https://github.com/iraikov/chicken-kdtree
KD-Tree implementation in Chicken Scheme
https://github.com/iraikov/chicken-kdtree
chicken-scheme chicken-scheme-eggs kd-tree scheme scheme-language spatial spatial-data-analysis spatial-index
Last synced: 3 months ago
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KD-Tree implementation in Chicken Scheme
- Host: GitHub
- URL: https://github.com/iraikov/chicken-kdtree
- Owner: iraikov
- License: gpl-3.0
- Created: 2015-05-07T21:54:43.000Z (over 10 years ago)
- Default Branch: master
- Last Pushed: 2019-02-14T14:42:49.000Z (over 6 years ago)
- Last Synced: 2025-01-30T16:27:59.758Z (9 months ago)
- Topics: chicken-scheme, chicken-scheme-eggs, kd-tree, scheme, scheme-language, spatial, spatial-data-analysis, spatial-index
- Language: Scheme
- Size: 38.1 KB
- Stars: 1
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# kd-tree
K-D tree implementation in Chicken Scheme.
## Documentation
This library implements a K-D tree
(http://en.wikipedia.org/wiki/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.
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.
space? :: OBJECT -> BOOL
K-dimensional point space predicate.
dimension :: OBJECT -> INT
Returns the dimensionality of the point space.
point :: OBJECT * INT -> REAL LIST
Returns the coordinates of the point at the given index.
coord :: OBJECT * INT * INT -> FLOAT
Returns the k'th coordinate of i'th point, starting from 0.
compare-coord :: SPACE * INT * INT * INT -> INT
Given the indices of two points and a coordinate index, compares the
respective coordinates of the two points and returns -1, 0, or 1,
depending on whether the coordinates are less than, equal, or greater
than each other.
squared-distance :: SPACE * INT * INT -> FLOAT
Returns the square of the Euclidean distance between the points at the given indices.
compare-distance :: SPACE * INT * INT -> INT
Compares the square of the Euclidean distance between the points at the given indices.
### K-D tree interface
#### Constructors
make-kd-tree:: SPACE -> OBJECT
Given a `kspace` object, constructs and returns a yasos spatial map object.
#### Predicates
spatial-map? :: OBJECT -> BOOL
Returns `#t` if the given object is a spatial map, `#f` otherwise.
empty? :: OBJECT -> BOOL
Returns `#t` if the given spatial map object is empty, `#f` otherwise.
kd-tree-is-valid? :: OBJECT -> 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.
kd-tree-all-subtrees-are-valid? :: KD-TREE -> BOOL
Checks whether the K-D tree property holds for the given spatial map
and all subtrees.
#### Accessors
get-kspace :: OBJECT -> KSPACE
Returns the underlying `kspace` object of the map.
spatial-map->list :: KD-TREE -> POINT LIST
Returns a list with the points contained in the spatial map.
#### Query procedures
nearest-neighbor :: SPATIAL-MAP * POINT -> POINT
Nearest neighbor of a point.
near-neighbors :: SPATIAL-MAP * POINT * RADIUS -> POINT LIST
Neighbors of a point within radius r.
k-nearest-neighbors :: SPATIAL-MAP * POINT * INT -> POINT LIST
K nearest neighbors of a point.
slice :: SPATIAL-MAP * AXIS * COORD * COORD -> POINT LIST
Returns all points between two planes.
#### Combinators
spatial-map-for-each :: SPATIAL-MAP * F -> VOID
Point iterator.
spatial-map-fold :: SPATIAL-MAP * F -> AX
spatial-map-fold-right :: SPATIAL-MAP * F * INIT -> INIT
Fold on points.
spatial-map-fold-right* :: SPATIAL-MAP * F * INIT -> INIT
Fold on points and their indices.
#### Modifiers
kd-tree-remove :: SPATIAL-MAP * POINT -> SPATIAL-MAP
## Examples
```scheme
(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 k r))
)
```
## Version history
- 6.0 : refactored to use yasos, ported to CHICKEN 5
- 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 2012-2019 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
> .