programming-examples/java/Data_Structures/SegmentsIntersectionScanline.java

import java.util.*;

public class SegmentsIntersectionScanline {

	public static Segment[] findIntersection(Segment[] s) {
		int n = s.length;
		Event[] events = new Event[n * 2];
		for (int i = 0, cnt = 0; i < n; ++i) {
			events[cnt++] = new Event(s[i].x1, s[i].y1, 1, s[i]);
			events[cnt++] = new Event(s[i].x2, s[i].y2, -1, s[i]);
		}
		Arrays.sort(events, eventComparator);
		NavigableSet<Segment> set = new TreeSet<>(segmentComparator);

		for (Event event : events) {
			Segment cur = event.segment;
			if (event.type == 1) {
				Segment floor = set.floor(cur);
				if (floor != null && isCrossOrTouchIntersect(cur, floor))
					return new Segment[]{cur, floor};
				Segment ceiling = set.ceiling(cur);
				if (ceiling != null && isCrossOrTouchIntersect(cur, ceiling))
					return new Segment[]{cur, ceiling};
				set.add(cur);
			} else {
				Segment lower = set.lower(cur);
				Segment higher = set.higher(cur);
				if (lower != null && higher != null && isCrossOrTouchIntersect(lower, higher))
					return new Segment[]{lower, higher};
				set.remove(cur);
			}
		}
		return null;
	}

	public static class Segment {
		final int x1, y1, x2, y2;

		public Segment(int x1, int y1, int x2, int y2) {
			if (x1 < x2 || x1 == x2 && y1 < y2) {
				this.x1 = x1;
				this.y1 = y1;
				this.x2 = x2;
				this.y2 = y2;
			} else {
				this.x1 = x2;
				this.y1 = y2;
				this.x2 = x1;
				this.y2 = y1;
			}
		}
	}

	static final Comparator<Segment> segmentComparator = (a, b) -> {
		if (a.x1 < b.x1) {
			long v = cross(a.x1, a.y1, a.x2, a.y2, b.x1, b.y1);
			if (v != 0)
				return v > 0 ? -1 : 1;
		} else if (a.x1 > b.x1) {
			long v = cross(b.x1, b.y1, b.x2, b.y2, a.x1, a.y1);
			if (v != 0)
				return v < 0 ? -1 : 1;
		}
		return Integer.compare(a.y1, b.y1);
	};

	static class Event {
		final int x, y;
		final int type;
		final Segment segment;

		public Event(int x, int y, int type, Segment segment) {
			this.x = x;
			this.y = y;
			this.type = type;
			this.segment = segment;
		}
	}

	static final Comparator<Event> eventComparator = (a, b) -> {
		if (a.x != b.x)
			return a.x < b.x ? -1 : 1;
		if (a.type != b.type)
			return a.type > b.type ? -1 : 1;
		return Integer.compare(a.y, b.y);
	};

	static long cross(long ax, long ay, long bx, long by, long cx, long cy) {
		return (bx - ax) * (cy - ay) - (by - ay) * (cx - ax);
	}

	static boolean isCrossOrTouchIntersect(Segment s1, Segment s2) {
		long x1 = s1.x1;
		long y1 = s1.y1;
		long x2 = s1.x2;
		long y2 = s1.y2;
		long x3 = s2.x1;
		long y3 = s2.y1;
		long x4 = s2.x2;
		long y4 = s2.y2;
		if (Math.max(x1, x2) < Math.min(x3, x4) || Math.max(x3, x4) < Math.min(x1, x2)
				|| Math.max(y1, y2) < Math.min(y3, y4) || Math.max(y3, y4) < Math.min(y1, y2))
			return false;
		long z1 = (x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1);
		long z2 = (x2 - x1) * (y4 - y1) - (y2 - y1) * (x4 - x1);
		long z3 = (x4 - x3) * (y1 - y3) - (y4 - y3) * (x1 - x3);
		long z4 = (x4 - x3) * (y2 - y3) - (y4 - y3) * (x2 - x3);
		return (z1 <= 0 || z2 <= 0) && (z1 >= 0 || z2 >= 0) && (z3 <= 0 || z4 <= 0) && (z3 >= 0 || z4 >= 0);
	}

	// random test
	public static void main(String[] args) {
		Random rnd = new Random();
		for (int step = 0; step < 100_000; step++) {
			int n = rnd.nextInt(100);
			Segment[] s = new Segment[n];
			for (int i = 0; i < n; i++) {
				int r = 20;
				int x1 = rnd.nextInt(r) - r / 2;
				int y1 = rnd.nextInt(r) - r / 2;
				int x2 = rnd.nextInt(r) - r / 2;
				int y2 = rnd.nextInt(r) - r / 2;
				s[i] = new Segment(x1, y1, x2, y2);
			}
			Segment[] intersection = findIntersection(s);
			boolean hasIntersection = hasIntersection(s);
			if (intersection == null == hasIntersection)
				throw new RuntimeException();
		}
	}

	static boolean hasIntersection(Segment[] s) {
		for (int i = 0; i < s.length; i++)
			for (int j = i + 1; j < s.length; j++)
				if (isCrossOrTouchIntersect(s[i], s[j]))
					return true;
		return false;
	}
}