3 releases
0.1.2 | Jan 14, 2024 |
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0.1.1 | Jan 7, 2024 |
0.1.0 | Jan 7, 2024 |
#605 in Algorithms
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1.5K
SLoC
Intervals on ℝⁿ
Mathematical intervals, i.g., [a, b], (a, b), [a, b), and (a, b] on ℝ (real number line). Also supports multi-dimensional axis-aligned boxes.
NOTE: Not yet stable.
Intervals on ℝ
Intervals like [a, b], (a, b), [a, b), and (a, b] for any PartialOrd
type.
Properties
lower_bound left . center right upper_bound
...------------>|<------- self -------------------->|<------------ ...
inf sup
[<------------ closure ------------>]
(<----------- interior ---------->)
Set operations
|<------------- a ----------------->| . p |<-------- c -------->|
|<--------------- b ------------------->|
|<--- a.intersection(&b) --->|
|<-- a.gap(&c) -->|
|<------------- a.hull(p) ------------->|
|<---------------------------------- a.span(&c) --------------------------->|
|<--------------------------------->| + |<------------------->| a.union(&c)
|<---->| a.difference(&b)
|<- δ -+---- c.dilate(δ) ----+- δ ->|
Examples
use inter_val::{Inclusive, Exclusive, Interval};
// Closed interval of i32
let a = Inclusive.at(0).to(Inclusive.at(10)); // [0, 10]
assert!(a.contains(&3));
// Half-open interval of f64
let b = Inclusive.at(1.23).to(Exclusive.at(4.56)); // [1.23, 4.56)
assert!(!b.contains(&4.56));
assert!(b.contains(&(4.56 - 0.000000000000001)));
// Intersection
let c = Inclusive.between(5, 15); // [5, 15]
let isect = a.intersection(&c).unwrap(); // [0, 10] ∩ [5, 15] = [5, 10]
assert_eq!(isect.inf(), &5);
assert_eq!(isect.sup(), &10);
// Span & Gap
let d = Inclusive.between(12, 15); // [12, 15]
let span = a.span(&d); // [0, 15]
let gap = a.gap(&d); // (10, 12)
assert_eq!(span, Inclusive.between(0, 15));
assert_eq!(gap.unwrap(), Exclusive.between(10, 12));
// Union
let union = a.union(&d);
assert_eq!(union.span, span);
assert_eq!(union.gap, gap);
assert_eq!(union.into_vec(), vec![a, d]);
// Hull
let hull = Interval::<_>::hull_many(vec![3, 9, 2, 5]).unwrap(); // [2, 9]
assert_eq!(hull, Inclusive.between(2, 9));
// Linear interpolation
assert_eq!(b.lerp(0.0), *b.inf());
assert_eq!(b.lerp(1.0), *b.sup());
assert_eq!(b.lerp(0.2), 0.8 * *b.inf() + 0.2 * *b.sup());
// Split
let (lower, upper) = b.split_at(3.45); // Split [1.23, 4.56) at 3.45
assert_eq!(lower.inf(), b.inf());
assert_eq!(lower.sup(), &3.45);
assert_eq!(upper.inf(), &3.45);
assert_eq!(upper.sup(), b.sup());
Axis-aligned box on ℝⁿ
Boxes represented by Cartesian product of intervals.
use inter_val::{Box2, Inclusive};
// [0.0, 10.0] × [5.0, 20.0]
let a: Box2<f64> = Box2::new(Inclusive.between(0.0, 10.0), Inclusive.between(5.0, 20.0));
// Another way to construct [0.0, 10.0] × [5.0, 20.0]
let b: Box2<f64> = Box2::between(&[0.0, 5.0], &[10.0, 20.0]);
assert_eq!(a, b);
// Hull
let b = a.hull(&[12.3, 7.5]);
assert_eq!(b, Box2::between(&[0.0, 5.0], &[12.3, 20.0]));
Future work
- Enhance
BoxN
. - Interval set.
- Sufficient tests.
Not promised :-)
Dependencies
~0.6–1.2MB
~26K SLoC