How to automatically generate image distortion rules?

Question

Algorithms

Hello!
There is an image:

As you can see, the lattice is distorted. It is necessary to generate distortion rules based on such an image, so that they can be applied to other images.
What is it for? For example:
1) We glue vinyl with a grid image on the car
2) We take pictures
3) We generate distortion rules
Now for all owners of a car of this model we can show how one or another airbrush will look like.
SP does not matter much, but I prefer php because. convenient for the project and speed does not play a big role.
I would like to get a link to a suitable case, or at least understand in which direction to move and what to google.
Thank you!

Answer 1

Apparently you can do without gluing the grid:
https://habr.com/en/post/134781/ (we can get 3D models)
Next, I will look for information on how to overlay a 2D image on a 3D object using Java

Answer 2

What is it for? For example:
1) We glue vinyl with a grid image on the car
2) We take pictures
3) We generate distortion rules
Looks too complicated. Why not just take a 3D model of a car, project textures (vinyls) onto it and get texture coordinates? In this way, you can show vinyls from different angles, overlaying the rendering of only the body on the photo of the car, and replace them without unnecessary generations, since the texture coordinates will be the same for everyone (unless, of course, the vinyls are of the same size)

Answer 3

1) We glue vinyl with a grid image on the car
2) We take pictures
3) We generate distortion rules
Now for all owners of a car of this model we can show how one or another airbrush will look like.

from what bastard? car shapes are different .. do you have 3D printing? use 3D scanning + preview , but if the work is manual, how do you suppose to take into account the vision of the master in the "rules of distortion"?
upd2 tip - it's CAD technology - maybe even the full lifecycle of your wishlist. 3DMax is quite popular, it's not free, but it's not the only product on the market