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  1. PO
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    <p>Based on the "gestures" tag I guess you not only want to know how close are these points to the smallest-circle (search for "Smallest-circle problem"), but you have to be concerned also about their order and spread:</p> <p><img src="https://i.stack.imgur.com/dMLiE.png" alt="enter image description here"></p> <ol> <li>I would start with the distance from the smallest-circle. If they are too far, you're done, it's not a circle.</li> <li>If they are close enough to your configured threshold, compute the angle between the vector defined by the circle center, first point and each other point (picture bellow)</li> <li>Check that each angle is greater than the previous.</li> <li>Check that difference between any two angles next to each other is not over some configured threshold.</li> <li>Check that the last point is close enough to the first one.</li> <li>You will probably think of some other checks eventually, so make it simple to extend.</li> </ol> <p><img src="https://i.stack.imgur.com/agHcN.png" alt="enter image description here"></p>
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    1. POI have a list of points and would like to determine if they form a circle
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    1. USVaclavSir
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      1. VTUpMod
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    1. COWhy do you assume that the points are provided in certain order? Also bear in mind that you cannot start analysing angles, as far as any geometrical figure can be generated from equivalent angles. First thing to be analysed is the defining feature of a circle (i.e., all the points at the same distance from the center); the angles can only come into picture at a later stage to determine if it is a whole a circle or a portion of it.
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      1. USvarocarbas
    2. COFor checking the last point close enough to the first, I'd suggest that the sum of angles to that point > 340 degrees or similar. Assuming it's a gesture you just want a minimum of a full circle and probably don't care if you exceed it (e.g. 1.5 rotations). @varocarbas the order of points is important if the source of points is a gesture on a touch screen
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      1. USColin Young
    3. CO@ColinYoung Please, take a look at my answer (CLARIFICATION 2). The order of the points (if any) is EXTREMELY important. I asked VaclavSir why he assumed that there is an order. If an order exists (you are drawing the circle manually), this fact has certainly to be taken care of; if there are a bunch of random points, you cannot bring this issue into account because would drive to wrong results. The OP didn't mention this issue and that's why I don't think that VaclavSir should have taken it into account (or he should have mentioned that his approach cannot be used with random points).
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