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

Depending slightly on the number of points that you are being used to compare with, what is below is pretty much guaranteed to be the get the list of points in approximate order assuming all points change at all iteration.

1) Rewrite the array into a single list of Manhattan distances with out[ i ] = abs( posn[ i ].x - player.x ) + abs( posn[ i ].y - player.y ) + abs( posn[ i ].z - player.z );

2) Now you can use radix sort on floating point numbers to order them.

Note that in practice this is going to be a lot faster than sorting the list of 3d positions because it significantly reduces the memory bandwidth requirements in the sort operation which all of the time is going to be spend and in which unpredictable accesses and writes are going to occur. This will run on O(N) time.

If many of the points are stationary at each direction there are far faster algorithms like using KD-Trees, although implementation is quite a bit more complex and it is much harder to get good memory access patterns.