# How can I do catenary curves between consecutively points?

Hi! I need catenary between this consecutively points. I made a pattern from this points for selecting “Point A” and “Point B”. But I couldn’t make serial catenary curves. I’m making this for creating a surface which is smooth transitions its peaks and pits. Like this:

Maybe my way is wrong, but I don’t know. I couldn’t handle it. Here is my documents:

growth deneme.3dm (113.4 KB)
Smooth Growth Curve Along Surface.gh (19.8 KB)

my take on this with kangaroo. There’s a bif room for improvement, it is nothing close, to be honest, but maybe you’ll find it usefull
Smooth Growth Curve Along Surface_dfytz.gh (53.4 KB)

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I’m very appreicated for your work. Actually this is really close to what I want. Can I adjust stretchness of cloth-like surface and making smooth transitions of height from outer edges from center? I have never used mesh before

Can we make this surface with only Nurbs objects? Because I don’t know is converting mesh to Nurbs friendly to production.

And the additional question: Do you think will my way work?

The idea is to turn it into mesh, then adjust the vertex position using the distance data from the curve.
The calculation may heavy.

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kinda works, but far from what you would expect

Smooth Growth Curve Along Surface_dfytz_catenary.gh (39.4 KB)
maybe if you could find another way of creating surface from these curves at the end. Now you need very high resolution for it to work properly

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Impressive, Li!

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Ah yes! I’m very appreicated for this. This solution is very very close to what I need. I have never used mesh but I think we can make its depth smoothly increasing from the edges to the center with closest point.

A question too: How can I convert this mesh surface to production-firendly? I can convert the mesh to Nurbs but there is so many polygons. So it crashed or slowed. I can reduce polygons but this time Nurbs surface being very angular (even converted without reducing polygons its still angular for production). I wish there is a way for making this surface with staying in only Nurbs objects.

Thanks so much for your work

Oh wow! This is exactly what I’m trying to make! But you showed me this is not working. Very very thank you. I think, I need to approach to this problem from a different way.

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Try to lower the length parameter to 0.5.
This parameter controls the edge length of the mesh face, so if you make it 0.5, that is 0.5mm in my GH definition. I found 0.2 is too much for me. My CPU is AMD 3700X, single core speed up to 4.4 GHz, the RAM is 32G.

How can I convert this mesh surface to production-firendly?
To my limited knowledge, many manufacturing softwares take mesh.
You can not convert it to Nurbs without compromising the accuracy of the creased edges.

I adjusted other parameters a little bit.

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I’m making this surface for a washbasin design. I’m thinking to use different patterns like this onto washbasin’s semi-wet surfaces. When I was intern in a ceramic firm, they have tried to mill mesh model with CNC. But the finish was triangular. I think the CAM program reads each face of mesh. This is too heavy process to mill.

I guess your work couldn’t get any better. Its finish is really same with which is in my head. Only problem is it’s mesh Maybe I should approach from different ways to solve this problem. Thank you so much

In fact I can do it by first converting Mesh to SubD and then SubD to Nurbs. But I don’t know is it friendly to CNC. SubD chipping some edges and making round corners of Mesh. Also this method is very very slow.

But this method works for simple Meshes.

My suggestion.
First, you need to convert it into a quad mesh using QuadRemesh.
Then, make it into SubD objects, keeping the edge creased is a must.
Third, build your final product using SubD.(or just change into a Brep and continue from there?)
Finally, change the Closed SubD objects into a Brep(Shown in the picture, just 3 steps).

So here, how to change it into a SubD is important. The first and second steps can be done at the same time using QuadRemesh. Just higher the edge length maybe to 2 (from 0.5), and use the guide curve and keep the edge creased. And one more thing, sometimes, the SubD will be broken after converting, maybe a hole or overlapping faces, so you need to repair it using the Rhino SubD function or just by hand.

This is the final Brep.

The setting I used:

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Quan Li, it is awesome! This surface is perfect. Thank you!

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If by any chance it would be made into a real thing, would you like to post a picture of that here?
I never saw this kind of pattern, and think this is a good idea and beautiful.

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Can I borrow your curves for some experiment?

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Sure! No need to ask I made it with Kangaroo2 solver, you can use that gowth simulation in the file.

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