Extracting Asymptotes from Hyperbola

Hello,

I know it is a bit "back to front", but I already have a series of parametric hyperbola from catia and was looking for a quick way of plotting their asymptotes. Does any one know an easy way to extract them in GHopper - I have searched far and wide with no luck!

Look forward to hearing...

Regards,

Replies to This Discussion

Permalink Reply by Andrew Heumann on March 24, 2014 at 9:40pm

can you post the rhino geometry?

Permalink Reply by michael wilson on March 24, 2014 at 9:58pm

Sure, here it is. Thanks for taking a look.

Regards,

Attachments:

for_GH_discussion.3dm, 194 KB

Permalink Reply by Jacek Urbanowicz on March 25, 2014 at 12:03am

Can you send Rhino 4 version?

Permalink Reply by Andrew Heumann on March 25, 2014 at 12:34am

equation of a vertical hyperbola in the XZ plane:

X^2/A^2 - Z^2/B^2 = 1

given a couple points on your hyperbolas we can solve for A and B. One easy point is where Z = 0 - if you do the algebra, x = a at this point. Pick another point, plug in x, y, and a, and solve for b.

To verify these equations are correct, you can plug in the parametric equations of a hyperbola and re-calc the points - that's x = a*cosh(t) and y = b*sinh(t).

finally, the equations of the asymptotes of a hyperbola are as follows:

z = -b/a * x

z = b/a * x

which are easy enough to plot. see the attached definition for the grasshopper solution.

Attachments: