JarCastingbox-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:
completewhich detects all pairs of intersections within a single set of boxesbipartitewhich detects pairs of intersections between two different sets of boxes
The parameters to the function are as follows:
boxesis 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.otherBoxesis an optional list of boxes whichboxesis tested against. If not specified, then the algorithm will report self intersections inboxesvisit(i,j)is a callback which is called once for each overlapping pair of boxes. Ifvisitreturns any value not equal toundefined, then the search is terminated immediately and this value is returned. Ifvisitis 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