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Fast n-dimensional orthogonal range searches for static point sets


Given a collection of points in n-dimensional space, preprocesses these points so that orthogonal range queries can be computed efficiently. Internally, this library is built using range trees.


var preprocess = require("static-range-query")
//Generate 10000 4D points 
var D = 4, N = 10000
var points = new Array(N)
for(var i=0; i<N; ++i) {
  var p = new Array(D)
  for(var j=0; j<N; ++j) {
    p[j] = Math.random() * 1000
  points[i] = p
//Construct query data structure 
var rangeQuery = preprocess(points)
//Now execute a range query! 
rangeQuery([2, 5, 0.25, -10], [10, 50, 5, 30], function(i) {
  console.log("In range: ", i , points[i])


npm install static-range-query


var rangeQuery = require("static-range-query")(points)

Preprocesses the point set so that orthogonal range queries can be evaluated efficiently.

  • points is an array of points (each point is represented as a tuple of D numbers)

Returns A rangeSearch() function (see below) which evaluates range queries on the point set.

Time Complexity O(points.length * log(points.length)^points[0].length)

Space Complexity O(points.length * log(points.length)^points[0].length)

Notes Internally, this function builds a range tree and binds it to the query method

rangeQuery(lo, hi, cb(index))

Evaluates a range query on the point set.

  • lo is a lower bound on the bounding rectangle to query
  • hi is an upper bound on the bounding rectangle to query
  • cb is a callback which gets called once per each point in the range with the index of a point.

Time Complexity O(log(points.length)^points[0].length + k) where k is the number of points processed in the range.

Note The points are visited in lexicographic order

Other Note You can terminate the search early by returning true from cb, for example:

rangeQuery([0, 0, 0], [100, 100, 100], function(i) {
  if(=== 100) {
    console.log("found it!")
    return true
  //Continue processing .... 
  return false


(c) 2013 Mikola Lysenko. MIT License