Most "thorough" distribution of points around a circle

Posted by hippietrail on Stack Overflow See other posts from Stack Overflow or by hippietrail
Published on 2011-01-11T03:24:46Z Indexed on 2011/01/11 13:53 UTC
Read the original article Hit count: 264

Filed under:

geometry

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distribution

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circle

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points

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standard-deviation

This question is intended to both abstract and focus one approach to my problem expressed at "Find the most colourful image in a collection of images".

Imagine we have a set of circles, each has a number of points around its circumference. We want to find a metric that gives a higher rating to a circle with points distributed evenly around the circle. Circles with some points scattered through the full 360° are better but circles with far greater numbers of points in one area compared to a smaller number in another area are less good.

The number of points is not limited.

Two or more points may coincide.

Coincidental points are still relevant. A circle with one point at 0° and one point at 180° is better than a circle with 100 points at 0° and 1000 points at 180°.

A circle with one point every degree around the circle is very good. A circle with a point every half degree around the circle is better.

In my other (colour based question) it was suggested that standard deviation would be useful but with caveat. Is this a good suggestion and does it cope with the closeness of 359° to 1°?

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