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kd-tree

K-D tree implementation.

Usage

(require-extension kd-tree)

Documentation

This library implements a k-d tree, a data structure for organizing and searching points in k-dimensional space.

The k-d tree is a binary search tree in which every branching node contains a k-dimensional point, and every leaf node contains a set of points. Every branching node represents a splitting hyperplane that divides the space into two parts, known as half-spaces.

Points to the left of the splitting hyperplane are contained in the left subtree of the node and points right of the hyperplane are contained in the right subtree. The splitting hyperplane is chosen so as to be perpendicular to one of the axes in the k-dimensional space. The axis at each branching level is chosen in a round-robin fashion. For instance, in 3-D space, at level 0, the chosen axis is X, so points are divided according to their X-coordinates; at level 1, the chosen axis is Y, so the points are divided according to their Y-coordinates; at the next branch level the chosen axis is Z, and so on.

Point

This library currently only supports points in 3D space.

make-point3d:procedure

3D point constructor.

point3d?procedure

3D point predicate.

point3d-xprocedure
point3d-yprocedure
point3d-zprocedure

Accessors for the x,y,z coordinates of a 3D point.

KD-tree

A K-D tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space.

Constructors

  
list->kd-tree:procedure

Given a list of points, constructs and returns a K-D tree object.

Predicates

kd-tree?procedure

Returns #t if the given object is a K-D tree, #f otherwise.

kd-tree-empty?procedure

Returns #t if the given K-D tree object is empty, #f otherwise.

kd-tree-is-valid?procedure

Checks whether the K-D tree property holds for the given tree. Specifically, it tests that all points in the left subtree lie to the left of the plane, p is on the plane, and all points in the right subtree lie to the right.

kd-tree-all-subtrees-are-valid?procedure

Checks whether the K-D tree property holds for the given tree and all subtrees.

Accessors

kd-tree->listprocedure

Returns a list with the points contained in the tree.

kd-tree->list*procedure

Returns a list where every element has the form (i . p), where i is the relative index of this point, and p is the point.

kd-tree-subtreesprocedure
kd-tree-pointprocedure

Combinators

kd-tree-mapprocedure
kd-tree-for-eachprocedure
kd-tree-for-each*procedure
kd-tree-fold-rightprocedure
kd-tree-fold-right*procedure

Query procedures

kd-tree-nearest-neighborprocedure
kd-tree-near-neighborsprocedure
kd-tree-near-neighbors*procedure
kd-tree-k-nearest-neighborsprocedure
kd-tree-sliceprocedure
kd-tree-slice*procedure

Modifiers

kd-tree-removeprocedure

Examples

About this egg

Author

Ivan Raikov

Version history

- 5.0 : added list->kd-tree* procedure to KdTree class

4.1-4.8
Using f64vector for internal point representation
4.0-4.1
Added with-distance? flag to kd-tree-near-neighbors
3.2
Bug fix in kd-tree-near-neighbors
2.0
Improvements to internal representation
1.0
Initial release

License

Copyright 2012-2016 Ivan Raikov.

This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or (at
your option) any later version.

This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

A full copy of the GPL license can be found at
<http://www.gnu.org/licenses/>.

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