Returns the entrance and exit intersections of a line segment with a circle

line_segment_and_circle_intersections.rs

// based on https://stackoverflow.com/a/1084899
// Vec2 is from the vek crate

type Entrance = Vec2<f32>;
type Exit = Vec2<f32>;

fn line_segment_and_circle_intersections(
	line_segment_start: Vec2<f32>,
	line_segment_end: Vec2<f32>,
	circle_center: Vec2<f32>,
	circle_radius: f32,
) -> (Option<Entrance>, Option<Exit>) {
	let d = line_segment_end - line_segment_start;
	let f = line_segment_start - circle_center;
	let a = d.dot(d);
	let b = 2.0 * f.dot(d);
	let c = f.dot(f) - circle_radius * circle_radius;
	let mut discriminant = b * b - 4.0 * a * c;
	if discriminant < 0.0 {
		return (None, None);
	}
	discriminant = discriminant.sqrt();
	let t1 = (-b - discriminant) / (2.0 * a);
	let t2 = (-b + discriminant) / (2.0 * a);
	let intersection1 = if t1 >= 0.0 && t1 <= 1.0 {
		Some(line_segment_start + (line_segment_end - line_segment_start) * t1)
	} else {
		None
	};
	let intersection2 = if t2 >= 0.0 && t2 <= 1.0 {
		Some(line_segment_start + (line_segment_end - line_segment_start) * t2)
	} else {
		None
	};
	(intersection1, intersection2)
}