How to make curved line into torus?

  • #1

Main Question or Discussion Point

Greetings,

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

where

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.

Thanks
 

Answers and Replies

  • #2
336
0
A comparison of the equations suggests that we set R=2, r=1 & (u,v) =(2t,3t).
 

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