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 30 def initialize(points) 31 raise "must pass in a hash" unless points.kind_of?(Hash) 32 @dimensions = points[ points.keys.first ].size 33 @root = build_tree(points.to_a) 34 @nearest = [] 35 end
Public Instance Methods
Find k closest points to given coordinates
# File lib/containers/kd_tree.rb 38 def find_nearest(target, k_nearest) 39 @nearest = [] 40 nearest(@root, target, k_nearest, 0) 41 end
Private Instance Methods
points is an array
# File lib/containers/kd_tree.rb 44 def build_tree(points, depth=0) 45 return if points.empty? 46 47 axis = depth % @dimensions 48 49 points.sort! { |a, b| a.last[axis] <=> b.last[axis] } 50 median = points.size / 2 51 52 node = Node.new(points[median].first, points[median].last, nil, nil) 53 node.left = build_tree(points[0...median], depth+1) 54 node.right = build_tree(points[median+1..-1], depth+1) 55 node 56 end
Update array of nearest elements if necessary
# File lib/containers/kd_tree.rb 69 def check_nearest(nearest, node, target, k_nearest) 70 d = distance2(node, target) 71 if nearest.size < k_nearest || d < nearest.last[0] 72 nearest.pop if nearest.size >= k_nearest 73 nearest << [d, node.id] 74 nearest.sort! { |a, b| a[0] <=> b[0] } 75 end 76 nearest 77 end
Euclidian distanced, squared, between a node and target coords
# File lib/containers/kd_tree.rb 60 def distance2(node, target) 61 return nil if node.nil? or target.nil? 62 c = (node.coords[0] - target[0]) 63 d = (node.coords[1] - target[1]) 64 c * c + d * d 65 end
Recursively find nearest coordinates, going down the appropriate branch as needed
# File lib/containers/kd_tree.rb 81 def nearest(node, target, k_nearest, depth) 82 axis = depth % @dimensions 83 84 if node.left.nil? && node.right.nil? # Leaf node 85 @nearest = check_nearest(@nearest, node, target, k_nearest) 86 return 87 end 88 89 # Go down the nearest split 90 if node.right.nil? || (node.left && target[axis] <= node.coords[axis]) 91 nearer = node.left 92 further = node.right 93 else 94 nearer = node.right 95 further = node.left 96 end 97 nearest(nearer, target, k_nearest, depth+1) 98 99 # See if we have to check other side 100 if further 101 if @nearest.size < k_nearest || (target[axis] - node.coords[axis])**2 < @nearest.last[0] 102 nearest(further, target, k_nearest, depth+1) 103 end 104 end 105 106 @nearest = check_nearest(@nearest, node, target, k_nearest) 107 end