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I was wondering if anybody knows a way to quantify the "density" of points contained within a polygon.

Here are my assumptions:

  1. The polygon is convex.
  2. All of the points' location is known.
  3. Currently, I would like to limit the problem to two dimensions, but would like to know the implications of moving it to higher dimensions (n-polytope).

I realize this is similar to the following question: Density of points on graph however I am only concerned about the density within the polygon.

Idea so far:

  1. Compute all the distances between each object in the polygon.
  2. Compute the standard deviation between the distances.
  3. A higher deviation would signify a greater variation between the distances between points.
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babernathy
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1 Answers1

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The most obvious and straight-forward definition of a point density would be number of points divided by total area of the polygon. Apparently that would be called the area number density. If this is not what you need, then you have to be more specific about what properties your density should satisfy.

MvG
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