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I want to project a 3d scene onto a virtual screen.

I know how a perspective projection matrix would look like in the regualar case (transforming the red marked part of space into an unit cube). I also know how I could calculate the fov given screen width height and position and a camera position. But I want to create a projection matrix that given a camera position and the postion orientation and scale of a screen would project the geometry onto that screen.(black line)

Could I apply some kind of shear matrix onto the regular perspective projection matrix after I calculated it? If so how would it look like.

picture in 2d

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