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=begin 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.
=end
class Containers::KDTree
Node = Struct.new(:id, :coords, :left, :right)
# Points is a hash of id => [coord, coord] pairs.
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
# Find k closest points to given coordinates
def find_nearest(target, k_nearest)
@nearest = []
nearest(@root, target, k_nearest, 0)
end
# points is an array
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
private :build_tree
# Euclidian distanced, squared, between a node and target coords
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
private :distance2
# Update array of nearest elements if necessary
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
private :check_nearest
# Recursively find nearest coordinates, going down the appropriate branch as needed
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
private :nearest
end