Suppose there is a point cloud having 50 000 points in the x-y-z 3D space. For every point in this cloud, what algorithms or data strictures should be implemented to find k neighbours of a given point which are within a distance of [R,r]? Naive way is to go through each of the 49 999 points for each of the 50 000 points and do a metric testing. But this approach will take large time. Just like there is kd tree to find nearest neighbour in small time so is there some real-time DS/algo implementation out there to pre-process the point clouds to achieve the goal inn shortest time?
Your problem is part of the topic of Nearest Neighbor Search, or more precisely, k-Nearest Neighbor Search. The answer to your question depends on the data structure you are using to store the points. If you use R-trees or variants like R*-trees, and you are doing multiple searches on your database, you will likely find a substantial performance improvement in two or three-dimensional space compared with naive linear search. In higher dimensions, space partitioning schemes tend to underperform linear search.