class Containers::KDTree
rdoc
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. MIT License Copyright (c) 2009 Kanwei Li 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. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Constants
- Node
Public Class Methods
new(points)
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Points is a hash of id => [coord, coord] pairs.
# File lib/containers/kd_tree.rb, line 51 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_nearest(target, k_nearest)
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Find k closest points to given coordinates
# File lib/containers/kd_tree.rb, line 59 def find_nearest(target, k_nearest) @nearest = [] nearest(@root, target, k_nearest, 0) end
Private Instance Methods
build_tree(points, depth=0)
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points is an array
# File lib/containers/kd_tree.rb, line 65 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
check_nearest(nearest, node, target, k_nearest)
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Update array of nearest elements if necessary
# File lib/containers/kd_tree.rb, line 90 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
distance2(node, target)
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Euclidian distanced, squared, between a node and target coords
# File lib/containers/kd_tree.rb, line 81 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
nearest(node, target, k_nearest, depth)
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Recursively find nearest coordinates, going down the appropriate branch as needed
# File lib/containers/kd_tree.rb, line 102 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