How to map a point onto a warped grid

Question

Say you have a collection of points with coordinates on a Cartesian coordinate system.

Answer 1

Ok, so this sounds like image warping. This is what you should do:

1. Create a Delaunay triangulation of your unwarped grid and use your knowledge of the correspondences between the warped and unwarped grid to create the triangulation for the warped grid. Now you know the corresponding triangles in each image and since there is no overlapping, you should be able to perform the next step without much difficulty.

2. Now, to find the corresponding point A, in the warped image:

   1. Find the triangle A lies in and use the transformation between the triangle in the unwarped grid and the warped grid to figure out the new position.

This is explained explicitly in detail here.

Another (much more complicated) method is the Thin Plate Spline (which is also explained in the slides above).