Q: Using Photoshop to perform a linear stretch / distortion

Hello hello,

I am looking for a technique that distorts a photo using the scheme shown below (before and after). In the desired after image, you'll note the following characteristics:

1. It "stretches" the image in two directions, horizontally and vertically about a single point.

2. It does so linearly, without creating any spherical or cylindrical distortion.

I know I'm not using the right vocabulary for this, which is why I'm including a photo of the desired final effect I'm looking for. (The reason that I have a photo is that there's an iOS app that creates this effect, but I want to do this in Photoshop because I need to light the scene with flash and I can't take the image with the app.)

And, to be clear on the before and after part: I printed the regular grid (below) out on a sheet of paper, taped it to the wall, and then took a picture with the app to get the "after" image below. I'm looking for a technique in Photoshop that distorts the grid in the same way the app does.

Any guidance on how to do this would be greatly appreciated. I've tried all of the tricks I could think of, and I still can't figure it out. Even help with the right vocabulary for this would be helpful, as I can keep searching other forums.