I have 2 shapefiles and after identifying their intersections I'd like to know the ratio of intersecting areas, e.g.
a given shape S in file1 intersects with shapes (x1,...,xn) in file2 with ?proportions (y1,...,yn) (y_i of shape x_i lies in S).
I do not think that planar areas (e.g. shapely) are appropriate for good estimations. How (what projections) should I use to get the closest approximations to the actual area ratios? What libraries in Python or command line tools allow for calculating areas on hyperplanes (local Earth surface)?