Quadtree data structure in Common Lisp

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Masayuki Takagi




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Quadtree is quadtree data structure in Common Lisp.


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)))


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)


[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.



Copyright (c) 2015 Masayuki Takagi (kamonama@gmail.com)


Licensed under the MIT License.

Dependencies (1)

  • prove

Dependents (0)

    • GitHub
    • Quicklisp