title: How to map a point onto a warped grid
body: <p>Say you have a collection of points with coordinates on a Cartesian coordinate system.</p>
  
  <p><img src="https://i.stack.imgur.com/SIWEQ.jpg" alt="an unwarped grid"></p>
  
  <p>You want to plot another point, and you know its coordinates in the same Cartesian coordinate system.</p>
  
  <p>However, the plot you're drawing on is distorted from the original.  Imagine taking the original plane, printing it on a rubber sheet, and stretching it in some places and pinching it in others, in an asymmetrical way (no overlapping or anything complex).  </p>
  
  <p><img src="https://i.stack.imgur.com/nRSLp.jpg" alt="a warped grid"> (<a href="http://www.retinamd.com/macular-degeneration-treatment.asp" rel="nofollow noreferrer">source</a>)</p>
  
  <p>You know the stretched and unstretched coordinates of each of your set of points, but not the underlying stretch function.  You know the unstretched coordinates of a new point.</p>
  
  <p>How can you estimate where to plot the new point in the stretched coordinates based on the stretched positions of nearby points?  It doesn't need to be exact, since you can't determine the actual stretch function from a set of remapped points unless you have more information.</p>
  
  <p>other possible keywords: warped distorted grid mesh plane coordinate unwarp</p>