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3D Isometric Camera Rotation - Seeking advice

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Blasphemy! How could a 3D implementation of an isometric view allow for smooth camera rotation? It can't. Aside for four possible viewing angles of an orthographic scene, all others are not isometric (they'd be axonometric). So now that I've got the technicalities out of the way, let me explain my situation. I am working on a simple 3D puzzle game that is played from an Isometric view. I want the player to be able to rotate around the center of the game "board" at 90 degree intervals. Gameplay is locked so that the player can only play at each of those 90 degree intervals, so all play will take place in an isometric view. I am at a loss for how to handle camera rotation around a fixed point while maintaining an isometric viewpoint. Most resources I have found deal with isometric mathematics that apply to 2D so a true camera rotation system is not something they'd cover. If anyone could provide some advice as to how to handle camera rotation with an orthographic scene I'd be greatly appreciative.

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Rotation 0:
: y goes from ylow to yhigh
: x goes from xlow to xhigh
: use tile/sprite rotations +0

Rotation 1:
: y goes from xlow to xhigh
: x goes from yhigh to ylow
: use tile/sprite rotations +1

Rotation 2:
: y goes from yhigh to ylow
: x goes from xhigh to xlow
: use tile/sprite rotations +2 or -2

Rotation 3:
: y goes from xhigh to xlow
: x goes from ylow to yhigh
: use tile/sprite rotations +3 or -1

Whether these rotations go clockwise or counterclockwise depends on which way your axes point when converted to screen-space. I'm sure you can figure it out.

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