RectangleBinPack
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GuillotineBinPack::MergeFreeList is not theta(n^2)
Calling erase which is O(n) in the middle of the loop makes the algorithm worse than theta(n^2). erase could be replaced with a swap between the erased element and the last element, and a pop_back (both are O(1)).
Great project, great article. I will use the Guillotine algorithm(s) in my project!