# Best Fit Cylinder to Single-curved surfaces?

Hello everyone,
I got into the problem of finding the best fit cylinder for single-curved surfaces.
This problem is not new, and I found a solution for it from 2017:

To better understand the solution I created my own grasshopper definition, which you may find attached.
240525 Curvature 2 with axes from hulls - CLEAN .gh (32.8 KB)

What I want to know: Is there a better solution for this?
Especially one that could work on several surfaces at once?

The current solution relies on a series of convex hulls to find the axis of the cylinder, but I find it difficult to adapt for several input surfaces.

Kind regards,

Hi Bogdan - I might extract an isocurve from each direction of the underlying surface and sample each with some points - or check for linearity first - then try to fit a circle to the points sampled.

-Pascal

Hi @pascal ,
I already tried that. It seems like the best fit curve is not parallel with the isocurves. This is visible by both comparing with the above solution and also with ânaked eyeâ observation.

After some PathMapper work I adapted the above definition to work on several surfaces at once.
Hereâs the updated file:
240526 Curvature 2 with axes from hulls - Multiple Srf Input- CLEAN .gh (53.0 KB)

@pascal , finding the best fit cylinder optimizes the manufacturing work for single-curved surfaces by using the radius to mechanically bending them in one direction first.
After this initial bend, it is much easier to adjust the torsion manually by twisting the edges into place.
This method can be used when building things like ships, planes, facade panels on Frank Gehry buildings etc.
Therefore I would still like to have a McNeel grasshopper component for it.
Should I hope for one coming in the near, or distant future ?
Kind regards.

I found a much faster method using the average Osculating circle.

240527 Average Osculating Circle.gh (291.2 KB)

Iâm trying to put something upâŠ but Iâm going for a method that use points only as input.
Using osculating circles is possible only when you have a nurbs surface.
Also your first method, it uses normals. You might not have normals.
Only points.
A point cloud, a 3d scan, etc.
Building up a method for surfaces only seems a bad investment, as you will still lack for a method when meshes or pointcloud will appear.

Yes, that is very true for the osculating circles. I am lucky to have the surface, but when you only have a point cloudâŠ not working anymore.

Based on this and my lack of knowledge, could something like this be viable when the current method is still a âguessâ?

Using patch from points, âno surfaceâ:

Noh, because the UV point at 0.5 ; 0.5 does not necessarily best describe the curvature of the surface. The curvature changes along the surface, therefore you have to find the average.

Also the best curvature direction is not parallel to the U nor the V curves.

The initial surface is not a cylinder.
It is defined by curves in one direction and lines in the other direction.

So, with my method:
I am taking sample points on the surface.
Create some Osculating Circles for those poins (Osculating circle - Wikipedia)
Find the Average Radius for them.

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Makes sense - you did say you were fortunate to have a surface, and that youâll be applying this to multiple surfaces. Are these other surfaces similar to the one in this file, meaning your current method should be sufficient?

Or, as you/Riccardo discussed, will you be working with point sets where a reference surface isnât present?

This makes me curious about âshape detectionâ (equally ignorant) when dealing with point clouds.

For a quickie, I baked the 50 points you populated the surface with, turned them into a point cloud, and exported them as a .ply to use within CloudCompare. It has an option to compute normals, and then use âshape detectionâ - which can be told to fit primitives, such as a cylinder, plus other parameters. Tried it. Didnât work

For me it is enough at this point using the average Osculatig Circle. I have curved nurbs surfaces which are just torsioned.
@maje90 said that he would like to try something using only points. But in my case, I have what I need.

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Ok, soâŠ local normals in a way or another must be found.
Math way probably go there too, but way too complex (eigenvalues, etc etcâŠ)

Hereâs a hack (that maybe also other have done, I did not check otherâs work ):
pick the normals (or calculate a raw equivalent as I did here) and use those normals as points for a circle fit operations. The plane of that circle is a good initial guess!
(if your starting points+normals are from a perfect cylinder, this step should already return the original cylinder plane!)

Grouped in this definition:

fitcylinder 003.gh (51.9 KB)

Then the rest is just thinning the result with some brute force iteratedâŠ

This whole script heavily rely on Rhino/Grasshopper circle fit to points function/component.

PS doing the same trick by fitting normals as points with circle fit but while searching best fitting cone surface, should be âsimpleâ as the resulting circle center would result displaced from 0,0,0 (while for cylinders it should always converge to 0,0,0âŠ). As the circle is unitary, calculating the initial guess of the cone angle should be an extremely simple step.

This probably is trivial tooâŠ

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