I was wondering if anyone could help me to determine the math behind how a toric generator produces its cross curve. I have attached a diagram of a generator wheel as if the person were looking at it straight on as opposed to from the top. As you can see, as the angle between the base and cross increase the radius of the right side of the wheel decreases, which causes the cross curve to increase. Another analogy is if you hold a coffee cup with the mouth facing you you see a complete circle, if you rotate the cup to the left it creates an ellipse. Mathematically why does this happen?
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