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There are many algorithms for binary map overlay operation in vector data format which take two layers of map and produce resultant layer i.e overlaid layer as output. I am wondering whether there are any algorithms which take more than two layers say 3 layers simultaneously and produce the overlay result?

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The low-level spatial predicate operators are all binary—i.e., compare geometry A to geometry B. For example, see the DE-9IM topological model, which is the basis for Intersects, Contains, etc. When you have more than two, say geometry C, then you might need to compare the combinations of geometries: AB, AC, BC. But it all really depends on what you are trying to determine.

For a specific coded example of how you handle more than two geometries, see Polygon overlay with Shapely. This example also features a cascaded union, which unions several (more than two) geometries, so I guess is a good example of an efficient map algorithm that take takes more than two inputs.

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