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Think origami. A UV map is like a flattened (unwrapped) 2D shell (skin) of your 3D mesh. If you were to cut out the map and fold it along the mesh lines, the result would be your 3d model. The U,V floating point values range from (0,0) to (1,1) The upper left corner of the UV map is (0,0) The lower right corner is (1,1) Each vertex in a mesh ...


Edit: my original solution didn't work. The eigenvalues of the mappping matrix only correspond to the scale factors for special orientation cases. Fortunately, I've found a solution that seems to hold in general. If we take a collection of unit vectors in UV space and map them into 3D, they will form an ellipse, whose major and minor axes correspond to the ...

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