How to design Horn shapes in Blender, using tractrix formula, and exponentials

How to design Horn shapes in Blender, using tractrix formula, and exponentials for the flare, as well as circle and elliptical mouths!?

The title pretty much says it all. I have tried to get python to write code, no success there yet. I am not sure how to execute math with the program in order to create surfaces.

If one had a tractrix profile of 2d, for example, one could rotate that around a circle to create a circle horn, but what If I wanted the mouth to be elliptical while the beginning of the line remain circle? how to program the transition mathematically?

Example************https://www.youtube.com/watch?v=Zz3NbflXZ3A&list=PLXsiVfmTaTKcGqdI0DlWx45BDGiXE-PJD&index=3

Welcome :tada:…

you may try the Z/XYZ-Math Surface function of the Extra Objects addon to directly type i some math formula…

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i got some algo for 2D tractrix
but not certain if you can work with if you dont know Python!

let me know

happy bl

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This is what appeared when I went edit mode; add>Math Function> XYZ MAth Surface

This is obviously the right direction and I am an obvious noob. Thank you so much. Now I have to figure out what formulas I need… the min/max/step features are self explanatory.

I was hoping chatgpt knew it well enough for me to kinda fake it till I make it lol… Seems like ChatGPT would of understood my request and the math rather easily, its a calculator… it also knows what I am try to manifest.

I feel like I’ve ran into a wall. The formulas I ask from chat gpt don’t work with blender. I thought tractrix curves where easy for something like ChatGpt

the shapes created here (XYZ Function) seem to be repetitive?

I need to create this
image
using math.

ChatGPT can’t even do elementary multiplication correctly consistently, so I think your hopes are severely misplaced. Is there any reason this has to be made with math? Because you could easily model this with a screw modifier in less than 5 minutes

I don’[t have to exactly copy a math formula, no idea what the screw modifier is. Are you sure I can do this with the screw tool? I mean the wall angles are consequential so in other words, the wall angles must acceptable, If not a tractrix curve and exponential curve will be desired, and then there’s the issue of creating an elliptical mouth at the big end and a round throat at the small end.
image

Yeah, it’s pretty simple:
Add some vertices:


Add a screw modifier and subdiv:

Rotate the top with Proportional Editing turned on (press O):

Voila:

It took longer to write this post than it did to do this, so it’s super easy :slight_smile: Tweak as needed

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I am at awe… let me process your instructions for second

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Fyi, I am super beginner, I am still trying to figure how to add vertices like you did…
I am trying…

Nonsense… All the math works in Blender…

Try Wikipedia instead:
image

In Desmos:

In GN:

Edit: fixed math…
File: Cone.blend (93.2 KB)

Good luck.

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ZeroSkilz please don’t leave! lol! I know I am far down on the food chain but I am willing do do the work, to become adept enough to execute what I need don’t leave lol! Please help (spoon feed) along the way lol!

Sorry… Power is about to go out… Hope others can help.
Good luck.

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I’m starting here

I made you a nodegroup you can use as a starting point. There’s a math input to which you can connect whatever formula, I added the one from Zeroskilz as well as a float curve for convenience. The top elliptical has a separate control.

horn
geoNodes_horn_v01.blend (963.4 KB)

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Is there a way for me to set the beginning radius?

sure thing, just use the float curve -
horn2
you can use math for it as well instead of a float curve, essentially all that input does is control the radius along the curve.

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I cant post anymore cause Ive reached my daily limit for a new user =(


something I am not doing right, but thank you for what youve helped me acccomplish so far!!

I think my issue is I have no control over z?

you can just open the .blend file I attached to my first post and play with it. should be all in there.

edit - yep, I called it math to indicate you can just use any formula instead of a float curve

1 Like