parabolic curves with curved crests

Hi All,

I have had a look thoroughly through the formations of my ferrofluid experiments. I think I would be better suited to creating a formation on grasshopper with a hexagonal grid rather than a radial grid. So I have made a start and I began with a catanary curve and I was successful but I do not feel that it represents that pattern of the fluid. I think that the parabolic surface would be better suited. I have had a look on grasshopper 3D and saw your link and I would like to persue it further.

http://www.grasshopper3d.com/forum/topics/parabolic-profiles-in-space

However, because of the pointed nature of the fluid, I need to create a pointed parabola with a curved crest.

My question really covers two points:

1) how can I create a parabola with a curved summit.

2) is it then possible to loft a single parabola making it 3D.

From here i need to be able to modify a group of these points so that points on a flat surface can be extruded into a parabolic field.

Any help would be much apprecicated

Attachments:

ferrofluid-525.jpg, 46 KB

Replies to This Discussion

Permalink Reply by WILLIAM GARFORTH-BLES on October 14, 2012 at 10:38am

Thinking about it further, perhaps if I could create a sine wave, this could help me create the ferrofluid pattern, what do you think? I am also unsure of how to manipulate the height of the deformation to simulate bring the magnet closer to the fluid.

Permalink Reply by Arthur Mamou-Mani on October 14, 2012 at 11:53am

Hi William,

Great experiments and fantastic geometry!

There must be a parametric equation describing the behaviour of ferrofluid under a magnetic field. I have started a thread in a mathematics forum. It seems the Maxwell's Equations and Navier-Stokes Equations were used for it (although I am not sure how they are combined). Once you have the parametric equation, you can represent it using the Isosurface component in Millipede.

For the "pointed parabola with a curved crest" I tried to do it using simple curves and fields in GH.

Have a look at my initial results on the file attached and image below.

Hope that helps and looking forward to seeing how you turn this to 3D!

Attachments:

William.3dm, 44 KB
William.gh, 9 KB

Permalink Reply by Arthur Mamou-Mani on October 14, 2012 at 2:14pm

Correction to my reply based on the answers in the physics forum:

"You won't need the full Navier-Stokes equations since the problem is static. Neither will you need the full Maxwell equations. That should simplify the problem a lot. You'll also need equations describing the interaction between the ferrofluid and the field."

You already have the field in 2D with the definition so i guess you just need to make the field 3D and find a more suitable geometry to represent the bumps.

Permalink Reply by TheChosenOne on October 14, 2012 at 2:09pm

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