You really don't develop completely new engines very often unless you are in the buisness of making engines for other people. It's always going to be a gorgeous frankenstein of the previous one, with certain systems gutted and completely redone and such.
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Didn't they mention building a complete new engine for Destiny in one of the videos?
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I obviously can't speak for Bungie, but I just know that it takes a crap ton of work to actually create a completely new engine from scratch. More likely than not, they redid a specific component of the engine or modified a specific component of the engine, but things like Physics and such you don't really touch or mess with.
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I believe Bungie uses the Havok proprietary physics engine anyways. The proper answer probably lies somewhere between the two. You NEVER throw out all of that work you put into an Engine.
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Even if you "start from scratch" a lot of programming relies on re-using algorithms for already fixed solutions, so it's never "completely new"