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Removing a point from a balanced k-d tree takes O(log n) time. Querying an axis-parallel range in a balanced k-d tree takes O(n 1−1/k +m) time, where m is the number of the reported points, and k the dimension of the k-d tree. Finding 1 nearest neighbour in a balanced k-d tree with randomly distributed points takes O(log n) time on average.
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The terms "min/max k-d tree" and "implicit k-d tree" are sometimes mixed up.This is because the first publication using the term "implicit k-d tree" [1] did actually use explicit min/max k-d trees but referred to them as "implicit k-d trees" to indicate that they may be used to ray trace implicitly given iso surfaces.
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If K = 1, a relaxed K-d tree is a binary search tree. As in a K-d tree, a relaxed K-d tree of size n induces a partition of the domain D into n+1 regions, each corresponding to a leaf in the K-d tree. The bounding box (or bounds array) of a node {x,j} is the region of the space delimited by the leaf in which x falls when it is inserted into the ...
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The min/max kdtree has - besides the properties of an kd-tree - the special property that an inner node's min/max values coincide each with a min/max value of either one child. This allows to discard the storage of min/max values at the leaf nodes by storing two bits at inner nodes, assigning min/max values to the children: Each inner node's ...
The key feature of the BIH is the storage of 2 planes per node (as opposed to 1 for the kd tree and 6 for an axis aligned bounding box hierarchy), which allows for overlapping children (just like a BVH), but at the same time featuring an order on the children along one dimension/axis (as it is the case for kd trees).