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<li><a class="reference internal" href="#">Projecting points using a parametric model</a></li>
<li><a class="reference internal" href="#the-code">The code</a></li>
<li><a class="reference internal" href="#the-explanation">The explanation</a></li>
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<div class="section" id="projecting-points-using-a-parametric-model">
<span id="project-inliers"></span><h1>Projecting points using a parametric model</h1>
<p>In this tutorial we will learn how to project points onto a parametric model
(e.g., plane, sphere, etc). The parametric model is given through a set of
coefficients – in the case of a plane, through its equation: ax + by + cz + d
= 0.</p>
</div>
<div class="section" id="the-code">
<h1>The code</h1>
<p>First, create a file, let’s say, <code class="docutils literal notranslate"><span class="pre">project_inliers.cpp</span></code> in your favorite
editor, and place the following inside it:</p>
<div class="highlight-cpp notranslate"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre> 1
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52</pre></div></td><td class="code"><div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf">&lt;iostream&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;pcl/point_cloud.h&gt; // for PointCloud</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;pcl/point_types.h&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;pcl/ModelCoefficients.h&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;pcl/filters/project_inliers.h&gt;</span><span class="cp"></span>
<span class="kt">int</span>
<span class="nf">main</span> <span class="p">()</span>
<span class="p">{</span>
<span class="n">pcl</span><span class="o">::</span><span class="n">PointCloud</span><span class="o">&lt;</span><span class="n">pcl</span><span class="o">::</span><span class="n">PointXYZ</span><span class="o">&gt;::</span><span class="n">Ptr</span> <span class="n">cloud</span> <span class="p">(</span><span class="k">new</span> <span class="n">pcl</span><span class="o">::</span><span class="n">PointCloud</span><span class="o">&lt;</span><span class="n">pcl</span><span class="o">::</span><span class="n">PointXYZ</span><span class="o">&gt;</span><span class="p">);</span>
<span class="n">pcl</span><span class="o">::</span><span class="n">PointCloud</span><span class="o">&lt;</span><span class="n">pcl</span><span class="o">::</span><span class="n">PointXYZ</span><span class="o">&gt;::</span><span class="n">Ptr</span> <span class="n">cloud_projected</span> <span class="p">(</span><span class="k">new</span> <span class="n">pcl</span><span class="o">::</span><span class="n">PointCloud</span><span class="o">&lt;</span><span class="n">pcl</span><span class="o">::</span><span class="n">PointXYZ</span><span class="o">&gt;</span><span class="p">);</span>
<span class="c1">// Fill in the cloud data</span>
<span class="n">cloud</span><span class="o">-&gt;</span><span class="n">width</span> <span class="o">=</span> <span class="mi">5</span><span class="p">;</span>
<span class="n">cloud</span><span class="o">-&gt;</span><span class="n">height</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span>
<span class="n">cloud</span><span class="o">-&gt;</span><span class="n">points</span><span class="p">.</span><span class="n">resize</span> <span class="p">(</span><span class="n">cloud</span><span class="o">-&gt;</span><span class="n">width</span> <span class="o">*</span> <span class="n">cloud</span><span class="o">-&gt;</span><span class="n">height</span><span class="p">);</span>
<span class="k">for</span> <span class="p">(</span><span class="k">auto</span><span class="o">&amp;</span> <span class="nl">point</span><span class="p">:</span> <span class="o">*</span><span class="n">cloud</span><span class="p">)</span>
<span class="p">{</span>
<span class="n">point</span><span class="p">.</span><span class="n">x</span> <span class="o">=</span> <span class="mi">1024</span> <span class="o">*</span> <span class="n">rand</span> <span class="p">()</span> <span class="o">/</span> <span class="p">(</span><span class="n">RAND_MAX</span> <span class="o">+</span> <span class="mf">1.0f</span><span class="p">);</span>
<span class="n">point</span><span class="p">.</span><span class="n">y</span> <span class="o">=</span> <span class="mi">1024</span> <span class="o">*</span> <span class="n">rand</span> <span class="p">()</span> <span class="o">/</span> <span class="p">(</span><span class="n">RAND_MAX</span> <span class="o">+</span> <span class="mf">1.0f</span><span class="p">);</span>
