1. kd-tree
  2. Documentation
    1. K-dimensional point space
    2. K-D tree interface
      1. Constructors
      2. Predicates
      3. Accessors
      4. Query procedures
      5. Combinators
      6. Modifiers
  3. Examples
  4. Repository
  5. Version history
  6. License

kd-tree

K-D tree implementation.

Documentation

This library implements a K-D tree, which is 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.

K-dimensional point space

Module kspace provides facilities for managament of K-dimensional point spaces.

[procedure] make-space:: COORDS -> SPACE

Given a list of coordinate collections of length K, constructs a yasos K-dimensional point space object. The coordinate collections can be SRFI-4 f32vectors, or collection objects as defined in the yasos collections module.

[procedure] space? :: OBJECT -> BOOL

K-dimensional point space predicate.

[procedure] dimension :: SPACE -> INT

Returns the dimensionality of the point space.

[procedure] size :: SPACE -> INT

Returns the number of points in the space.

[procedure] point :: SPACE * INT -> REAL LIST

Returns the coordinates of the point at the given index.

[procedure] coord :: SPACE * INT * INT -> FLOAT

Returns the k'th coordinate of i'th point, starting from 0.

[procedure] compare-coord :: SPACE * INT * INT * INT -> BOOL

Given the indices of two points and a coordinate index, returns #t if the first point's coordinate is less than the second point's coordinate on that axis, #f otherwise.

[procedure] squared-distance :: SPACE * POINT * POINT -> FLOAT

Returns the square of the Euclidean distance between two points. Each POINT argument may be either a point index (INT) or a coordinate list (REAL LIST).

[procedure] compare-distance :: SPACE * POINT * POINT * POINT -> INT

(compare-distance space origin p1 p2) compares the squared distance of p1 from origin to the squared distance of p2 from origin, returning a negative, zero, or positive number accordingly. As with squared-distance, each POINT argument may be either a point index or a coordinate list.

K-D tree interface

Constructors

[procedure] make-kd-tree:: SPACE -> SPATIAL-MAP

Given a kspace object, constructs and returns a yasos spatial map object.

Predicates

[procedure] spatial-map? :: OBJECT -> BOOL

Returns #t if the given object is a spatial map, #f otherwise.

[procedure] empty? :: SPATIAL-MAP -> BOOL

Returns #t if the given spatial map object is empty, #f otherwise.

[procedure] is-valid? :: SPATIAL-MAP -> BOOL

Checks whether the K-D tree property holds for the given spatial map. 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.

[procedure] all-subtrees-are-valid? :: SPATIAL-MAP -> BOOL

Checks whether the K-D tree property holds for the given spatial map and all of its subtrees.

Accessors

[procedure] get-kspace :: SPATIAL-MAP -> SPACE

Returns the underlying kspace object of the map.

[procedure] size :: SPATIAL-MAP -> INT

Returns the number of points currently in the spatial map.

[procedure] dimension :: SPATIAL-MAP -> INT

Returns the dimensionality of the spatial map.

[procedure] spatial-map->list :: SPATIAL-MAP -> POINT LIST

Returns a list with the points contained in the spatial map.

Query procedures

[procedure] nearest-neighbor :: SPATIAL-MAP * POINT -> POINT

Nearest neighbor of a point.

[procedure] near-neighbors :: SPATIAL-MAP * POINT * RADIUS -> POINT LIST

Neighbors of a point within radius r.

[procedure] k-nearest-neighbors :: SPATIAL-MAP * POINT * INT -> POINT LIST

K nearest neighbors of a point. If there are fewer than K points in the map, all of them are returned.

[procedure] slice :: SPATIAL-MAP * AXIS * COORD * COORD -> POINT LIST

Returns all points whose coordinate on the given axis lies between the two given bounds (inclusive).

Combinators

[procedure] spatial-map-for-each :: SPATIAL-MAP * F -> VOID

Applies the given procedure to every point in the spatial map, for effect.

[procedure] spatial-map-fold-right :: SPATIAL-MAP * F * INIT -> INIT

Right fold over the points in the spatial map.

[procedure] spatial-map-fold-right* :: SPATIAL-MAP * F * INIT -> INIT

Right fold over the points in the spatial map and their indices.

Modifiers

[procedure] remove :: SPATIAL-MAP * POINT * TOLERANCE -> SPATIAL-MAP

Returns a new spatial map with the point within TOLERANCE of the given point removed. Does not modify the original spatial map.

Examples

 
(import scheme (chicken base)
        yasos random-mtzig kspace kd-tree)

(let* ((n (inexact->exact 1e5)) (k 40) (r 1.0) (randst (init 9))

       ;; generate random coordinates
       (xs (randn/f32! n randst))
       (ys (randn/f32! n randst))
       (zs (randn/f32! n randst))
       ;; create a kspace
       (pts (list xs ys zs))
       (kspace3d (make-space pts))
       ;; create the spatial map
       (kdt (make-kd-tree kspace3d))
       ;; choose a random point index
       (xi (inexact->exact (modulo (random! randst) n)))
       ;; retrieve the coordinates of the chosen point
       (x  (point kspace3d xi)))

    (print "nearest-neighbor of " x ": " (nearest-neighbor kdt x))
    (print k " nearest neighbors of " x ": " (k-nearest-neighbors kdt x k))
    (print "near neighbors of " x " within " r ": " (near-neighbors kdt x r)))

Repository

https://github.com/iraikov/chicken-kdtree

Version history

License

 
Copyright 2012-2026 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/.