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So if a node has 2*2 subnodes it is called a quadtree (2*2=4). If a node has 2*2*2 subnodes it is called an octree (2*2*2=8). Therefore if you work in 2D it is often good to use a quadtree and in 3D it is good practise to use an octree.

But are there any trees with an arbitrary number of subnodes in 3D? Like a tree with nnn subnodes. What is it called and are there any scientific works already for this?

Thanks in advance.

kke
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    A tree with three children per node is called a ternary tree. With 16 children per node would likely be called a hex tree. Beyond that, you'd probably just use the number: a 32-tree would have 32 children per node, etc. As for uses, I suppose if you were working in 6 dimensions, a 64-tree might come in handy. – Jim Mischel Aug 25 '15 at 01:04

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I believe you want the k-D tree:

https://en.wikipedia.org/wiki/K-d_tree

  • k-d trees are actually binary -- two children per node, though they can handle an arbitrary number of dimensions (but each node is only dealing with one dimension). –  Jan 05 '18 at 15:36