图形硬件上的最近邻搜索

Question

Given a huge collection of points (float64) in 2d space...

Is there a way to determine the nearest neighbour using a feature of OpenGL or DirectX?

I've implemented a kd-tree, which is still not fast enough.

Answer 1

A kd-tree should work just fine. But here's some hints.

I implemented a kd-tree once for a million point data set once. Here's what I learned out of it:

Did you try profiling your code? You might find that there are easy optimizations to make such as common helper functions needing to be forced inline.

Did you actually test your code to validate that it was culling out tree branches for partitions that are easily identified as "too far away". If you aren't careful, you can easily have a bug that does needless distance computations on points too far away.

Easiest thing: Where comparing linear distance between points, you don't need to take the SQRT of (x2-x1)*(y2-y1).

Most of the time spent in my code was just building the tree from the original data set, including multiple full sorts on each iteration deciding which axis was the best to partition on. An easier algorithm would be to just alternate between partitioning on the x and y axis for each tree branch and to cache the sorting order for each axis. It may not build the most optimal search tree, but the overall savings can be enormous.