class Containers::KDTree
A kd-tree is a binary tree that allows one to store points (of any space dimension: 2D, 3D, etc). The structure of the resulting tree makes it so that large portions of the tree are pruned during queries.
One very good use of the tree is to allow nearest neighbor searching. Let's say you have a number of points in 2D space, and you want to find the nearest 2 points from a specific point:
First, put the points into the tree:
kdtree = Containers::KDTree.new( {0 => [4, 3], 1 => [3, 4], 2 => [-1, 2], 3 => [6, 4], 4 => [3, -5], 5 => [-2, -5] })
Then, query on the tree:
puts kd.find_nearest([0, 0], 2) => [[5, 2], [9, 1]]
The result is an array of [distance, id] pairs. There seems to be a bug in this version.
Note that the point queried on does not have to exist in the tree. However, if it does exist, it will be returned.
Constants
- Node
Public Class Methods
Points is a hash of id => [coord, coord] pairs.
# File lib/containers/kd_tree.rb, line 30 def initialize(points) raise "must pass in a hash" unless points.kind_of?(Hash) @dimensions = points[ points.keys.first ].size @root = build_tree(points.to_a) @nearest = [] end
Public Instance Methods
Find k closest points to given coordinates
# File lib/containers/kd_tree.rb, line 38 def find_nearest(target, k_nearest) @nearest = [] nearest(@root, target, k_nearest, 0) end
Private Instance Methods
points is an array
# File lib/containers/kd_tree.rb, line 44 def build_tree(points, depth=0) return if points.empty? axis = depth % @dimensions points.sort! { |a, b| a.last[axis] <=> b.last[axis] } median = points.size / 2 node = Node.new(points[median].first, points[median].last, nil, nil) node.left = build_tree(points[0...median], depth+1) node.right = build_tree(points[median+1..-1], depth+1) node end
Update array of nearest elements if necessary
# File lib/containers/kd_tree.rb, line 69 def check_nearest(nearest, node, target, k_nearest) d = distance2(node, target) if nearest.size < k_nearest || d < nearest.last[0] nearest.pop if nearest.size >= k_nearest nearest << [d, node.id] nearest.sort! { |a, b| a[0] <=> b[0] } end nearest end
Euclidian distanced, squared, between a node and target coords
# File lib/containers/kd_tree.rb, line 60 def distance2(node, target) return nil if node.nil? or target.nil? c = (node.coords[0] - target[0]) d = (node.coords[1] - target[1]) c * c + d * d end
Recursively find nearest coordinates, going down the appropriate branch as needed
# File lib/containers/kd_tree.rb, line 81 def nearest(node, target, k_nearest, depth) axis = depth % @dimensions if node.left.nil? && node.right.nil? # Leaf node @nearest = check_nearest(@nearest, node, target, k_nearest) return end # Go down the nearest split if node.right.nil? || (node.left && target[axis] <= node.coords[axis]) nearer = node.left further = node.right else nearer = node.right further = node.left end nearest(nearer, target, k_nearest, depth+1) # See if we have to check other side if further if @nearest.size < k_nearest || (target[axis] - node.coords[axis])**2 < @nearest.last[0] nearest(further, target, k_nearest, depth+1) end end @nearest = check_nearest(@nearest, node, target, k_nearest) end