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; k < 1000; k++)</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  {</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < ru.size(); i++)</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  ru[i] = rng.<a class="code" href="classompl_1_1RNG.html#a75aacd082ebc60a2e63120d6a384f835">gaussian01</a>();</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  ru *= radius_ / ru.norm();</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="keywordflow">if</span> (inPolytope(ru))</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  }</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> }</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  </div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  </div>
<div class="line"><a name="l00369"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#ac7362faa11728b8b8777ec89bfea64a3"> 369</a></span> <span class="keywordtype">void</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#ac7362faa11728b8b8777ec89bfea64a3">ompl::base::AtlasChart::generateHalfspace</a>(<a class="code" href="classompl_1_1base_1_1AtlasChart.html">AtlasChart</a> *c1, <a class="code" href="classompl_1_1base_1_1AtlasChart.html">AtlasChart</a> *c2)</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> {</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  <span class="keywordflow">if</span> (c1 == c2)</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  <span class="keywordflow">throw</span> <a class="code" href="classompl_1_1Exception.html">ompl::Exception</a>(<span class="stringliteral">"ompl::base::AtlasChart::generateHalfspace(): "</span></div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="stringliteral">"Must use two different charts."</span>);</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="comment">// c1, c2 will delete l1, l2, respectively, upon destruction.</span></div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  Halfspace *l1, *l2;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  l1 = <span class="keyword">new</span> Halfspace(c1, c2);</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  l2 = <span class="keyword">new</span> Halfspace(c2, c1);</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  l1->setComplement(l2);</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  l2->setComplement(l1);</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  c1-><a class="code" href="classompl_1_1base_1_1AtlasChart.html#a1b8ec45dee3a4db7ca6b6f41e31e341a">addBoundary</a>(l1);</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  c2-><a class="code" href="classompl_1_1base_1_1AtlasChart.html#a1b8ec45dee3a4db7ca6b6f41e31e341a">addBoundary</a>(l2);</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> }</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  </div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  </div>
<div class="line"><a name="l00387"></a><span class="lineno"><a class="line" href="classompl_1_1base_1_1AtlasChart.html#a1b8ec45dee3a4db7ca6b6f41e31e341a"> 387</a></span> <span class="keywordtype">void</span> <a class="code" href="classompl_1_1base_1_1AtlasChart.html#a1b8ec45dee3a4db7ca6b6f41e31e341a">ompl::base::AtlasChart::addBoundary</a>(Halfspace *halfspace)</div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> {</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  polytope_.push_back(halfspace);</div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> }</div>
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<div class="ttc" id="aclassompl_1_1RNG_html"><div class="ttname"><a href="classompl_1_1RNG.html">ompl::RNG</a></div><div class="ttdoc">Random number generation. An instance of this class cannot be used by multiple threads at once (membe...</div><div class="ttdef"><b>Definition:</b> <a href="RandomNumbers_8h_source.html#l00088">RandomNumbers.h:88</a></div></div>
<div class="ttc" id="aclassompl_1_1RNG_html_a75aacd082ebc60a2e63120d6a384f835"><div class="ttname"><a href="classompl_1_1RNG.html#a75aacd082ebc60a2e63120d6a384f835">ompl::RNG::gaussian01</a></div><div class="ttdeci">double gaussian01()</div><div class="ttdoc">Generate a random real using a normal distribution with mean 0 and variance 1.</div><div class="ttdef"><b>Definition:</b> <a href="RandomNumbers_8h_source.html#l00156">RandomNumbers.h:156</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a1363834e31fd5c979046ace59608630f"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a1363834e31fd5c979046ace59608630f">ompl::base::AtlasChart::estimateIsFrontier</a></div><div class="ttdeci">bool estimateIsFrontier() const</div><div class="ttdoc">Use sampling to make a quick estimate as to whether this chart's polytope boundary is completely defi...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00352">AtlasChart.cpp:352</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasStateSpace_1_1StateType_html"><div class="ttname"><a href="classompl_1_1base_1_1AtlasStateSpace_1_1StateType.html">ompl::base::AtlasStateSpace::StateType</a></div><div class="ttdoc">A state in an atlas represented as a real vector in ambient space and a chart that it belongs to.</div><div class="ttdef"><b>Definition:</b> <a href="AtlasStateSpace_8h_source.html#l00167">AtlasStateSpace.h:167</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_af8b404d3158c034b027be68d5f9ba903"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#af8b404d3158c034b027be68d5f9ba903">ompl::base::AtlasChart::owningNeighbor</a></div><div class="ttdeci">const AtlasChart * owningNeighbor(const Eigen::Ref< const Eigen::VectorXd > &x) const</div><div class="ttdoc">Try to find an owner for ambient point \x from among the neighbors of this chart. Returns nullptr if ...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00262">AtlasChart.cpp:262</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_aa47b5b21a44f6df48a3fc582a71c8e0b"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#aa47b5b21a44f6df48a3fc582a71c8e0b">ompl::base::AtlasChart::constraint_</a></div><div class="ttdeci">const Constraint * constraint_</div><div class="ttdoc">The constraint function that defines the manifold.</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8h_source.html#l00335">AtlasChart.h:335</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a95f3c07160e1628ccf0dee0cc33179dd"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a95f3c07160e1628ccf0dee0cc33179dd">ompl::base::AtlasChart::toPolygon</a></div><div class="ttdeci">bool toPolygon(std::vector< Eigen::VectorXd > &vertices) const</div><div class="ttdoc">For manifolds of dimension 2, return in order in vertices the polygon boundary of this chart,...