Dear João Baker

please find the attached formulas

I hope it will help you

best wishes

Dear Ahmed,

Thanks for your help.

Is these formulas applied to find a cylinder center considering minimum cylinder circumscribed or a least square cylinder?

Regards,

João Baker

Dear Joao:

I am afraid that the equation Ahmed provided will work only if you have the set of points evenly distributed around the center (i.e. sampled at equally step angles)  If so then it will provide the average circle (i.e. not the circumscribed nor Inscribed circle). In this case this is the easiest way to do it.

To solve your stated problem accurately you need to do more complicated calculations by generating sets of  principle equations for each 3 points as we know that in Euclidean space, there is a unique circle passing through any given three non-collinear.

Perhaps the basic info provided in

en.wikipedia.org/wiki/Circumscribed_circle

may help you to understand the principles of this issue.

Brief investigation can also be found in

http://www.vnulib.edu.vn:8000/dspace/bitstream/123456789/3926/1/sedevtK410-01.pdf

But again this is very basic investigation.

I have just forgot to add, in case of calculating cylindericity (cylinder is a 3D shape) rather than roundness (circle of 2D) then you need to extend the solution into 3D space rather than 2D (X-Y cartesian presentation). 

Dear All,

Please find the attached file contains comparison between proposed formulas and Least square method for the case study in the paper

best wishes