AABBTREE - A d-dimensional bounding-box tree.

AABB-TREE provides d-dimensional aabb-tree construction and search for arbitrary collections of spatial objects. These tree-based indexing structures are useful when seeking to implement efficient spatial queries, reducing the complexity of intersection tests between collections of objects. Specifically, given two "well-distributed" collections P and Q, use of aabb-type acceleration allows the set of intersections to be computed in O(|P|*log(|Q|)), which is typically a significant improvement over the O(|P|*|Q|) operations required by "brute-force" type methods.
Given a collection of objects, an aabb-tree partitions the axis-aligned bounding-boxes (AABB's) associated with the elements in the collection into a (binary) "tree" -- a hierarchy of "nodes" (hyper-rectangles) that each store a subset of the collection. In contrast to other geometric tree types (quadtrees, kd-trees, etc), aabb-trees are applicable to collections of general objects, rather than just points.

See AABBDEMO to get started with a set of example problems:

aabbdemo(1); % build a tree for a 2-dimensional triangulation.
aabbdemo(2); % build a tree for a 3-dimensional triangulation.
aabbdemo(3); % compare a "fast" "aabb-accelerated" search with a "slow" brute-force computation.

Additional information and references are available via the Github repository (http://github.com/dengwirda/aabb-tree).