interval.js

Library implementing mathematical real numbers intervals arithmetics).
Available operations:

- union (A∪B)
- difference (A\B)
- intersection (A∩B)
- exclusion (A△B)
- inversion (A')
- subset (A⊆B)
- superset (A⊇B)
- contains (A∍x)

Utils functions:

- toString()
- count()
- forEach()
- forEachPoint()
- intervals()

Installation

Install with npm:
``npm install intervaljs`

Install with bower:
`bower install intervaljs`

Initializations

##### new Interval(start, [end=start])
Create Interval object.
`js
new Interval().toString(); // ''
new Interval(2).toString(); // '{2}'
new Interval(1, 3).toString(); // [1;3]
`

##### new Interval.Endpoint(value, [open=false])
Create complex interval Endpoint.
`js
var eStart = new Interval.Endpoint(2, false); // 'endpoint closed'
var eEnd = new Interval.Endpoint(3, true); // 'endpoint open'

new Interval(eStart, eEnd).toString() // [2, 3) - left closed, right open
`

API

##### .union(intervalObj) or .union(start, [end=start])
A∪B - Add intervals to interval.

`js
new Interval(1, 3)
.union(5, 7)
.union(new Interval(6, Infinity))
.toString();
// [1;3], [5;Infinity)
`

##### .difference(interval) or .difference(start, [end=start])
A\B - Substract interval from interval.

`js
new Interval(1, 8)
.diference(5, 9)
.diference(3)
.toString();
// [1;3), (3,5)
`

##### .intersection(interval) or .intersection(start, [end=start])
A∩B - Common part of intervals.

`js
var interval = new Interval(2, 6)
.intersection(4, 8);
// [4;6]
`

##### .exclusion(interval) or .exclusion(start, [end=start])
A△B - Exclusive OR or intervals.

`js
var interval = new Interval(2, 6)
.exclusion(4, 8);
// [2;4), (6;8]
`

##### .inversion()
A' - Invert interval.

`js
new Interval(1, 8)
.inversion()
// (-Infinity;1), (8,Infinity)
`

##### .subset(interval) or .subset(start, [end=start])
A⊆B - Check if interval is a subset of other interval

`js
new Interval(5, 8)
.subset(1, 8)
// true
new Interval(1, 8)
.subset(2, 5);
// false
`


##### .superset(interval) or .superset(start, [end=start])
A⊇B - Check if interval is a superset for other interval

`js
new Interval(1, 8)
.superset(5, 8)
// true
new Interval(1, 8)
.diference(5, 9)
.superset(2, 5);
// false

var i1 = new Interval(1, 4)
.union(6, 9)
var i2 = new Interval(1, 9)
.diference(4, 6)
i1.superset(i2)
// true
`


##### .contains(value)
A∍x - Check if interval contains a memeber.

`js
new Interval(1, 8)
.contains(5)
// true

`

Utils

##### .intervals()
Return intervals array

`js
var arr = new Interval(1, 6)
.union(8)
.intervals()

arr.length;
// 2
`

##### .forEach(callback(start, end), [step=0])
Iterate throught interval parts borders, with minimal step for open endpoints.
For step equal 0, function return border values skipping open/close atributes.

`js
new Interval(1, 6)
.difference(4, 8) // we have [1;4)
.forEach(function(start, end) {
// start is 1
// end = 4
}, 0) // step = 0

// same case with step value
new Interval(1, 6)
.difference(4, 8) // we have [1;4)
.forEach(function(start, end) {
// start is 1
// end = 3.5
}, 0.5) // step = 0.5
`

##### .forEachPoint(callback(point), [step=1])
Iterate throught interval points with assigned step (default 1)

`js
new Interval(1, 6)
.diference(4, 8)
.forEach(function(point) {
// point = 1, then 2, then 3
})
`

##### .count()
Return count of intervals

`js
new Interval(1, 6)
.union(8)
.count()
// 2
`

##### .toString()
Output intervals string

`js
new Interval(1, 6)
.diference(3, 4)
.union(8)
.toString()
// [1;3), (4,6], {8}
``