Is there a way to identify whether a face is of circular shape and it's center?. All I have is the face and it's vertices.


closed as unclear what you're asking by Hans Lundmark, Lord Shark the Unknown, KReiser, Rebellos, Cesareo Dec 7 '18 at 11:50

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  • $\begingroup$ Are you asking, given the numerical coordinates of some points in the plane, how do you tell if they lie on a circle? If so, are you concerned about numerical imprecision? $\endgroup$ – kimchi lover Dec 6 '18 at 15:45
  • $\begingroup$ Yes. I am not concerned. $\endgroup$ – Chandu Dec 6 '18 at 23:44

Three non-aligned points are enough to unambiguously define a circle. You find the center as the intersection of two mediatrices. http://www.manufacturinget.org/2011/07/construct-circle-through-three-points/

When you have the center, you can check that all points are at the same distance from it.

  • $\begingroup$ This condition will identify a square face too as circle? $\endgroup$ – Chandu Dec 7 '18 at 1:29
  • $\begingroup$ @Chandu: are you serious ? $\endgroup$ – Yves Daoust Dec 7 '18 at 8:47

Given a list of $(x_i,y_i)$ pairs, representing points in the plain, see if you can predict $x_i^2+y_i^2$ with an affine function of $(x_i,y_i)$, by, say, least squares. If your points lie exactly on a circle, the residual sum of squares should equal 0.

  • 1
    $\begingroup$ The little that I can understand of this answer, is wrong. $\endgroup$ – Yves Daoust Dec 7 '18 at 0:35

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