# Air Pot and Complex Functions

When a friend of mine asked me to model a vase for him, I discovered that the geometry of the vase is very similar to the imaginary plot of the logistic function.

I think I’ve already made some progress in my first attempt at plotting it, but sure that I’m definitely missing some information on complex function analysis I turn to you in the forum hoping to ignite your curiosity as it did me.

I would like to know how to obtain the graph in the middle, as I’m not able or don’t understand why I cant plot it.

Also, I would like to know if there are general guidelines to iterate a the graph of the function by tweaking the equations.

Airpot.gh (17.2 KB)

Where is the vase?

Just to achieve similar geometry I think making it as a mesh then converting to SubD would be far simpler.
If you do want to explore plotting functions of complex variables though, the sort of contour plot shown in your Mathematica screenshot can be done in GH by converting the vertex coordinates to a complex number, taking a function of that and moving the vertices of a mesh vertically by the result, like this:

complexcontour.gh (10.6 KB)
The same will work for other complex functions.

No thickness, no bottom, no logistic functions.

air_pot_2021Feb16a.gh (26.9 KB)

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On the error that you are getting I don’t really know what is happening, I don’t have quad panels in the script. I used it, but it’s not there anymore so I don’t know why are you getting that.

Anyway I had already tried a easier way as well, but I wanted to try with maths only

Your script is really good! I will look into it.

My ‘U Count’ slider should be configured to generate only even integers.

I can’t learn anything from a screen image of your code, posting a GH file is always better.

Your rendered geometry shows that you cut holes into the cylinder instead of the subsurface pieces I used, and I’ve made that very small change to my model as well (below).

air_pot_2021Feb17a.gh (27.0 KB)

This is definitely a case where thicken must happen on both sides of the surface. Would be nice to see a thickened mesh version of this.

Hi @greeso :
here a parametric surface with a possible NURBS topology of such a shape (parametric equations in the notes). But the pattern on a vase I would generate from SubD primitives Parametric_vs_SubD_jM.3dm (1.5 MB)

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You’re right, I was sorry it was still a bit rough and I only took one screen. (I attach it below)

However your approach of subdividing the surface is much better.
I’ll try to see if I can offset the surface in order to print it, as you suggested!

AirPot_17022021_1.gh (4.1 MB)

As the others above have shown, it is certainly easier to model it in SubD or parametrically, but the similarity still fascinates me.

Thanks for the tip and the script, I’ll look into Mathematica aswell

4.1 MB?! Wow, what’s in it? Oh, I see, an internalized copy of what the model produces? Ouch!

Seems to work without the plugin?

I thought it would be better to save time calculating the surface rather than from the internet connection my bad