KD-Tree

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23:14
Thu
09
Jul 2009

KD-Tree

People at forums are usually advised to learn BSP, quadtree or octree as space partitioning data structure, but there are many more interesting structures than these three. This time my choice for home project is KD-tree. It's actually something between BSP and octree. Just like BSP it's a binary tree (each non-leaf node has two child nodes) and optimal splitting plane is estimated each time by special algorithm, but splitting planes are always aligned to one of three main axes and thus each node can be described by an AABB (axis-aligned bounding box), just like in octree.

As my tree is designed to manage objects and not geometry, nothing can be split and some of objects may intersect splitting planes. How to deal with them? I simply assign them to the parent node, so not only leaves are allowed to contain list of objects. To avoid too many small objects intersecting splitting planes to degrade performance by falling into top level nodes (it's called "sticky planes" or something like that :) I adopted "loose octree" idea to my KD-tree. It simply means I extend each node’s bounding box so that each node's children slightly overlap each other and small objects intersecting splitting plane fall into one of the children.

My KD-tree is also dynamic, which means it reorganizes itself as objects get added, removed and moved in the tree. It's actually quite simple. Each time an object is added to a node, that node can be split into two children if it's object number exceeds constant limit. Similarly node can be merged by deleting it's children each time an object is removed from one of its children, if the number of objects in that node and its children drops under constant minimum.

For additional performance, I allocate tree nodes from my own "Free List" memory pool and I keep objects connected to each node as doubly-linked list.

I also came up with an idea how to easily visualize quality of my space partitioning technique. I keep track of the number of tree nodes and objects on each depth level. This way I can tell from these several numbers whether tree is more "tall" or "wide" and whether most of objects stay in leaves instead of some top-level nodes.

Here are some screenshots and a video from my recent code:

KD-tree KD-tree KD-tree

Comments (3) | Tags: rendering video gallery algorithms math | Author: Adam Sawicki | Share

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