<span class="n">point</span><span class="p">.</span><span class="n">z</span> <span class="o">=</span> <span class="mi">1024</span> <span class="o">*</span> <span class="n">rand</span> <span class="p">()</span> <span class="o">/</span> <span class="p">(</span><span class="n">RAND_MAX</span> <span class="o">+</span> <span class="mf">1.0f</span><span class="p">);</span>
<span class="p">}</span>
<span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;Cloud before projection: &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="k">const</span> <span class="k">auto</span><span class="o">&amp;</span> <span class="nl">point</span><span class="p">:</span> <span class="o">*</span><span class="n">cloud</span><span class="p">)</span>
<span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">x</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">y</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">z</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
<span class="c1">// Create a set of planar coefficients with X=Y=0,Z=1</span>
<span class="n">pcl</span><span class="o">::</span><span class="n">ModelCoefficients</span><span class="o">::</span><span class="n">Ptr</span> <span class="n">coefficients</span> <span class="p">(</span><span class="k">new</span> <span class="n">pcl</span><span class="o">::</span><span class="n">ModelCoefficients</span> <span class="p">());</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">.</span><span class="n">resize</span> <span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">;</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span>
<span class="c1">// Create the filtering object</span>
<span class="n">pcl</span><span class="o">::</span><span class="n">ProjectInliers</span><span class="o">&lt;</span><span class="n">pcl</span><span class="o">::</span><span class="n">PointXYZ</span><span class="o">&gt;</span> <span class="n">proj</span><span class="p">;</span>
<span class="n">proj</span><span class="p">.</span><span class="n">setModelType</span> <span class="p">(</span><span class="n">pcl</span><span class="o">::</span><span class="n">SACMODEL_PLANE</span><span class="p">);</span>
<span class="n">proj</span><span class="p">.</span><span class="n">setInputCloud</span> <span class="p">(</span><span class="n">cloud</span><span class="p">);</span>
<span class="n">proj</span><span class="p">.</span><span class="n">setModelCoefficients</span> <span class="p">(</span><span class="n">coefficients</span><span class="p">);</span>
<span class="n">proj</span><span class="p">.</span><span class="n">filter</span> <span class="p">(</span><span class="o">*</span><span class="n">cloud_projected</span><span class="p">);</span>
<span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;Cloud after projection: &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="k">const</span> <span class="k">auto</span><span class="o">&amp;</span> <span class="nl">point</span><span class="p">:</span> <span class="o">*</span><span class="n">cloud_projected</span><span class="p">)</span>
<span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">x</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">y</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">z</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
<span class="k">return</span> <span class="p">(</span><span class="mi">0</span><span class="p">);</span>
<span class="p">}</span>
</pre></div>
</td></tr></table></div>
</div>
<div class="section" id="the-explanation">
<h1>The explanation</h1>
<p>Now, let’s break down the code piece by piece.</p>
<p>We first import the ModelCoefficients structure then the ProjectInliers filter.</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span><span class="cp">#include</span> <span class="cpf">&lt;pcl/ModelCoefficients.h&gt;</span><span class="cp"></span>
<span class="cp">#include</span> <span class="cpf">&lt;pcl/filters/project_inliers.h&gt;</span><span class="cp"></span>
</pre></div>
</div>
<p>We then create the point cloud structure, fill in the respective values, and
display the content on screen.</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span> <span class="n">cloud</span><span class="o">-&gt;</span><span class="n">width</span> <span class="o">=</span> <span class="mi">5</span><span class="p">;</span>
<span class="n">cloud</span><span class="o">-&gt;</span><span class="n">height</span> <span class="o">=</span> <span class="mi">1</span><span class="p">;</span>
<span class="n">cloud</span><span class="o">-&gt;</span><span class="n">points</span><span class="p">.</span><span class="n">resize</span> <span class="p">(</span><span class="n">cloud</span><span class="o">-&gt;</span><span class="n">width</span> <span class="o">*</span> <span class="n">cloud</span><span class="o">-&gt;</span><span class="n">height</span><span class="p">);</span>
