I'm writing some code and I need to determine if an array of points is in the shape of a perfect circle( not only the outline all points inside) and this code needs to be rather quick. One method I thought of is I take the average and the mean of all the points. If it is a perfect circle then these two should be equal(or very close to equal), but if it is a malformed circle then they would differ. The problem that i'm having is that my method seems very bad and I think the average and mean would be the same for any shape that is x and y symmetric.
Any ideas ?