# How to identify a face is circle using it's vertices [closed]

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, CesareoDec 7 '18 at 11:50

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• 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? – kimchi lover Dec 6 '18 at 15:45
• Yes. I am not concerned. – Chandu Dec 6 '18 at 23:44

## 2 Answers

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.

• This condition will identify a square face too as circle? – Chandu Dec 7 '18 at 1:29
• @Chandu: are you serious ? – 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.

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