Why is this? I thought the z axis would normally be considered up? Is there a reason?
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As others have said, it is an arbitrary convention. But here’s how it arises naturally, and in OpenGL (not specifically relevant to XNA):
If you have a 2D image displayed on a monitor, it has X and Y coordinates and the Y coordinate is up (or perhaps down). If you have this 2D image be a projection of a 3D scene, then you gain a Z coordinate; keeping the coordinate transformation as simple as possible, Y is still up (and Z is outward).