Figure 8

Replies to This Discussion

Permalink Reply by Vittorio Menna on March 7, 2010 at 12:09pm

hi tyler,
i made a quick definition using the parametric equations i found on wikipedia - http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29
i hope it can help you
vittorio

Attachments:

• figure_eight.jpg, 248 KB
• figure_eight.ghx, 100 KB

Permalink Reply by Daniel Piker on March 7, 2010 at 2:51pm

Why not just place a clockwise and anti-clockwise helix next to each other, then take one turn alternately from each:

Or if you want to get mathematical about it, Bernoulli's Lemniscate has the simple parametric form:

x=cos(t)/(1+(sin(t))^2)
y=sin(t)*cos(t)/(1+(sin(t))^2)

So if you just then set z=t, you would have a rising 'figure 8 spiral' curve that you could use to sweep your surface.

Permalink Reply by Vittorio Menna on March 7, 2010 at 6:18pm

daniel is right,
i played a little bit around with it, here it is:

Attachments:

• bernoulli's_lemniscate.jpg, 173 KB
• bernoulli's_lemniscate.ghx, 121 KB

Permalink Reply by Tyler Zalmanzig on March 7, 2010 at 8:15pm

Thank you for the reply I will give that a shot and see if I can make it work for my project.