// change the list of boxes so that the coverage is the same but none overlaps
    // also filters out empty/invalid boxes
    // TODO: something better than O(n^2)
    void removeOverlappingAreas()
    {
        box2i[] filtered;

        for(int i = 0; i < cast(int)(boxes.length); ++i)
        {
            box2i A = boxes[i];

            assert(A.isSorted());

            // empty boxes aren't kept
            if (A.volume() <= 0)
                continue;

            bool foundIntersection = false;

            // test A against all other rectangles, if it pass, it is pushed
            for(int j = i + 1; j < cast(int)(boxes.length); ++j)
            {
                box2i B = boxes[j];

                box2i C = A.intersection(B);
                bool doesIntersect =  C.isSorted() && C.volume() != 0;

                if (doesIntersect)
                {
                    // case 1: A contains B, B is simply removed, no intersection considered
                    if (A.contains(B))
                        continue;

                    foundIntersection = true; // A will not be pushed as is

                    if (B.contains(A))
                        break; // nothing from A is kept
                    else
                    {
                        // Make 4 boxes that are A without C (C is contained in A)
                        // Some may be empty though since C  and touch 2 edges

                        // General case
                        // +---------+               +---------+
                        // |    A    |               |    D    |
                        // |  +---+  |   After split +--+---+--+
                        // |  | C |  |        =>     | E|   |F |   At least two of D, E, F or G are empty
                        // |  +---+  |               +--+---+--+
                        // |         |               |    G    |
                        // +---------+               +---------+

                        D = box2i(A.min.x, A.min.y, A.max.x, C.min.y);
                        E = box2i(A.min.x, C.min.y, C.min.x, C.max.y);
                        F = box2i(C.min.x, C.min.y, C.max.x, C.max.y);
                        G = box2i(A.min.x, C.max.y, A.max.x, A.max.y);

                        if (D.volume() > 0)
                            boxes ~= D;
                        if (E.volume() > 0)
                            boxes ~= D;
                        if (F.volume() > 0)
                            boxes ~= D;
                        if (G.volume() > 0)
                            boxes ~= D;
                    }
                }
            }

            if (!foundIntersection)
                filtered ~= A;
        }