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Dynamic cameras in 2D 'Schmup' game

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Take a quick look at this video from the last stage of 1997's 'Einhander':


In general terms (I don't mean to provide several pages of code), how does one go about achieving that manner of 'dynamic' cam in a Schmup? Right now I have a very static 2D camera, but in Einhander it almost looks like they integrated 2D and, at least, the illusion of 3D. How do you go about that? Particularly using XNA? I'm thinking quaternions but I'm having trouble wrapping my mind around the process...



p.s. Forgot to mention the actual gameplay doesn't start 'til 1:20. The boss battle starting around 2:40 is particularly amazing to me from a technical standpoint.

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That's pretty clearly a 3D game through and through, which just happens to have its gameplay limited to 2 dimensions at a time. The gist of things is that everything is probably happening in 3 true dimensions, and the camera/player/enemies are simply forced into a 2D plane orthogonal to the camera vector.

There shouldn't be any necessity for quaternions, standard matrices should do just as well. Quaternions might carry their standard "advantages" as per usual over matrices, but matrix math is more straight-forward if Quaternions are an uncomfortable subject.

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