There was a full 15 minutes of true CGI in the first film, an incredible accomplishment back in 1982. It was in fact too much CGI for any one company to produce, they had to hire 4 different companies to handle the workload (MAGI, Triple-I, Robert Abel and Associates, and Digital Effects). They broke up the VFX scenes between them, trying to play to the individual strengths of each company's rendering system. If you pay close attention to the film you can tell which scenes were done by which company.
The backgrounds shown during the live action scenes (with actors) were mostly hand drawn.
Thanks for that link. I went back and watched a few clips. My goodness
how that's different from my memories of 1982! Weird thing is I can't
remember that I saw that 15 minutes of embryonic CGI as being
"computer graphics", long before I'd played Wolfenstein and having
only seen vector graphics in arcade consoles at the pier. How our
perceptions have changed.
The backgrounds shown during the live action scenes (with actors) were mostly hand drawn.
Much more info here https://www.youtube.com/watch?v=Tm4i6D3XXBQ