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| title | date | draft | description | tags | categories | series | favorite | disable_feed | |||||
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| Kd Tree Revisited | 2024-08-17T14:20:22+01:00 | false | Simplifying the nearest neighbour search |
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After giving it a bit of thought, I've found a way to simplify the nearest
neighbour search (i.e: the closest method) for the KdTree I implemented in
[my previous post]({{< relref "../2024-08-10-kd-tree/index.md" >}}).
The improvement
That post implemented the nearest neighbour search by keeping track of the
tree's boundaries (through AABB), and each of its sub-trees (through
AABB.split), and testing for the early exit condition by computing the
distance of the search's origin to each sub-tree's boundaries.
Instead of explicitly keeping track of each sub-tree's boundaries, we can implicitly compute it when recursing down the tree.
To check for the distance between the queried point and the splitting plane of inner nodes: we simply need to project the origin onto that plane, thus giving us a minimal bound on the distance of the points stored on the other side.
This can be easily computed from the axis and mid values which are stored in
the inner nodes: to project the node on the plane we simply replace its
coordinate for this axis by mid.