I have some 2d points data and I generated a convex hull mesh. Looking by eye, it seems that the points are not uniformly distributed inside the convex. I wonder what is the best way to characterize this asymmetry? An example is like this:


{{1.70411, -0.82218}, {1.47802, 0.85122}, {3.19453, 2.18674}, {0.583261, -0.7624}, {1.20318, -0.487035}, {1.0349, -0.087872}, {1.06771, 0.370179}, {0.645045, -0.545495}, {1.42052, 0.839666}, {0.055145, -0.0183668}, {0.43104, 0.29658}, {0.443926, 0.304759}, {4.31065, -0.836811}, {4.12503, 2.28684}}

convex hull mesh:

enter image description here

  • $\begingroup$ Are you simply looking to measure the degree of general nonuniformity, or are you specifically after something relating to symmetry. If symmetry is really the issue, can you be more specific about the sense in which you mean it, given the convex polygonal region is not itself symmetric? [Indeed, I wouldn't think to describe a uniform distribution of points over that figure as "symmetric", even though it's possible to create a set of transformations (interchanges of identically-shaped small interior regions for example) that would leave that uniformity unaltered] $\endgroup$ – Glen_b Dec 13 '16 at 0:34

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