Quickly and robustly determines which region contains a given query point


Locates a point in a collection of regions. Point location is exact, takes O(log(n)) time, and the data structure has a space requirement of O(n log(n)).


//First create a list of vertices 
var vertices = [
  [0, 0],
  [1, 0],
  [1, 1],
  [0, 1],
  [2, 0],
  [3, 0],
  [3, 1],
  [2, 1],
  [2.25, 0.25],
  [2.75, 0.25],
  [2.75, 0.75],
  [2.25, 0.75]
//Regions are defined by lists of loops of vertex indices 
var regions = [
  //First region, just a square, one loop 
    [0, 1, 2, 3]
  //Second region, square with a hole in the middle 
    [4, 5, 6, 7],
    [11, 10, 9, 8]    //Note inner loop has opposite orientation 
//Now we create the data structure 
var classifyPoint = require("point-in-region")(vertices, regions)
//And we can use it to classify which region contains a given point 
var assert = require("assert")
assert.equal(classifyPoint([0.5, 0.5]), 0)
assert.equal(classifyPoint([2.1, 0.1]), 1)
assert.equal(classifyPoint([100000, 10000]), -1)  //Outside points return -1 
assert.equal(classifyPoint([2.5, 0.5]), -1)  //Point in center hole is outside region 

Here is an in browser demo you can try out yourself:


npm install point-in-region


Preprocesses a collection of regions to answer point location queries efficiently.

  • positions is a list of vertex positions for each of the regions
  • regions is a list of regions encoded as lists of clockwise oriented loops of indices

Returns A point membership classification function for the region set

Note The regions must obey certain topological and geometric properties for this classification to be correct. Specifically:

  • Any two edges are either disjoint, identical, or meet at exactly one common end point
  • The interior of each edge touches at most two regions

Returns the index of the region containing point

  • point is a 2D point encoded as a length 2 array

Returns The index of the region containing point or -1 if it is not in any region.


(c) 2014 Mikola Lysenko. MIT License