How can a game be 2.5D?
I have been told that when the game is basically a side-scrolling game with 3D elements in the background/environment, it becomes a 2.5D game. Is there any correct explanation for this term?
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Games are said to be in 2 dimensions, when you can only move in the X and Y axis (ie. left, right, up and down or similar).
3 dimensional games let you move in more more axis (usually the Z axis).
A 2.5 dimensional game is a game that works much like a 2 dimensional game, but usually allows you some limited control of the third (Z) axis. An example of this would be Little Big Planet, where you usually just move in the X and Y axis, but can step "into" the Z axis in a limited fashion (I think there are like 3 "planes", front, middle, back). There are also some fighting games that allow this.
This is not to be confused with games that are done with 2d or 3d graphics.
One correct interpretation is in Holger's answer. In more technical articles however, you may encounter a substantially different usage of this term.
More specifically, it indicates that the third dimension is represented in some restricted way.
Since there are no overhangs in the picture above, it could be represented in 2.5D.