title: Given a Fundamental Matrix and Image Points in one image plane, find exactly corresponding points in second Image Plane
body: <p>As a relative beginner in this topic, I have read the literature but I am not sure about how to manipulate the equations to my purposes and would like advice on tackling this topic.</p>
  <p>Preamble:
  I have 2 cameras in a stereo rig which have been calibrated, thus extracting data structures such as each camera's Camera Matrix K1 and K2, as well as the Fundamental, Essential, Rotation and Translation matrices, F, E, R and T respectively. Also after rectifying one has the projection matrices P1 and P2 as well as the disparity matrix Q.</p>
  <p>My aim is however to test the triangulation method of OpenCV, and to this end I would like to use synthetic Images where the correspondence between the points in image1 and image2 is exact.
  My idea was to take an image of a chessboard with one camera, and use <code>findCorners()</code> and <code>cornerSubPix()</code> to get image points in the left camera, let's call them imagePoints1.</p>
  <p>To get synthetically generated Image Points with exactly corresponding points on the left camera's image plane, I intend to use the property
  x2'Fx1 = 0, given the F matrix and x1 (which represents one homogenous 2D point from imagePoints1)
  to generate said set of Image Points.</p>
  <p>This is where I am stuck, since he obvious solution would be to have a zero-vector to make this equation work. Otherwise I get a parametric solution. How do I then get non-zero points that fulfill this property x2'Fx1 = 0 given x1 and F ?</p>
  <p>Thank you.</p>