## spatial-trees

Various spatial tree implementations.

## TOC »

## Usage

(require-extension kd-tree)

## Documentation

The `spatial-tree` library is intended to contain a collection of spatial tree implementations. A spatial tree is a data structure for organizing and searching points in an n-dimensional space. The present implementation code implements a single spatial tree structure, the k-d tree.

### Point

This library currently only supported points in 3D space.

`make-point3d:: DOUBLE * DOUBLE * DOUBLE -> POINT3D`procedure3D point constructor.

`point3d? :: POINT3D -> BOOL`procedure3D point predicate.

`point3d-x :: POINT3D -> DOUBLE`procedure`point3d-y :: POINT3D -> DOUBLE`procedure`point3d-z :: POINT3D -> DOUBLE`procedureAccessors 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:: POINT3D LIST -> KD-TREE`procedureGiven a list of points, constructs and returns a K-D tree object.

#### Predicates

`kd-tree? :: KD-TREE -> BOOL`procedureReturns

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

`kd-tree-empty? :: KD-TREE -> BOOL`procedureReturns

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

`kd-tree-is-valid? :: KD-TREE -> BOOL`procedureChecks 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? :: KD-TREE -> BOOL`procedureChecks whether the K-D tree property holds for the given tree and all subtrees.

#### Accessors

`kd-tree->list :: KD-TREE -> POINT3D LIST`procedureReturns a list with the points contained in the tree.

`kd-tree->list* :: KD-TREE -> (INT . POINT3D) LIST`procedureReturns 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-point :: KD-TREE -> POINT3D`procedure

#### Combinators

`kd-tree-map`procedure

`kd-tree-for-each`procedure

`kd-tree-for-each*`procedure

`kd-tree-fold-right`procedure

`kd-tree-fold-right*`procedure

#### Query procedures

`kd-tree-nearest-neighbor`procedure

`kd-tree-near-neighbors`procedure

`kd-tree-near-neighbors*`procedure

`kd-tree-k-nearest-neighbors`procedure

`kd-tree-slice`procedure

`kd-tree-slice*`procedure

#### Modifiers

`kd-tree-remove`procedure

## Examples

## About this egg

### Author

### Version history

- 2.0
- Improvements to internal representation
- 1.0
- Initial release

### License

Copyright 2012 Ivan Raikov and the Okinawa Institute of Science and Technology. 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/>.