Hi!
I'm very new to graphic design programs and I may be dealing with a limitation, I'm not sure.
I am trying to edit an image so that, when projected through lens at an angle it will appear to be the original image.
I've drawn the shape based on an algorithm I wrote for 25 degrees and a light cone of 36.48 degrees.
I'll attach the original and the shape it needs to fit below.
https://i.stack.imgur.com/prYbI.png
(Hope that works! )

I've tried plenty of methods, interpolation, envelope, extrude, perspective etc. all seem to destroy the image as it doesn't like moving the object as a while, rather a collection of different object (or paths).
Can anyone assist with a way that I can make a controlled distortion to this image?

PS, this is one of many images, thus I would prefer a method that may take time to set up, but not too long to repeat.
PPS, if someone is aware of another program that is capable of this easily, I'm willing to try it!

THANKS!


EDIT: I believe the term I'm trying to find is keystone correction.
Maybe a simpler fix, I have added photos of using perceptive, is there away to achieve this, without losing the shading etc?
https://i.stack.imgur.com/BpTxg.png
https://i.stack.imgur.com/prYbI.png