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Billboarding is what we do when we want something to face the screen,
e.g. a fire texture (if we go to the side and look at it, we don't
want it to be rotated and flat-looking - we want it to still face us).
Old 3D engines like Doom95 & Wolfenstein3D used this for stuff like
fire sprites and even enemies. Now it's often used for particles.

Thanks to Stefan Monov for sending this information.