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2D squre to isometric formula

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Using only 2D affine transformations, how do you transform a square into an isometric view?

I found an article that shows using a 45 degree rotation and a 15 degree skew on both x and y, but I'm interested in the general formula for deriving how to do this.

I'd also like to be able to rotate the isometric view (so if there's a square centered at the origin, rotating about that origin, I'd like to be able to fake that from an isometric view)

Any ideas?

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