title: Parallel ellisoid projection onto a plane, numerical method
body: <p>I am having the following problem. I need to find the <strong>contour points of a ellipsoidal rotated body on the xy-plane</strong> (see <a href="https://www.dropbox.com/sh/nqb7fnwra0bdx1g/AAA93I-gt-GVyBzG2ZL--hUTa?dl=0" rel="nofollow">image</a> for more detail). Now, I have found the analytic solution to this problem (using <a href="http://www.geometrictools.com/Documentation/PerspectiveProjectionEllipsoid.pdf" rel="nofollow">this</a> method).</p>
  
  <p>However, due to the use of symbolic values I use in Matlab this process is slow (and I need to repeat it this process thousands of times). </p>
  
  <p>I have all information regarding the ellipsoid (all axes and centerpoint) and the rotation it has undergone from a position where its principle axes are aligned with the XYZ-axes.</p>
  
  <p>I need a faster way to solve this problem. I can easily find all points on the surface of the ellipsoid and project these on the XY-plane (not knowing which points define the contour). However, then, I need to find the points that define the contour in the XY-plane. See picture on dropbox.</p>
  
  <p>My questions:</p>
  
  <p>1) Is there a fast way to find the points defining the contour as in image 2?</p>
  
  <p>2) Or, is there another numerical methods to find the contour of a projection of a rotated ellipsoid?</p>
  
  <p>3) Or, is there a way to solve the analitical solution in Matlab without using symbolic values?</p>