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TL;DR: process collisions Manhattan-distance style http://en.wiktionary.org/wiki/Manhattan_distance, each axis independently one-by-one (move in X, then move in Y, then in Z, rince and repeat) properly rounding each axis before processing the next. AABB / Voxel collision systems work the same way old tile-based 2D games did, you add a 3rd dimension but ...

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