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00283">AtlasChart.cpp:283</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_ad85f550b77dadee97c78cf4fdf90b03f"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#ad85f550b77dadee97c78cf4fdf90b03f">ompl::base::AtlasChart::psiInverse</a></div><div class="ttdeci">void psiInverse(const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::Ref< Eigen::VectorXd > out) const</div><div class="ttdoc">Logarithmic mapping. Project ambient point x onto the chart and store the result in out,...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00232">AtlasChart.cpp:232</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_ac7362faa11728b8b8777ec89bfea64a3"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#ac7362faa11728b8b8777ec89bfea64a3">ompl::base::AtlasChart::generateHalfspace</a></div><div class="ttdeci">static void generateHalfspace(AtlasChart *c1, AtlasChart *c2)</div><div class="ttdoc">Create two complementary halfspaces dividing the space between charts c1 and c2, and add them to the ...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00369">AtlasChart.cpp:369</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasStateSpace_html"><div class="ttname"><a href="classompl_1_1base_1_1AtlasStateSpace.html">ompl::base::AtlasStateSpace</a></div><div class="ttdoc">ConstrainedStateSpace encapsulating a planner-agnostic atlas algorithm for planning on a constraint m...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasStateSpace_8h_source.html#l00159">AtlasStateSpace.h:159</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a593871dafb4eded9ba4152375636f6b1"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a593871dafb4eded9ba4152375636f6b1">ompl::base::AtlasChart::psi</a></div><div class="ttdeci">bool psi(const Eigen::Ref< const Eigen::VectorXd > &u, Eigen::Ref< Eigen::VectorXd > out) const</div><div class="ttdoc">Exponential mapping. Project chart point u onto the manifold and store the result in out,...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00190">AtlasChart.cpp:190</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a788555d0c062181c6a3b104bd8c4d585"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a788555d0c062181c6a3b104bd8c4d585">ompl::base::AtlasChart::~AtlasChart</a></div><div class="ttdeci">~AtlasChart()</div><div class="ttdoc">Destructor.</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00172">AtlasChart.cpp:172</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a1b8ec45dee3a4db7ca6b6f41e31e341a"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a1b8ec45dee3a4db7ca6b6f41e31e341a">ompl::base::AtlasChart::addBoundary</a></div><div class="ttdeci">void addBoundary(Halfspace *halfspace)</div><div class="ttdoc">Introduce a new halfspace to the chart's bounding polytope. This chart assumes responsibility for del...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00387">AtlasChart.cpp:387</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html">ompl::base::AtlasChart</a></div><div class="ttdoc">Tangent space and bounding polytope approximating some patch of the manifold.</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8h_source.html#l00116">AtlasChart.h:116</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a1c95639fbf7570db68cd26c17780b3ca"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a1c95639fbf7570db68cd26c17780b3ca">ompl::base::AtlasChart::clear</a></div><div class="ttdeci">void clear()</div><div class="ttdoc">Forget all acquired information such as the halfspace boundary.</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00177">AtlasChart.cpp:177</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a87c309b951f651df5b9f999c289a6d46"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a87c309b951f651df5b9f999c289a6d46">ompl::base::AtlasChart::borderCheck</a></div><div class="ttdeci">void borderCheck(const Eigen::Ref< const Eigen::VectorXd > &v) const</div><div class="ttdoc">Check if chart point v lies very close to any part of the boundary. Wherever it does,...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00256">AtlasChart.cpp:256</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1Constraint_html_a7f15239c4bbc8b1b8a36e7579d47346c"><div class="ttname"><a href="classompl_1_1base_1_1Constraint.html#a7f15239c4bbc8b1b8a36e7579d47346c">ompl::base::Constraint::jacobian</a></div><div class="ttdeci">virtual void jacobian(const State *state, Eigen::Ref< Eigen::MatrixXd > out) const</div><div class="ttdoc">Compute the Jacobian of the constraint function at state. Result is returned in out,...</div><div class="ttdef"><b>Definition:</b> <a href="Constraint_8cpp_source.html#l00045">Constraint.cpp:45</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_a05629a40e81a141f70084c186d0e8b1e"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#a05629a40e81a141f70084c186d0e8b1e">ompl::base::AtlasChart::inPolytope</a></div><div class="ttdeci">bool inPolytope(const Eigen::Ref< const Eigen::VectorXd > &u, const Halfspace *ignore1=nullptr, const Halfspace *ignore2=nullptr) const</div><div class="ttdoc">Check if a point u on the chart lies within its polytope boundary. Can ignore up to 2 of the halfspac...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00238">AtlasChart.cpp:238</a></div></div>
<div class="ttc" id="aclassompl_1_1Exception_html"><div class="ttname"><a href="classompl_1_1Exception.html">ompl::Exception</a></div><div class="ttdoc">The exception type for ompl.</div><div class="ttdef"><b>Definition:</b> <a href="Exception_8h_source.html#l00078">Exception.h:78</a></div></div>
<div class="ttc" id="aclassompl_1_1base_1_1AtlasChart_html_af3a07a6b5b871980e26c0bfda1b4ceb1"><div class="ttname"><a href="classompl_1_1base_1_1AtlasChart.html#af3a07a6b5b871980e26c0bfda1b4ceb1">ompl::base::AtlasChart::phi</a></div><div class="ttdeci">void phi(const Eigen::Ref< const Eigen::VectorXd > &u, Eigen::Ref< Eigen::VectorXd > out) const</div><div class="ttdoc">Rewrite a chart point u in ambient space coordinates and store the result in out, which should be all...</div><div class="ttdef"><b>Definition:</b> <a href="AtlasChart_8cpp_source.html#l00185">AtlasChart.cpp:185</a></div></div>
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