algorithmic modeling for Rhino

How I can transfer this parametric demonstration of Mathematica into Grasshopper?

Hello everyone,

I am an architect, and trying to transfer this specific parametric demonstration (which is a parametric minimal surface) into Grasshopper; so that I'll able to manipulate both the shape and its surface. 

However, I don't have that much knowledge about both grasshopper and Mathematica.. I mean I can only make assumptions and think about relations of certain functions but that's all. 

If you can help me on this, I would appreciate it so much. 

You can see a screenshot of the code and model of the demonstration from mathematica in attachment.

And here is the mathematica code;

Module[{\[CurlyEpsilon] = 10^-6, c1 = Tan[a1], c2 = Tan[a2],
c3 = Tan[a3], c4 = Tan[a4], c5 = Tan[a5], c6 = Tan[a6]},
c6 Sin[3 x] Sin[2 y] Sin[z] + c4 Sin[2 x] Sin[3 y] Sin[z] +
c5 Sin[3 x] Sin[y] Sin[2 z] + c2 Sin[x] Sin[3 y] Sin[2 z] +
c3 Sin[2 x] Sin[y] Sin[3 z] + c1 Sin[x] Sin[2 y] Sin[3 z] ==
0], {x, \[CurlyEpsilon],
Pi - \[CurlyEpsilon]}, {y, \[CurlyEpsilon],
Pi - \[CurlyEpsilon]}, {z, \[CurlyEpsilon], Pi - \[CurlyEpsilon]},
Mesh -> False, ImageSize -> {400, 400}, Boxed -> False,
Axes -> False, NormalsFunction -> "Average",
PlotPoints -> ControlActive[10, 30],
PerformanceGoal -> "Speed"]], {{a1, 1,
"\!\(\*SubscriptBox[\(\[Alpha]\), \(1\)]\)"}, -Pi/2 - 0.01,
Pi/2 + 0.01,
ImageSize -> Tiny}, {{a2, 1,
"\!\(\*SubscriptBox[\(\[Alpha]\), \(2\)]\)"}, -Pi/2 - 0.01,
Pi/2 + 0.01,
ImageSize -> Tiny}, {{a3, 1,
"\!\(\*SubscriptBox[\(\[Alpha]\), \(3\)]\)"}, -Pi/2 - 0.01,
Pi/2 + 0.01,
ImageSize -> Tiny}, {{a4, 1,
"\!\(\*SubscriptBox[\(\[Alpha]\), \(4\)]\)"}, -Pi/2 - 0.01,
Pi/2 + 0.01,
ImageSize -> Tiny}, {{a5, 1,
"\!\(\*SubscriptBox[\(\[Alpha]\), \(5\)]\)"}, -Pi/2 - 0.01,
Pi/2 + 0.01,
ImageSize -> Tiny}, {{a6, 1,
"\!\(\*SubscriptBox[\(\[Alpha]\), \(6\)]\)"}, -Pi/2 - 0.01,
Pi/2 + 0.01, ImageSize -> Tiny}, AutorunSequencing -> {1, 3, 5},
ControlPlacement -> Left]

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Replies to This Discussion


1) Watch thislink for any plot function from mathematica to grasshopper

2) open this gh file for your model. Create a folder with name Mantis on the C drive Or change the destination link of the export path input. 


Hummm..  What component is after Mesh and the following after the first pipeline?


1- the first component from left is for welding the vertices ---> use Edit mesh plugin

2- the second one is for smoothing the mesh by adding a kind of subdivision ----> use weaverbird plugin

Ahhhhh! Ok! I'm crazy looking for this component in Grasshopper! LOL

Thakns! :D


Thank you! I think it is what I'm looking for a long time.

I created a folder named Mantis on the C drive just like you said but I'm having this error, related with something else than the code itself but I don't how to solve it; 

1. Solution exception:Could not load file or assembly 'Wolfram.NETLink, Version=1.2.1740.23578, Culture=neutral, PublicKeyToken=null' or one of its dependencies. The system cannot find the file specified.

Can you help about this?

Maybe, the solution is the real "Wolfram.NETLink.dll" in Mathematica. Looking for C:\Program Files\Wolfram Research\Mathematica\10.4\SystemFiles\Links\NETLink, then copy the dll, and, now, go to C:\Users\YOUR ACCOUNT\AppData\Roaming\Grasshopper\Libraries, AND OVERWRITE ! :D Easy!

The solver is the real dll version from your Mathematica path!


Thank you it worked!

Is there any way to work on the parametric model' (came out by the equation) surfaces/vertices/curves in grasshopper?

Hummm. The formats to export in Mathematica are meshes.. Is better transform to surfaces or nurbs. But, Rhino, per se, ist no good.

Perhaps, other plugins, (to buy...), but trial mode can solve this.

I actually want to work on the parametric model.

Let's say deconstract brep and assign functions to the equation model in grasshopper so that it will work parametric. 

I don't know if it makes sense combining the solution to debrep but as an example for my purpose ;

In the export to rhino, you have a mesh, any litghs, and a curves. Try to manipulate this. Delete the mesh and ligths. My work is more complex: Topological Surfaces non orientables, like Steiner surfaces, Móbius band o Kleiner bottle.  Very funny! All the model whit naked edges, or mainfolds, etc.. :D






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