Fix the quadrant overlap test in a quadtree

Your collision culling uses a quadtree: each node splits into four child quadrants, and a range query descends into every child the range overlaps. Objects on a divider or an edge went missing from queries. The fix computes the four child boxes and tests each one against the range.

An assistant wrote overlapping_quadrants(node, range_box). It is in the editor. It has a bug. Find it and fix it.

Input and output:

• node: the node's box, [x, y, w, h], with y growing downward. All values are integers.
• range_box: the query box, [rx, ry, rw, rh].
• Return the indexes of the children the range overlaps, in ascending order: 0 top left, 1 top right, 2 bottom left, 3 bottom right.

Rules the tests check:

• If either list does not have exactly 4 items, or any width or height is negative, return [].
• Split at midx = x + floor(w / 2) and midy = y + floor(h / 2).
• The children, each as [cx, cy, cw, ch]:
  • 0: [x, y, midx - x, midy - y]
  • 1: [midx, y, x + w - midx, midy - y]
  • 2: [x, midy, midx - x, y + h - midy]
  • 3: [midx, midy, x + w - midx, y + h - midy]
• So when a size is odd, the right and bottom children are 1 larger, and the four children cover the node exactly.
• A child overlaps the range when rx <= cx + cw and rx + rw >= cx, and ry <= cy + ch and ry + rh >= cy. Touching edges count.