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#1 2023-02-15 00:30:05

Registered: 2022-03-07
Posts: 75

Torus projection

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 ?

Thank you for helping me with the sphube-line intersection.
I would need some more time, there.


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