Points to matrix

i have exact same problem as oschatz had some years ago. anybody who has a solution?

the following problem occurs always again when calibrating projectors which exact position and orientation is unknown onto a known projection screen.

given are four points in space which lie on a plane.

x and y are given. without loss of generality z is zero for all four points.

what is the the 3d transformation matrix (projection, scale, translate, rotate) which would transform a quad, so that its projection onto the xy plane has the given four coordinates?

anybody has some mathematical pointers or insights for this?

here is an old thread, but no answer ;)

thx and greets


it’s called Homography, and more straightforward way called BezierGrid

I think what you are looking for is more along the lines of some of @elliotwood 's contributions. homography will not work on objects that are not flat.

If you are projecting onto flat stuff, then homography will be fine.

comparing the two available approaches: projection-mapping-primer