How could I get the coordinates of the circumscribed circle giving the 3 points coords ?

Hi All

I have the coordinates of 3 points thrgouh which, a circle should pass . Having the coordinates of the points in 3D, how could I have the coordinates of the center of circumscribed circle ?

also : if one of the points has some deviations and causes a circumscribed circle couldn't pass through the 3 points, is there a way to determine the required coordinates of the third point in a way that the circle could be constructed to find the deviation in space ?

[John D'Errico]

Um, given any three points in space, you can always find a circle that passes exactly through three points UNLESS they are collinear. That would be the only exception. But you ask what if you have noise. Noise generally won't make points collinear - in fact, that event has essentially zero probability.

Answer 1

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/55304-best-fit-3d-circle-to-a-set-of-points

[Walter Roberson]

https://www.physicsforums.com/threads/equation-of-a-circle-through-3-points-in-3d-space.173847/

https://math.stackexchange.com/questions/1076177/3d-coordinates-of-circle-center-given-three-point-on-the-circle

Answer 2

[Image Analyst]

See the FAQ: How to create a circle and How_can_I_fit_a_circle_to_a_set_of_XY_data?

[Walter Roberson]

That is 2d though.

[Image Analyst]

True. Can you change the FAQ to add the 3-D case?