I generated 40 different Venn diagrams that each represent a specific 'trial' of an experiment (they are actually different samples in a genetic study). The Venn diagrams represent the overlap between 5 different sets (5-way Venns) and they are generated directly as SVGs from Python by replacing the labels in the example Venn from Wikipedia.
My question is: how would you proceed to create a heatmap of the density of every set intersection. In other words, I would like to add a 2D color heatmap over the Venn diagram which would represent the density of the different regions of the diagram over all the samples. Alternatively, a 3D density map could be used, which would give me a new dimension for projecting the density. I thought of using the Gaussian probability density function for the z.