Once upon a time, back in the ancient years of 2009 and 2010, Bungie was developing its final Halo game - Halo: Reach - with intentions to then go their own way. Microsoft created a new studio named 343 Industries to take over after the split from Bungie. 343 co-developed the Halo Legends animated series and worked with Bungie on Halo: Reach to learn the Halo development ropes, and then worked with Saber Interactive and Certain Affinity to develop Halo: Combat Evolved Anniversary. Halo Anniversary (2011) was the first appearance of the classic graphics toggle feature.
From what I’ve been told, the way it works is that modern hardware is capable of doing much more than simply running the old game engine with upscaled visuals, so Saber Interactive built a “secondary engine” to work in tandem with the original. This technology basically uses the extra memory and cycles to load and handle the computations needed for both old and new graphics simultaneously so you can hot swap between them with load time since both sets of graphics are loaded at all times. Saber also worked on Halo 2 Anniversary and brought their hot swapping tech to H2A as well.
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