/sci/ - Science & Math

How do I calculate the probability that within some defined space two shapes will overlap? I mean shapes, not simple objects. For instance, if you took paper cutout circles and skinny swastikas of equal area they would not intersect at the same frequency. I would want to do it by defining each object as a polygon, counting the sparseness/coverage, ie the degree of non-overlap, by taking each point in its outline and drawing a line between it and every other point in the polygon, then adding those distances. And then this quantity would be multiplied by some constant and the cross sectional area of the polygon to find the probability of overlap. Does something like this approach make sense? Also, what if there are two kinds of polygon (shapes) you’re dealing with?

Here is a problem which illustrates what I’m trying to solve for a particular dataset: there is a Xerox machine, a box of thin swastika paper cutouts, and a box of heart cutouts. Dump the boxes onto the machine. What is the probability that a given heart will land on a swastika?

Forgive me for the redundancy, unclarity and mathematical illiteracy. I have only used math to calculate tips since high school.