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The current implementation of the convex hull check is inefficient due to the incorrect use of HashMap.
Instead of checking if there is a key O(1) in the set, it checks if the map contains a value O(n).
I think this is an implementation error as previous commits mention a HashSet, which makes sense to me.
I'm also not a fan of converting each domain definition point to a string representation, which will be hashed again to get an int representation. i suggest combining the int array into a single int and using that as a hash instead.
I also added a comment describing how the check works, because it took me a while to figure out that DefinitionDomain_Grid contains all valid points and not the points of the hull boundary (even though ‘Domain’ should have given me the hint).