How do i map points from one grid to another?

Question

Let's say i have a 2d linear grid and a point in said grid. How do i map the point from that grid into a related non-linear grid?

The red dot is the point in the regular grid and i want to know how to figure out where the point would go in a similar deformed grid (an example one is shown). I'm thinking of using the difference between the points in the non-deformed grid and the deformed one to derive a solution but i'm not sure how.

Answer 1

You might want to read up on Affine transformations. There isn't much magic going on here, just a little translation and shearing. This is all done just with a matrix multiplication for the coordinate pairs (in homogenous coordinates), so it's very easy to do. But can be a little hard to understand :-)