How can I circle fit 6 points and find the center?

I am trying to approximate the center of a bone (the humerus) to establish a long axis for motion tracking. To do this I have "digitized" points around the humerus at 2 heights to try to make 2 circles. By digitize I mean that an x, y , and z point exists in space for each point that I have "digitized". I have 6 points in space for each height, so 12 points overall. I was wondering how fit a circle around each set of 6 points and find the exact center (x,y,z coordinates) of each circle so I can create a vector that extends through the 2 points. Any help would be appreciated,thank you.

Answer 1

[D. Plotnick]

Least squares fitting: examples in

2D: https://www.mathworks.com/matlabcentral/fileexchange/22643-circle-fit--pratt-method-

3D: https://www.mathworks.com/matlabcentral/fileexchange/34129-sphere-fit--least-squared-