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I'm not a computer graphics expert (though have at least a little experience with video game dev), but ~~considering Toy Story uses ray-traced lighting~~ I would say it at least depends on whether you have a ray-tracing capable GPU. If you don't, probably not. I would guess you could get something at least pretty close out of a modern day game engine otherwise.
Ray tracing at 24fps is not a big ask for a modern gaming PC.
Full raytracing (path tracing) might be.
I think they can do it for very basic looking games like Quake 2.
That said, I doubt you'd actually need full RT for visuals like Toy Story 1. Or indeed on most things.
They got pretty good at faking most of it. RT can basically just be used for reflections, shadows and global illumination and most of us wouldn't notice the difference.
Maybe, what I said is admittedly mostly based on the experience I have with Blender's Cycles renderer, which is definitely not real time.
But you could definitely get something that looks as good (or better) as Toy Story using eevee.
Did Toy Story use ray tracing back then?
AFAIK, A Bug’s Life is the first Pixar movie that used ray tracing to some extent, and that was for a few reflections. Monster’s University is the first Pixar movie that was fully ray traced.
You're right, it looks like they didn't (at least for most things?). They do mention raytracing briefly, and that the sampling stage can "combine point samples from this algorithm with point samples from other algorithms that have capabilities such as ray tracing", but it seems like they describe something like shadow mapping for shadows and regular raster shading techniques ("textures have also been used for refractions and shadows")?
Interesting paper. I skimmed through it quickly, but it seems like they wanted to avoid relying on ray tracing.
Most of the paper is way above my understanding, so I’m not qualified.
Physically Based Rendering (the freely available book) won its authors a special Academy award in 2014. That book is still the teaching standard for ray tracing so far as I know. In the intro, they discuss Pixar adding ray tracing (based on pbrt) to their RenderMan software in the early 2000s.
A Bugs Life and TS2 could have benefit from some of that, but I'd guess Monsters Inc was the first full outing for it, and certainly by Nemo they must have been doing mostly ray tracing.