PolygonsIntersection.java

package Geometry;
import java.awt.Polygon;
import java.awt.geom.Area;
import java.awt.geom.PathIterator;
import java.util.*;

public class PolygonsIntersection {

	public static double overlap(Point[] polygon1, Point[] polygon2) {
		Point[][] polygons = {polygon1, polygon2};
		Set<Double> xs = new TreeSet<>();
		for (Point point : polygon1)
			xs.add(point.x);
		for (Point point : polygon2)
			xs.add(point.x);

		for (int i1 = 0, j1 = polygon1.length - 1; i1 < polygon1.length; j1 = i1++) {
			for (int i2 = 0, j2 = polygon2.length - 1; i2 < polygon2.length; j2 = i2++) {
				Point intersection = getSegmentsIntersection(polygon1[i1], polygon1[j1], polygon2[i2], polygon2[j2]);
				if (intersection != null) {
					xs.add(intersection.x);
				}
			}
		}

		Double[] xsa = xs.toArray(new Double[xs.size()]);
		double res = 0.0;
		for (int k = 0; k + 1 < xsa.length; k++) {
			double x = (xsa[k] + xsa[k + 1]) * 0.5;
			Point sweep0 = new Point(x, 0);
			Point sweep1 = new Point(x, 1);
			List<Event> events = new ArrayList<>();

			for (int p = 0; p < 2; p++) {
				Point[] polygon = polygons[p];
				double area = 0;
				for (int i = 0, j = polygon.length - 1; i < polygon.length; j = i++)
					area += (polygon[j].x - polygon[i].x) * (polygon[j].y + polygon[i].y);
				for (int j = 0, i = polygon.length - 1; j < polygon.length; i = j++) {
					Point intersection = getLinesIntersection(polygon[j], polygon[i], sweep0, sweep1);
					if (intersection != null) {
						double y = intersection.y;
						double x0 = polygon[i].x;
						double x1 = polygon[j].x;
						if (x0 < x && x1 > x) {
							events.add(new Event(y, (int) Math.signum(area) * (1 << p)));
						} else if (x0 > x && x1 < x) {
							events.add(new Event(y, -(int) Math.signum(area) * (1 << p)));
						}
					}
				}
			}

			Collections.sort(events);

			double a = 0.0;
			int mask = 0;
			for (int j = 0; j < events.size(); j++) {
				if (mask == 3)
					a += events.get(j).y - events.get(j - 1).y;
				mask += events.get(j).maskDelta;
			}

			res += a * (xsa[k + 1] - xsa[k]);
		}
		return res;
	}

	static class Point {
		double x;
		double y;

		Point(double x, double y) {
			this.x = x;
			this.y = y;
		}
	}

	static class Event implements Comparable<Event> {
		public double y;
		public int maskDelta;

		public Event(double y, int maskDelta) {
			this.y = y;
			this.maskDelta = maskDelta;
		}

		@Override
		public int compareTo(Event o) {
			if (y != o.y)
				return Double.compare(y, o.y);
			return Integer.compare(maskDelta, o.maskDelta);
		}
	}

	static final double eps = 1e-9;

	static Point getLinesIntersection(Point p1, Point p2, Point p3, Point p4) {
		double a1 = p2.y - p1.y;
		double b1 = p1.x - p2.x;
		double c1 = -(p1.x * p2.y - p2.x * p1.y);
		double a2 = p4.y - p3.y;
		double b2 = p3.x - p4.x;
		double c2 = -(p3.x * p4.y - p4.x * p3.y);
		double det = a1 * b2 - a2 * b1;
		if (Math.abs(det) < eps)
			return null;
		double x = -(c1 * b2 - c2 * b1) / det;
		double y = -(a1 * c2 - a2 * c1) / det;
		return new Point(x, y);
	}

	static Point getSegmentsIntersection(Point p1, Point p2, Point p3, Point p4) {
		if (!isCrossIntersect(p1, p2, p3, p4))
			return null;
		return getLinesIntersection(p1, p2, p3, p4);
	}

	static boolean isCrossIntersect(Point p1, Point p2, Point p3, Point p4) {
		double z1 = (p2.x - p1.x) * (p3.y - p1.y) - (p2.y - p1.y) * (p3.x - p1.x);
		double z2 = (p2.x - p1.x) * (p4.y - p1.y) - (p2.y - p1.y) * (p4.x - p1.x);
		double z3 = (p4.x - p3.x) * (p1.y - p3.y) - (p4.y - p3.y) * (p1.x - p3.x);
		double z4 = (p4.x - p3.x) * (p2.y - p3.y) - (p4.y - p3.y) * (p2.x - p3.x);
		return (z1 < -eps || z2 < -eps) && (z1 > eps || z2 > eps) && (z3 < -eps || z4 < -eps) && (z3 > eps || z4 > eps);
	}

