title: Projective Geometry - Find Plane in 3D using eigen
body: <p>I'm trying to construct a plane out of three points in 3D.
  I want to use projective geometry to achieve this.</p>
  
  <p>As far as I know, one can "simply" solve the following to find a plane:</p>
  
  <pre><code>A * x = 0 ,where
  A is a 3x4 Matrix - each row being one of the points (x,y,z,1)
  x is the plane I want to find
  </code></pre>
  
  <p>I know that I need to have a constrain. Therefore I want to set <code>x(3) = 1</code>.
  Can someone please point me to the right method to use?</p>
  
  <p>So far I have the following code:</p>
  
  <pre><code>Eigen::Vector4f p1(0,0,1,1);
  Eigen::Vector4f p2(1,0,0,1);
  Eigen::Vector4f p3(0,1,0,1);
  
  Eigen::Matrix&lt;float,3,4&gt; A;
  A &lt;&lt; p1.transpose(), p2.transpose(), p3.transpose();
  
  // Throws compile error
  // Eigen::Vector4f Plane = A.jacobiSvd(ComputeThinU | ComputeThinV).solve(Vector4f::Zero()); 
  
  //throws runtime error (row-number do not match)
  // Eigen::Vector4f Plane = A.fullPivHouseholderQr().solce(Eigen::Vector4f::Zero()); 
  </code></pre>