Finding deviation of coordinates placed on boundaries of a rectilinear shape

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I have elements placed on boundary of a rectilinear shape as depicted in the diagram. The intention is to find a metric (like for e.g. avg, std. deviation) which gives me how well the elements are clubbed together or separated throughout (as a whole for orange colors - not per line grouping) and the factor by which each elements loosely/strongly follows the grouping?

Ideally std. deviation would have done the job which provides the factor (x times) deviating from the mean (beautifully explained here: std-dev) but in this case std. deviation is a not a good matric to find grouping since the elements are not fundamentally meant to follow a center.

The data provided are the coordinates of the elements (orange one) : (x1,y1),(x2,y2),(x3,y3)....(xn,yn) and the coordinates of the rectilinear shape.

orange elements placed along the boundary

1 Answers

Compute the Euclidean distances between the points and the closest lines. Then consider either the mean distance or the root-mean-squared distance. (Zero in case of perfect alignment.)

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