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I'm confused, why does M^-1 transform the triangle into the unit triangle and the ray into an orthogonal ray? And by unit triangle, do you mean the one shown in the third picture on this slide, or the right triangle shown previously?


I also don't quite understand why the ray will be back project to the orthogonal direction. Is there any intuition for that?


Why does M^(-1) transform ray's direction to be orthogonal to the plane?


What is the "z-axis" on the third graphic? Like instead of the X,Y,Z on the second graphic we have (U,V,????)