Quadtrees

Implementation of Quadtrees using the julia programming language. This package is intended to be used with the Alexya.jl package and the Luxor.jl package, but it can be used independently.

import Pkg; Pkg.add("Quadtrees")

Or

julia> ] add Quadtrees

First, import the Quadtrees module:

using Quadtrees

# or

import Quadtrees: Quadtree

Then, define the data type you need to use with the quadtree. Remember that your type must have a 2D position.

mutable struct Particle
    x::Real
    y::Real
    radius::Real
end

Before constructing the quadtree object, you need to define the Quadtrees.position method for your type:

Quadtrees.position(p::Particle) = (p.x, p.y)

The Quadtrees.position method is used to determine the position of each element in the quadtree, so it's important to define it, otherwise your code won't work.

Then, create your quadtree.

qt = Quadtree{Particle}((0, 0), 400, 400, 4)

The Quadtree constructor accept four parameters:

1. A tuple of two real numbers (x, y), that determines the quadtree's center position.
2. The quadtree's width.
3. The quadtree's height.
4. The quadtree's capacity (how many items it will have before dividing).

Then, create your objects (Particles in this case), and insert then in your quadtree.

for i in 0:999
    # two random numbers between 0 and 200
    x, y = rand(Float64, 2) * 200
    # add 1 to make sure the radius is not zero
    radius = rand(Float64) * 49 + 1
    p = Particle(x, y, radius)
    # insert the particle into the quadtree.
    insert!(qt, p)
end

Now you can search the quadtree for items (Particles, in this case), that are located within a circular range, located at (x, y) with radius r.

For example, searching for particles within a range located at (5, 10) with radius 50:

# s for search
sx, sy = 5, 10
sr = 50
result = search(qt, sx, sy, sr)

The return is an array of the object type that the quadtree contains.

Note: If no object is within the range, the result will be an empty array.

Now you can do whatever you want with the objects that the search found:

For example, i'll make each particle object 20% bigger:

for particle in result
    particle.radius += particle.radius * .20
end

1. implement the clear method.
2. dynamic quadtree.

MIT License

Copyright (c) 2021 Jorge Pereira jorge.brito.json@gmail.com

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

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