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 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 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 { 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 x = new ArrayList<>(); List 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); } }