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I have multiple sets of random points and I want to find the one that is most "round"

My thoughts are that if I were trying to find which set matched a particular function then the best set would be the one with the lowest averaged absolute error. This method would not work for a circle as a group of points on the circumference could have the lowest average even though this is obviously not matching the circle very well.

This lead me to thinking that if the nearest points on the circumference to each random point had a uniform distribution around the circumference of the circle then this combined with the smallest error mentioned above could give a value of roundness.

These methods raise the question of how to weight each part to determine roundness?

Is there a completely better way to do this or how could I improve my own methods?

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  • $\begingroup$ I think your definition of "roundness" needs clarifying. Are you trying to factor in the density of the points or just how well a cluster fits within a circle? $\endgroup$
    – CFD
    Aug 11, 2020 at 2:29
  • $\begingroup$ Neither, I'm trying to find out how well points are modelled by a certain function, this function just happens to be a circle $\endgroup$ Aug 11, 2020 at 9:58

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