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box-intersect

This modules finds all intersection in a set of n boxes in d-dimensions, or between a pair of sets with n and m boxes respectively. The time taken is O((n+m) log^d(n+m)) and the algorithm uses a temporary scratch memory of size O(n+m). This memory is pooled so that after the first execution no additional memory is allocated. Some possible applications of this library include:

  • Collision detection
  • Polygon clipping
  • Batched box stabbing queries
  • Mesh boolean operations (CSG)

The algorithm in this package is based on the one described in the following paper:

A detailed experimental analysis of the performance of this module as well as comparisons with other libraries for box intersection can be found in the following repository:

For more information on this problem, please see the following series of blog posts:

Example

Detecting overlaps in a set of boxes

Here is how to detect all pairs of overlapping boxes in a single set of boxes:

var boxIntersect = require('box-intersect')

//Boxes are listed as flattened 2*d length arrays
var boxes = [
  [1, 1, 2, 2],   //Interpretation: [minX, minY, maxX, maxY]
  [0, -1, 3, 2],
  [2, 1, 4, 5],
  [0.5, 3, 1, 10]
]

//Default behavior reports list of intersections
console.log('overlaps:', boxIntersect(boxes))

//Note:  Boxes are closed

//Can also use a visitor to report all crossings
var result = boxIntersect(boxes, function(i,j) {
  console.log('overlap:', boxes[i], boxes[j])

  //Can early out by returning any value
  if(i === 2 || j === 2) {
    return 2
  }
})

console.log('early out result:', result)

Output

overlap: [ [ 0, 1 ], [ 0, 2 ], [ 1, 2 ] ]
overlap: [ 1, 1, 2, 2 ] [ 0, -1, 3, 2 ]
overlap: [ 1, 1, 2, 2 ] [ 2, 1, 4, 5 ]
early out result: 2

Bipartite intersection

You can also detect all intersections between two different sets of boxes:

var boxIntersect = require('box-intersect')

//Again, boxes are given as flattened lists of coordinates
var red = [
  [0, 0, 0, 8, 1, 1],  //Format: [minX, minY, minZ, maxX, maxY, maxZ]
  [0, 0, 0, 1, 8, 1],
  [0, 0, 0, 1, 1, 8]
]

var blue = [
  [5, 0, 0, 6, 10, 10],
  [0, 5, 0, 10, 6, 10],
  [0, 0, 5, 10, 10, 10]
]

//Report all crossings
console.log('crossings=', boxIntersect(red, blue))

//Again can use a visitor:
boxIntersect(red, blue, function(r, b) {
  console.log('overlap:', red[r], blue[b])
})

Output

crossings= [ [ 0, 0 ], [ 1, 1 ], [ 2, 2 ] ]
overlap: [ 0, 0, 0, 8, 1, 1 ] [ 5, 0, 0, 6, 10, 10 ]
overlap: [ 0, 0, 0, 1, 8, 1 ] [ 0, 5, 0, 10, 6, 10 ]
overlap: [ 0, 0, 0, 1, 1, 8 ] [ 0, 0, 5, 10, 10, 10 ]

Install

Using npm, just run the following command:

npm install box-intersect

This module works in any reasonable CommonJS environment, such as browsersify, iojs or node.js.

API

var boxIntersect = require('box-intersect')

boxIntersect(boxes[, otherBoxes, visit])

Finds all pairs intersections in a set of boxes. There are two basic modes of operation for this function:

  • complete which detects all pairs of intersections within a single set of boxes
  • bipartite which detects pairs of intersections between two different sets of boxes

The parameters to the function are as follows:

  • boxes is a list of boxes. Boxes are represented as length 2*d arrays where the first d-components are the lower bound of the box and then the next d components are the upper bound.
  • otherBoxes is an optional list of boxes which boxes is tested against. If not specified, then the algorithm will report self intersections in boxes
  • visit(i,j) is a callback which is called once for each overlapping pair of boxes. If visit returns any value not equal to undefined, then the search is terminated immediately and this value is returned. If visit is not specified, then a list of intersecting pairs is returned.

Returns If visit was specified, then the last returned value of visit. Otherwise an array of pairs of intersecting boxes.

Note The boxes are treated as cartesian products of closed intervals. For example, the boxes [1,1,2,2] and [0,0,1,1] will be reported as intersecting by this module.

License

(c) 2014 Mikola Lysenko. MIT License