This is the quadtree Reference Manual, version 0.1, generated automatically by Declt version 4.0 beta 2 "William Riker" on Tue Jul 15 06:21:07 2025 GMT+0.
The main system appears first, followed by any subsystem dependency.
quadtreeQuadtree data structure in Common Lisp
Masayuki Takagi
MIT
# Quadtree
[](https://travis-ci.org/takagi/quadtree)
[](https://coveralls.io/r/takagi/quadtree?branch=master)
Quadtree is quadtree data structure in Common Lisp.
## Usage
Here shows how to store points into a quadtree.
First, define point structure.
(defstruct (point (:constructor make-point (x y)))
(x 0d0 :read-only t)
(y 0d0 :read-only t))
Then, implement an intersection test method for the point structure, which is called when inserting points to a quadtree.
(defmethod quadtree:intersect-p (quadtree (point point))
(destructuring-bind (x0 y0 x1 y1) (quadtree:boundary quadtree)
(let ((x (point-x point))
(y (point-y point)))
(and (<= x0 x x1) (<= y0 y y1)))))
Now, make and bulid a quadtree with its boundary, query it to get points stored in the leaf that contains specified ‘x‘ and ‘y‘.
(let ((points (list (make-point 0.0d0 0.0d0)
(make-point 1.0d0 1.0d0)
(make-point 0.1d0 0.1d0)
(make-point 0.1d0 0.2d0)
(make-point 0.2d0 0.1d0)
(make-point 0.2d0 0.2d0)
(make-point 0.2d0 0.3d0)
(make-point 0.2d0 0.4d0)
(make-point 0.3d0 0.2d0)
(make-point 0.3d0 0.3d0))))
;; make a quadtree with its boundary
(let ((qt (quadtree:make 0.0d0 0.0d0 1.0d0 1.0d0)))
;; build the quadtree
(loop for point in points
do (quadtree:insert qt point))
;; query the quadtree
(is (length (quadtree:query qt 0.1 0.1)) 5)))
## Installation
Since quadtree is just requesting to Quicklisp, plese use its local-projects feature for now.
$ cd quicklisp/local-projects
$ git clone git://github.com/takagi/quadtree.git
After approved, you can install via Quicklisp.
(ql:quickload :quadtree)
## API
### [Special Variable] \*max-depth\*
Specifies the maximum depth of a newly created quadtree.
### [Special Variable] \*max-capacity\*
Specifies the maximum capacity of leaves of a newly created quadtree.
### [Function] make
MAKE x0 y0 x1 y1 &key max-depth max-capacity => quadtree
Creates an empty quadtree with the boundary of ‘x0‘, ‘y0‘, ‘x1‘ and ‘y1‘. ‘max-depth‘ specifies the maxinum depth of a quadtree and its default value is provided by ‘*max-depth*‘ special variable. ‘max-capacity‘ is the maxinum capacity of a quadtree leaf, subdevided if the value is exceeded, and its default value is provided by ‘*max-capacity*‘ special variable. However, leaves at the maximum depth contain all inserted objects regardless of the capacity.
### [Function] insert
INSERT quadtree object => boolean
Inserts ‘object‘ to ‘quadtree‘. If suceeded, returns ‘t‘. Otherwise, returns ‘nil‘. The case it fails to inserted an object to a quadtree is that it is out of boundary of the quadtree. If the number of objects in a leaf is exceeded, the leaf is subdevided into four subtrees and its objects are distributed to them.
### [Function] query
QUERY quadtree x y &optional neighbor-p => object-list
Queries objects at the point ‘(x, y)‘ to ‘quadtree‘. If ‘neighbor-p‘ is ‘nil‘, returns objects stored in the leaf that contains the point. Otherwise, additionally returns objects stored in leaves neighboring top, bottom, left and right to the leaf that contains the point. The default value of ‘neighbor-p‘ is ‘nil‘.
### [Function] clear
CLEAR quadtree => boolean
Clears the contents of ‘quadtree‘. The return value is always ‘t‘.
### [Function] boundary
BOUNDARY quadtree => boundary
Returns the boundary of ‘quadtree‘, represented by a list of ‘x0‘, ‘y0‘, ‘x1‘ and ‘y1‘. It is intended to be used in following ‘intersect-p‘ function to determine if an object intersects a quadtree.
### [Generic Function] intersect-p
INTERSECT-P quadtree object => boolean
Called when ‘object‘ is being inserted to ‘quadtree‘ which stores objects and returns if ‘object‘ intersects ‘quadtree‘. Library users should implement this generic function as the object’s structure or class they are storing into a quadtree.
## Author
* Masayuki Takagi (kamonama@gmail.com)
## Copyright
Copyright (c) 2015 Masayuki Takagi (kamonama@gmail.com)
## License
Licensed under the MIT License.
0.1
src (module).
Modules are listed depth-first from the system components tree.
Files are sorted by type and then listed depth-first from the systems components trees.
quadtree/src/quadtree.lispsrc (module).
*max-capacity* (special variable).
*max-depth* (special variable).
boundary (function).
clear (function).
insert (function).
intersect-p (generic function).
make (function).
query (function).
%make (function).
%make-quadtree (function).
copy-quadtree (function).
full-p (function).
leaf-p (function).
max-depth-p (function).
node-p (function).
point-intersect-p (function).
quadtree (structure).
quadtree-boundary (reader).
(setf quadtree-boundary) (writer).
quadtree-depth (reader).
(setf quadtree-depth) (writer).
quadtree-max-capacity (reader).
(setf quadtree-max-capacity) (writer).
quadtree-max-depth (reader).
(setf quadtree-max-depth) (writer).
quadtree-ne (reader).
(setf quadtree-ne) (writer).
quadtree-nw (reader).
(setf quadtree-nw) (writer).
quadtree-objects (reader).
(setf quadtree-objects) (writer).
quadtree-p (function).
quadtree-se (reader).
(setf quadtree-se) (writer).
quadtree-sw (reader).
(setf quadtree-sw) (writer).
root-p (function).
subdevide (function).
Packages are listed by definition order.
quadtreecommon-lisp.
*max-capacity* (special variable).
*max-depth* (special variable).
boundary (function).
clear (function).
insert (function).
intersect-p (generic function).
make (function).
query (function).
%make (function).
%make-quadtree (function).
copy-quadtree (function).
full-p (function).
leaf-p (function).
max-depth-p (function).
node-p (function).
point-intersect-p (function).
quadtree (structure).
quadtree-boundary (reader).
(setf quadtree-boundary) (writer).
quadtree-depth (reader).
(setf quadtree-depth) (writer).
quadtree-max-capacity (reader).
(setf quadtree-max-capacity) (writer).
quadtree-max-depth (reader).
(setf quadtree-max-depth) (writer).
quadtree-ne (reader).
(setf quadtree-ne) (writer).
quadtree-nw (reader).
(setf quadtree-nw) (writer).
quadtree-objects (reader).
(setf quadtree-objects) (writer).
quadtree-p (function).
quadtree-se (reader).
(setf quadtree-se) (writer).
quadtree-sw (reader).
(setf quadtree-sw) (writer).
root-p (function).
subdevide (function).
Definitions are sorted by export status, category, package, and then by lexicographic order.
Returns if the object intersects the quadtree
ne.
nw.
se.
sw.
structure-object.
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