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posts: kd-tree-revisited: add presentation

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Bruno BELANYI 2024-08-16 08:41:49 +01:00
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content/posts/2024-08-11-kd-tree-revisited/index.md
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@ -20,3 +20,21 @@ neighbour search (i.e: the `closest` method) for the `KdTree` I implemented in
[my previous post]({{< relref "../2024-08-10-kd-tree/index.md" >}}). [my previous post]({{< relref "../2024-08-10-kd-tree/index.md" >}}).
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## 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`.