|Mar22-10, 03:02 PM||#1|
How to make curved line into torus?
I am trying to figure out how to modify the equations for a trefoil knot to make it toroidal.
A trefoil knot is:
x = (2 + cos 3t)cos 2t
y = (2 + cos 3t)sin 2t
z = sin 3t
A torus is:
x(u, v) = (R + r cos v) cos u
y(u, v) = (R + r cos v) sin u
z(u,v) = r sin v
u, v are in the interval [0, 2π),
R is the distance from the center of the tube to the center of the torus,
r is the radius of the tube.
|Apr9-10, 05:58 AM||#2|
A comparison of the equations suggests that we set R=2, r=1 & (u,v) =(2t,3t).
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