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.

This crate is educational, not ready for any production purpose. It has been adopted as a glam and cgmath library here: Linestring.

Interactive step-by-step example:

cargo run --example fltk_gui --features console_trace

Intersection function API example:

use intersect2d::{intersect, Intersection};
let line1 = geo::Line::<f64>::from([(100.0,150.),(150.0,100.)]);
let line2 = geo::Line::<f64>::from([(100.0,150.),(150.0,100.)]);
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
println!("{:?}", rv.unwrap().single());

Sweep-line API example:

let lines = vec![
    geo::Line::<f64>::from([(200.0,200.),(350.0,300.)]),
    geo::Line::<f64>::from([(400.0,200.),(250.0,300.)]),
];
let results = intersect2d::algorithm::AlgorithmData::<f64>::default()
    .with_ignore_end_point_intersections(false)?
    .with_lines(lines.into_iter())?
    .compute()?;
for (point, line) in results {
    println!("Intersection @{:?} Involved lines:{:?}", point, line);
}

Detection of self-intersecting geo:

let coordinates = vec![(200., 200.), (300., 300.), (400., 200.), (200., 300.)];
let line_string = geo::LineString::<f32>::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 = intersect2d::algorithm::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 {
    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::<f64>::from([(200.0,200.),(350.0,300.)]),
    geo::Line::<f64>::from([(400.0,200.),(250.0,300.)]),
];
if lines.is_self_intersecting_inclusive()? {
    println!("Intersection detected");
}
for intersections in lines.self_intersections_inclusive()? {
    println!("Intersection: {:?}", intersections);
}

Todo

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