Optimize Center of Circle given noisy data points on arbitrary Plane?

I don't seem to find an algorithm to calculate the center of a circle given a set of noisy data (on the circumference of the circle) on an arbitrary Plane in 3D.

I did try different approached as to calculating the center by only taking 3 points at a time and then averaging the centers, yet I believe there must be a better solution to optimize the center by minimizing the distance to all points. Does anyone have an Idea?

Any Ideas or approaches would be highly appreciated!

Answer 1

[Torsten]

https://de.mathworks.com/matlabcentral/answers/475212-circle-least-squares-fit-for-3d-data

[Peter Bauman]

perfect, thanks a lot! works like a charm. I don't know why I did not find that post

Answer 2

[Matt J]

Go to the examples tab of this FEX submission

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

and scroll down to the section, Fitting a 2D Shape to 3D Points.

Answer 3

[Image Analyst]

Can youi adapt the FAQ from 2-D to 3-D?

https://matlab.fandom.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data?