<span class="k">for</span> <span class="p">(</span><span class="k">auto</span><span class="o">&amp;</span> <span class="nl">point</span><span class="p">:</span> <span class="o">*</span><span class="n">cloud</span><span class="p">)</span>
<span class="p">{</span>
<span class="n">point</span><span class="p">.</span><span class="n">x</span> <span class="o">=</span> <span class="mi">1024</span> <span class="o">*</span> <span class="n">rand</span> <span class="p">()</span> <span class="o">/</span> <span class="p">(</span><span class="n">RAND_MAX</span> <span class="o">+</span> <span class="mf">1.0f</span><span class="p">);</span>
<span class="n">point</span><span class="p">.</span><span class="n">y</span> <span class="o">=</span> <span class="mi">1024</span> <span class="o">*</span> <span class="n">rand</span> <span class="p">()</span> <span class="o">/</span> <span class="p">(</span><span class="n">RAND_MAX</span> <span class="o">+</span> <span class="mf">1.0f</span><span class="p">);</span>
<span class="n">point</span><span class="p">.</span><span class="n">z</span> <span class="o">=</span> <span class="mi">1024</span> <span class="o">*</span> <span class="n">rand</span> <span class="p">()</span> <span class="o">/</span> <span class="p">(</span><span class="n">RAND_MAX</span> <span class="o">+</span> <span class="mf">1.0f</span><span class="p">);</span>
<span class="p">}</span>
<span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;Cloud before projection: &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="k">const</span> <span class="k">auto</span><span class="o">&amp;</span> <span class="nl">point</span><span class="p">:</span> <span class="o">*</span><span class="n">cloud</span><span class="p">)</span>
<span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">x</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">y</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">z</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
</pre></div>
</div>
<p>We fill in the ModelCoefficients values. In this case, we use a plane model,
with ax+by+cz+d=0, where a=b=d=0, and c=1, or said differently, the X-Y plane.</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span> <span class="n">pcl</span><span class="o">::</span><span class="n">ModelCoefficients</span><span class="o">::</span><span class="n">Ptr</span> <span class="n">coefficients</span> <span class="p">(</span><span class="k">new</span> <span class="n">pcl</span><span class="o">::</span><span class="n">ModelCoefficients</span> <span class="p">());</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">.</span><span class="n">resize</span> <span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">;</span>
<span class="n">coefficients</span><span class="o">-&gt;</span><span class="n">values</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">;</span>
</pre></div>
</div>
<p>We create the ProjectInliers object and use the ModelCoefficients defined above
as the model to project onto.</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span> <span class="n">pcl</span><span class="o">::</span><span class="n">ProjectInliers</span><span class="o">&lt;</span><span class="n">pcl</span><span class="o">::</span><span class="n">PointXYZ</span><span class="o">&gt;</span> <span class="n">proj</span><span class="p">;</span>
<span class="n">proj</span><span class="p">.</span><span class="n">setModelType</span> <span class="p">(</span><span class="n">pcl</span><span class="o">::</span><span class="n">SACMODEL_PLANE</span><span class="p">);</span>
<span class="n">proj</span><span class="p">.</span><span class="n">setInputCloud</span> <span class="p">(</span><span class="n">cloud</span><span class="p">);</span>
<span class="n">proj</span><span class="p">.</span><span class="n">setModelCoefficients</span> <span class="p">(</span><span class="n">coefficients</span><span class="p">);</span>
<span class="n">proj</span><span class="p">.</span><span class="n">filter</span> <span class="p">(</span><span class="o">*</span><span class="n">cloud_projected</span><span class="p">);</span>
</pre></div>
</div>
<p>Finally we show the content of the projected cloud.</p>
<div class="highlight-cpp notranslate"><div class="highlight"><pre><span></span> <span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot;Cloud after projection: &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
<span class="k">for</span> <span class="p">(</span><span class="k">const</span> <span class="k">auto</span><span class="o">&amp;</span> <span class="nl">point</span><span class="p">:</span> <span class="o">*</span><span class="n">cloud_projected</span><span class="p">)</span>
