#intersection #geometry #sweepline

intersect2d

Line segment intersection detection

7 unstable releases (3 breaking)

0.4.1 Jul 15, 2021
0.4.0 Apr 26, 2021
0.3.1 Feb 28, 2021
0.2.0 Feb 8, 2021
0.1.2 Feb 7, 2021

#123 in Algorithms

33 downloads per month

AGPL-3.0

105KB
2K SLoC

crates.io Documentation Workflow Workflow dependency status

intersect2d

After watching Philipp Kindermann's excellent sweep-line videos I think I finally understand how this algorithm works.

This is my humble take on an implementation of the segment line intersection sweep-line algorithm.

The library crate also contains a line intersection function.

Code still in development, not ready for any purpose.

Rusty voronoi

Interactive step-by-step example:

cargo run --example fltk_gui --features console_trace

Most of this crate have been adapted for nalgebra, cgmath, mint and plain vector here.

Intersection function API example:

use intersection2d::{intersect, Intersection};
use geo;

let line1:geo::Line::<f64> = [(100.0,150.),(150.0,100.)].into();
let line2:geo::Line::<f64> = [(100.0,150.),(150.0,100.)].into();

let _rv = intersect(&line1, &line2);
match _rv {
    Some(Intersection::Intersection(_a)) => panic!("expected an overlap"),
    Some(Intersection::OverLap(a)) => println!("{:?}", a),
    None =>  panic!("expected an overlap"),
}
// you can also get a single intersection point from the Intersection enum.
// Albeit geometrically incorrect, it makes things easy
if let Some(_rv) =_rv {
    println!("{:?}", _rv.single());
}

Sweep-line API example:

use geo;
use intersect2d::algorithm::AlgorithmData;

let _l = vec![
    geo::Line::new(
        geo::Coordinate { x: 200., y: 200. },
        geo::Coordinate { x: 350., y: 300. },
    ),
    geo::Line::new(
        geo::Coordinate { x: 400., y: 200. },
        geo::Coordinate { x: 250., y: 300. },
    ),
];
let results = AlgorithmData::<f64>::default()
    .with_ignore_end_point_intersections(false)?
    .with_lines(_l.into_iter())?
    .compute()?;
for (p, l) in results.iter() {
    println!("Intersection @{:?} Involved lines:{:?}", p, l);
}

Detection of self-intersecting geo::LineString:

let coordinates = vec![(200., 200.), (300., 300.), (400., 200.), (200., 300.)];
let line_string = geo::LineString::from(coordinates);

// Obviously this example only makes sense for LinesStrings with many points.
// A simple brute force O(n²) intersection test will be faster than this O(nlog(n)+k) 
// sweep-line algorithm if n is small enough.  
let result = AlgorithmData::<f32>::default()
    .with_ignore_end_point_intersections(true)?
    .with_stop_at_first_intersection(true)?
    .with_lines(line_string.lines())?
    .compute()?;
for (p, l) in result.iter() {
    println!("Intersection detected @{:?} Involved lines:{:?}", p, l);
}

or using the SelfIntersectingExclusive trait:

// SelfIntersectingExclusive does not report endpoint intersections
use intersect2d::SelfIntersectingExclusive;

let coordinates = vec![(200., 200.), (300., 300.), (400., 200.), (200., 300.)];
let line_string = geo::LineString::from(coordinates);

if line_string.is_self_intersecting()? {
    println!("Intersection detected");
}

for intersections in line_string.self_intersections()? {
    println!("Intersection: {:?}", intersections);
}

You can also check a bunch of geo::Line for self intersections using the SelfIntersectingInclusive trait:

// SelfIntersectingInclusive reports endpoint intersections
use intersect2d::SelfIntersectingInclusive;
let lines = vec![
    geo::Line::new(
        geo::Coordinate { x: 200., y: 200. },
        geo::Coordinate { x: 350., y: 300. },
    ),
    geo::Line::new(
        geo::Coordinate { x: 400., y: 200. },
        geo::Coordinate { x: 250., y: 300. },
    ),
];
if lines.is_self_intersecting_inclusive()? {
    println!("Intersection detected");
}
for intersections in lines.self_intersections_inclusive()? {
    println!("Intersection: {:?}", intersections);
}

Todo

  • Error handling
  • Benchmark and optimize
  • Stable overlapping co-linear line detection

Dependencies

~3.5MB
~76K SLoC