Optimising the drawing of overlapping rectangles

Question

I have a large number of rectangles, and some overlap others; each rectangle has an absolute z-order and a colour. (Each \'rectangle\' is actually the axis-aligned bou

Answer 1

Start by drawing in a random (but correct) order, for example in strict z order. When drawing each frame, either count the number of color changes, or possibly the actual time a complete frame takes. Each frame, try swapping the order of two rectangles. The rectangles to be swapped must not overlap, therefore they can be drawn in any order without violating correctness; aside from that they can be chosen at random, or do a linear pass through the list, or... If doing the swap reduces the number of color changes, keep the new order, if not revert it and try a different swap in the next frame. If doing the swap neither reduces nor increases the number of color changes, keep it with 50% odds. For any rectangles which did not overlap in a previous frame but which start overlapping due to a move, simply exchange them so they are in z order.

This has some relationship to sorting algorithms which swap pairs of items, except that we cannot compare items, we need to go through the whole list and count color changes. This will perform very badly at first but converge to a good order relatively quick, and will adapt to scene changes. I think it is probably not worth it to go through and calculate an optimum order every frame; this will get to, and maintain, a near-optimum order with very little extra work.

Referring to the drawing you have: Initial draw order picked at random: 1,6,2,4,5,8,3,7 (5 color changes). Swap 5,8. New order: 1,6,2,4,8,5,3,7 (4 color changes) => Keep new order.