Perpendicular Parabolas.

Replies to This Discussion

Permalink Reply by Chris Tietjen on September 23, 2011 at 7:17pm

If you cut a true hyperbolic paraboloid with planes parallel to the xy plane you will get hyperbolic intersections (by definition), not circular arc ones.  How does this effect what you wish to do? 

 

Chris 

Permalink Reply by Colin Bachelor on September 24, 2011 at 7:16pm

I need the ends to connect to the circle to get that curve. Basically I want to be able to use the circles to deform the hyperbolic paraboloid. What I have modeled is one component of a series that gets mirrored from the center of one of the circles.

Permalink Reply by Chris Tietjen on September 25, 2011 at 6:21am

Here it is in Rhino.  Create the hypar using parabolas, extract some UV curves (or use planes to get intersections) from the asymtotes up to about halfway to the circles, get the arc of the circle for the final curve then loft these.  This gives one quarter of the final form.  Next use mirror/copy to complete.  Trim back along the intersections of the surfaces using isocurves and then loft.  In the very center at the saddle point use network surface.  This requires duplicating and splitting various curves.  I'm not sure how you would do all of that in GH.  Be sure to unhide in the 3dm to see construction lines.

 

Chris

Attachments:

• HybebrolicParaboloidToCircles.3dm, 445 KB

Permalink Reply by Chris Tietjen on September 25, 2011 at 6:39am

In the description above I should have said that I used network surface rather than loft in the second sentence. 

Permalink Reply by Chris Tietjen on September 25, 2011 at 8:27am

This is a much better result.  Here I trimmed out the saddle section of the hypar and then used the same curves from the above method to generate the transition surface to the circles.  I used blend to join up the pieces.  It's not perfect but looks pretty good in the environment map analysis.  This seems like it would be fairly easy, except perhaps for the blends, to do in GH.

 

Chris

Permalink Reply by Chris Tietjen on September 25, 2011 at 10:47am

Here's a screenshot of the hypar to circles solution with Grasshopper.  The environment map shows the transitions.  I'll post the definition later tonight.  I need to organize it so it can be easily understood.

 

Chris

Permalink Reply by Colin Bachelor on September 25, 2011 at 12:28pm

This is EXACTLY what I was trying to do! Can't wait to see how you did it in grasshopper :D

Permalink Reply by Chris Tietjen on September 25, 2011 at 1:43pm

Here's what I've got.  I was unable to get a trimming solution in GH so you have to bake the trim curves and the final modified hypar together and trim in Rhino. 

Chris

Attachments:

• HyparToCircles.gh, 30 KB

Permalink Reply by Colin Bachelor on September 28, 2011 at 4:39pm

Thank you Chris! This has been extremely helpful :D

I think one of the problems in my file was that i set up the grid in a way that the parabolic function couldn't go to the points I wanted it to.

The way you did the model was easier than what I was doing, so thank you very much :)

Permalink Reply by Chris Tietjen on September 28, 2011 at 5:34pm

Glad to hear that this was helpful. 

 

Chris

Permalink Reply by Dimitry A. Demin on September 26, 2011 at 6:29am

hyperbolic surfaces are also a kind of minimal surfaces in some cases. you can use kangaroo for the form-generation.



Permalink Reply by Jon on April 3, 2013 at 3:07am

hi dimitry,

i put a question about the reverse-way-to-make-a-hyperbolic-paraboloid-surface:

http://www.grasshopper3d.com/forum/topics/reverse-way-to-make-a-hyp...

i am so glad when u could have a look on this. thx!