How can I quantify the number of polygons that cover a a particular point?

Hello, I have a population of polygons, each representing a particular region in space. I would like to know the distribution of these polygons across space. I can visualize this by plotting them as patches and decreasing the transparency. Thus, as more polygons cover a particular area, it appears darker as they 'pile-up' over it. However, I would like to quantify this. How can I look at each pixel in my plot and see how many polygons are sitting above it? I imagine this like a surface plot except instead of each point representing a value it represents the 'depth' of polygons that have been plotted there.

A solution I have considered is to fill each polygon with ones (so I have a matrix representing the entire space, with ones where the polygon lies and zeros elsewhere) and then summing the matrices; but I don't know how to do this.

Any help is appreciated.

Answer 1

[Walter Roberson]

Perhaps inpolygon() would be useful for this.

[David]

Maybe, but the points that I want to test as in or out of the polygon would be the entire background space. I'm not sure how to do this either.

Answer 2

[David]

I have solved this (a bit amateurishly) by using two vectors that represent all of the background space, along with the polygon, as inputs to inpolygon.