# How do I find a center of rotation having a set of 3D points ?

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Aurélien Thomas on 3 Mar 2020
Answered: Image Analyst on 3 Mar 2020
I have to find the position of a center of rotation for an object. For that I have the X,Y and Z coordinate of my object.
To clarify : The coordinates are from a pendulum oscillating and I have to find the center of the pivotating link
I haven't found a solution yet and I don't really know how to proceed.

#### 1 Comment

James Tursa on 3 Mar 2020
You have 3D coordinates of the endpoint? Can't you just fit a circle/sphere to those points and then the center of the circle/sphere would be your pivoting link?

Image Analyst on 3 Mar 2020

Stijn Haenen on 3 Mar 2020
If each point represent the same amount of mass, the center of rotation is just the average position of all poisitions, when each point has its own mass you should use this formula to compute the center of mass:
R=1/sum(m_i)*sum(r_i * m_i)

#### 1 Comment

Image Analyst on 3 Mar 2020
The center of a circle is not at the center of the average of points in some arc that's a portion of the circle (like their pendulum).