	// random test
	public static void main(String[] args) {
		for (int step = 0; step < 1000; step++) {
			int n = rnd.nextInt(20) + 3;
			int range = 10;
			Point[] polygon1 = convert(getRandomPolygon(n, range, range));
			Point[] polygon2 = convert(getRandomPolygon(n, range, range));

			double res1 = overlap(polygon1, polygon2);
			double res2 = overlap2(polygon1, polygon2);

			if (Math.abs(res1 - res2) > 1e-9)
				throw new RuntimeException();
		}
	}

	static Point[] convert(int[][] xy) {
		Point[] polygon = new Point[xy[0].length];
		for (int i = 0; i < xy[0].length; i++) {
			polygon[i] = new Point(xy[0][i], xy[1][i]);
		}
		return polygon;
	}

	static double overlap2(Point[] points1, Point[] points2) {
		Area a = new Area(getPolygon(points1));
		a.intersect(new Area(getPolygon(points2)));
		double pt[] = new double[6];
		List<Double> x = new ArrayList<>();
		List<Double> y = new ArrayList<>();
		double area = 0;
		for (PathIterator p = a.getPathIterator(null); !p.isDone(); p.next()) {
			if (p.currentSegment(pt) == PathIterator.SEG_CLOSE) {
				double cur = 0;
				for (int i = 0, j = x.size() - 1; i < x.size(); j = i++)
					cur += x.get(i) * y.get(j) - x.get(j) * y.get(i);
				x.clear();
				y.clear();
				area += Math.abs(cur / 2);
			} else {
				x.add(pt[0]);
				y.add(pt[1]);
			}
		}
		return area;
	}

	static Polygon getPolygon(Point[] points) {
		Polygon polygon = new Polygon();
		for (Point point : points)
			polygon.addPoint((int) point.x, (int) point.y);
		return polygon;
	}

	static Random rnd = new Random(1);

	static int[][] getRandomPolygon(int n, int maxWidth, int maxHeight) {
		int[] x = new int[n];
		int[] y = new int[n];
		int[] p = new int[n];
		while (true) {
			for (int i = 0; i < n; i++) {
				x[i] = rnd.nextInt(maxWidth);
				y[i] = rnd.nextInt(maxHeight);
				p[i] = i;
			}
			for (boolean improved = true; improved; ) {
				improved = false;
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < n; j++) {
						int[] p1 = p.clone();
						reverse(p1, i, j);
						if (len(x, y, p) > len(x, y, p1)) {
							p = p1;
							improved = true;
						}
					}
				}
			}
			int[] tx = x.clone();
			int[] ty = y.clone();
			for (int i = 0; i < n; i++) {
				x[i] = tx[p[i]];
				y[i] = ty[p[i]];
			}
			boolean ok = true;
			for (int i = 0; i < n; i++) {
				long x1 = x[(i - 1 + n) % n] - x[i];
				long y1 = y[(i - 1 + n) % n] - y[i];
				long x2 = x[(i + 1) % n] - x[i];
				long y2 = y[(i + 1) % n] - y[i];
				ok &= x1 * y2 - x2 * y1 != 0 || x1 * x2 + y1 * y2 <= 0;
			}
			for (int i2 = 0, i1 = p.length - 1; i2 < p.length; i1 = i2++)
				for (int j2 = 0, j1 = p.length - 1; j2 < p.length; j1 = j2++)
					ok &= i1 == j1 || i1 == j2 || i2 == j1
							|| !isCrossOrTouchIntersect(x[i1], y[i1], x[i2], y[i2], x[j1], y[j1], x[j2], y[j2]);
			if (ok)
				return new int[][]{x, y};
		}
	}

	// http://en.wikipedia.org/wiki/2-opt
	static void reverse(int[] p, int i, int j) {
		int n = p.length;
		// reverse order from i to j
		while (i != j) {
			int t = p[j];
			p[j] = p[i];
			p[i] = t;
			i = (i + 1) % n;
			if (i == j) break;
			j = (j - 1 + n) % n;
		}
	}

	static double len(int[] x, int[] y, int[] p) {
		double res = 0;
		for (int i = 0, j = p.length - 1; i < p.length; j = i++) {
			double dx = x[p[i]] - x[p[j]];
			double dy = y[p[i]] - y[p[j]];
			res += Math.sqrt(dx * dx + dy * dy);
		}
		return res;
	}

	static boolean isCrossOrTouchIntersect(long x1, long y1, long x2, long y2, long x3, long y3, long x4, long y4) {
		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);
	}
}