Enneper surface

I am trying to recreate the Enneper surface seen in the image below...

I admit right off the bat that I have no clue how to achieve this. I was playing with the lunchbox plugin and researched algorithms from http://mathworld.wolfram.com, but did not get anywhere. Does anybody know how I can deform the typical enneper wing to something more pointed as seen below.

Replies to This Discussion

Permalink Reply by Chris Hanley on July 18, 2017 at 4:39pm

A fairly quick approach might be to bake an enneper surface into rhino, and then in Rhino, use cageedit to push some control points around and see how the shape responds to being modified. From there, you could figure out which approach you might take to modifying the shape.

There are a few posts the speak about various mathematical surface creation techniques.

Permalink Reply by Oliver Hampel on July 20, 2017 at 7:50am

Hi Chris,

Thanks for taking the time to answer my questions. This sure is a solution that works, but I was hoping for an all grasshopper way.

Oliver

Permalink Reply by Kim hauer on July 20, 2017 at 10:51am

there is a GH way!, please do some searching at this forum

Attachments:

Parametric EQ 11.gh, 14 KB

Permalink Reply by Oliver Hampel on July 21, 2017 at 11:07am

This what I was looking for! Greatly Appreciated!!!

Permalink Reply by Juan P. López Coronel on July 21, 2017 at 10:22am

I like the paths proposed by Chris and Kim.

They are very appropriate.

Permalink Reply by Kim hauer on July 21, 2017 at 11:02am

thanks Juan, for showing us how to manipulate the container of the Enneper, could you please post the revised script. I would find it useful to add this feature, when playing with other parametric surface formulas.

Permalink Reply by Oliver Hampel on July 21, 2017 at 11:08am

Awesome!!!

Permalink Reply by Chris Hanley on July 21, 2017 at 11:44am

A search of this forum for "mathematical surfaces" will most likely turn up a few various examples and approaches. There is a free tool called k3dsurf(?), (I think...), that has a bunch of parametric surfaces and their corresponding equations. It's a good exercise, (if the goal is to learn how to translate the equations into gh), to find one and try to translate it into GH using an example file like the one posted above.

Permalink Reply by Oliver Hampel on July 21, 2017 at 11:55am

That's what I struggled with... The translation of an equation found on any of the online resources into a GH readable format. Thanx Chris

Permalink Reply by Chris Hanley on July 21, 2017 at 12:02pm

There are much more elegant ways to accomplish this now, but here is a file I used when I was experimenting with translating the forms from K3DFSurf into GH. It should be considered a starting point, certainly not the ultimate resource.

Attachments:

20120402_MathematicalSrfs_CAH.gh, 45 KB

Permalink Reply by Kim hauer on July 21, 2017 at 3:28pm

thanks Chris for your example. The GH script, I posted, involved nothing less than a simple cut and paste of the same K3DSurf equation code for x,y, & z :)

Permalink Reply by Juan P. López Coronel on July 21, 2017 at 4:01pm

Very good your file Chris.