<span class="n">std</span><span class="o">::</span><span class="n">cerr</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span> <span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">x</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">y</span> <span class="o">&lt;&lt;</span> <span class="s">&quot; &quot;</span>
<span class="o">&lt;&lt;</span> <span class="n">point</span><span class="p">.</span><span class="n">z</span> <span class="o">&lt;&lt;</span> <span class="n">std</span><span class="o">::</span><span class="n">endl</span><span class="p">;</span>
</pre></div>
</div>
</div>
<div class="section" id="compiling-and-running-the-program">
<h1>Compiling and running the program</h1>
<p>Add the following lines to your CMakeLists.txt file:</p>
<div class="highlight-cmake notranslate"><table class="highlighttable"><tr><td class="linenos"><div class="linenodiv"><pre> 1
2
3
4
5
6
7
8
9
10
11
12</pre></div></td><td class="code"><div class="highlight"><pre><span></span><span class="nb">cmake_minimum_required</span><span class="p">(</span><span class="s">VERSION</span> <span class="s">3.5</span> <span class="s">FATAL_ERROR</span><span class="p">)</span>
<span class="nb">project</span><span class="p">(</span><span class="s">project_inliers</span><span class="p">)</span>
<span class="nb">find_package</span><span class="p">(</span><span class="s">PCL</span> <span class="s">1.2</span> <span class="s">REQUIRED</span><span class="p">)</span>
<span class="nb">include_directories</span><span class="p">(</span><span class="o">${</span><span class="nv">PCL_INCLUDE_DIRS</span><span class="o">}</span><span class="p">)</span>
<span class="nb">link_directories</span><span class="p">(</span><span class="o">${</span><span class="nv">PCL_LIBRARY_DIRS</span><span class="o">}</span><span class="p">)</span>
<span class="nb">add_definitions</span><span class="p">(</span><span class="o">${</span><span class="nv">PCL_DEFINITIONS</span><span class="o">}</span><span class="p">)</span>
<span class="nb">add_executable</span> <span class="p">(</span><span class="s">project_inliers</span> <span class="s">project_inliers.cpp</span><span class="p">)</span>
<span class="nb">target_link_libraries</span> <span class="p">(</span><span class="s">project_inliers</span> <span class="o">${</span><span class="nv">PCL_LIBRARIES</span><span class="o">}</span><span class="p">)</span>
</pre></div>
</td></tr></table></div>
<p>After you have made the executable, you can run it. Simply do:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>$ ./project_inliers
</pre></div>
</div>
<p>You will see something similar to:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cloud</span> <span class="n">before</span> <span class="n">projection</span><span class="p">:</span>
<span class="mf">0.352222</span> <span class="o">-</span><span class="mf">0.151883</span> <span class="o">-</span><span class="mf">0.106395</span>
<span class="o">-</span><span class="mf">0.397406</span> <span class="o">-</span><span class="mf">0.473106</span> <span class="mf">0.292602</span>
<span class="o">-</span><span class="mf">0.731898</span> <span class="mf">0.667105</span> <span class="mf">0.441304</span>
<span class="o">-</span><span class="mf">0.734766</span> <span class="mf">0.854581</span> <span class="o">-</span><span class="mf">0.0361733</span>
<span class="o">-</span><span class="mf">0.4607</span> <span class="o">-</span><span class="mf">0.277468</span> <span class="o">-</span><span class="mf">0.916762</span>
<span class="n">Cloud</span> <span class="n">after</span> <span class="n">projection</span><span class="p">:</span>
<span class="mf">0.352222</span> <span class="o">-</span><span class="mf">0.151883</span> <span class="mi">0</span>
<span class="o">-</span><span class="mf">0.397406</span> <span class="o">-</span><span class="mf">0.473106</span> <span class="mi">0</span>
<span class="o">-</span><span class="mf">0.731898</span> <span class="mf">0.667105</span> <span class="mi">0</span>
<span class="o">-</span><span class="mf">0.734766</span> <span class="mf">0.854581</span> <span class="mi">0</span>
<span class="o">-</span><span class="mf">0.4607</span> <span class="o">-</span><span class="mf">0.277468</span> <span class="mi">0</span>
</pre></div>
</div>
<p>A graphical display of the projection process is shown below.</p>
<img alt="_images/project_inliers_2.png" src="_images/project_inliers_2.png" />
<p>Note that the coordinate axes are represented as red (x), green (y), and blue
(z). The five points are represented with red as the points before projection
and green as the points after projection. Note that their z now lies on the X-Y
plane.</p>
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