The torus is one of few surfaces which can be parametrized with one patch.
It is the easiest example surface for the study of geodesics (see anaglyphs below).
The torus can be thought of as a rectangular piece of rubber, rolled and stretched around.
The geodesic surrounds the hole twice and swings up and down 5 times.
The geodesic surrounds the hole ones and circles the torus 4 times.
The geodesic is a 7-2-knot on the torus.
The geodesic is a 11-2-knot on the torus.
The geodesic is not quite asymptotic to the inner equator. it approaches
the equator from above and leaves in the same direction.
The geodesic is not quite asymptotic to the inner equator. it approaches
the equator, crosses it and leaves to the other side.
torus st
torus sw
Torus Surface Parametric Equations
halftwists := Round(ff);
x = aa * (cos(v) + u * cos(halftwists * v / 2) * cos(v));
y := aa * (sin(v) + u * cos(halftwists * v / 2) * sin(v));
z := aa * u * sin(v / 2);
