##They Didn’t?
If you watch the scene in the movie where the pilots are briefed on the Death Star plans, you see that the blueprints show this:
The actual Death Star looks like this:
Those plans are not correct. One obvious difference is that the blueprints show the equatorial trench running through the middle of the main dish, whereas the real Death Star has its dish slightly above it.
Although Jyn guessed that her father chose his pet name for her, “Stardust,” as the code name for the Death Star plans, her assumption was clearly mistaken. The plans that she stole, codename Stardust, must have been a rejected proposed redesign of the Death Star plans. It could not have been the original version, since we saw a blueprint that looked closer to what was built in Episode III. (If Galen Erso ever had a bastard child, he might have named the design the Imperial brass and bureaucracy and the rest of the committee got their fingerprints on after her.) By good luck, the Achilles’ heel from Stardust made it into the final design. But luck it was.
The Real-World Explanation
The CGI animation was the work of by Larry Cuba and others at the Circle Graphics Habitat at the University of Illinois at Chicago, later renamed the Electronics Visualization Laboratory (EViL).
The anonymous, unsourced claim made on Wookieepedia that the CGI was done at the Jet Propulsion Laboratory and left uncredited so as to prevent the artists’ employers from finding out they’d done it on work computers is completely false. Larry Cuba does have a screen credit for “computer animation and graphic display,” although his collaborators and the university do not. The institution was fully aware of the project and uses the fact that it did the CGI for Star Wars heavily in its marketing to this day.
This documentary by Cuba describes the process. As he explains (at 1:15), the Death Star model had not yet been constructed, so he was working from a matte painting in which the dish was in shadow as his reference.
The original PDP-11/45 that created the wireframe model of the Death Star is still up and running fully operational (with video of the old-school minicomputer).
Out-of-universe, and probably in-universe as well, the plans depict an earlier concept of the Death Star, different from what was constructed.
