Very fast 3D distance check?

Question

Is there a way to do a quick and dirty 3D distance check where the results are rough, but it is very very fast? I need to do depth sorting. I use STL sort like this

Answer 1

If your operation happens a lot, it might be worth to put it into some 3D data structure. You probably need the distance sorting to decide which object is visible, or some similar task. In order of complexity you can use:

1. Uniform (cubic) subdivision

   Divide the used space into cells, and assign the objects to the cells. Fast access to element, neighbours are trivial, but empty cells take up a lot of space.

2. Quadtree

   Given a threshold, divide used space recursively into four quads until less then threshold number of object is inside. Logarithmic access element if objects don't stack upon each other, neighbours are not hard to find, space efficient solution.

3. Octree

   Same as Quadtree, but divides into 8, optimal even if objects are above each other.

4. Kd tree

   Given some heuristic cost function, and a threshold, split space into two halves with a plane where the cost function is minimal. (Eg.: same amount of objects at each side.) Repeat recursively until threshold reached. Always logarithmic, neighbours are harder to get, space efficient (and works in all dimensions).

Using any of the above data structures, you can start from a position, and go from neighbour to neighbour to list the objects in increasing distance. You can stop at desired cut distance. You can also skip cells that cannot be seen from the camera.

For the distance check, you can do one of the above mentioned routines, but ultimately they wont scale well with increasing number of objects. These can be used to display data that takes hundreds of gigabytes of hard disc space.