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I'm after the equations of the projection
of a rotated torus on the xy-plane.
Imagine you have a donut,
which is shaped like a torus.
Now you symetrically poke it on a stick,
so the stick goes twice through the donut.
You place the stick before the x-axis and rotate it
with a light source before it.
See the borders of the shadow of the donut ?
I would like to find the equations of them.
If the donut is paralel to the xy-plane, you have 2 circles.
One bigger and one smaller.
If the donut is paralell to the xz-plane, you have 1 circle,
cut, pulled apart along x and a rectangle in between.
What if the donut is rotated by 45° ?
What if the donut is rotated by another angle ?
@Bob:
Thank you for helping me with the sphube-line intersection.
I would need some more time, there.
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