programming-examples/java/Data_Structures/PointInPolygon.java

import java.awt.*;
import java.util.Random;

public class PointInPolygon {

	public static int pointInPolygon(int qx, int qy, int[] x, int[] y) {
		int n = x.length;
		int cnt = 0;
		for (int i = 0, j = n - 1; i < n; j = i++) {
			if (y[i] == qy && (x[i] == qx || y[j] == qy && (x[i] <= qx || x[j] <= qx) && (x[i] >= qx || x[j] >= qx)))
				return 0; // boundary
			if ((y[i] > qy) != (y[j] > qy)) {
				long det = ((long) x[i] - qx) * ((long) y[j] - qy) - ((long) x[j] - qx) * ((long) y[i] - qy);
				if (det == 0)
					return 0; // boundary
				if ((det > 0) != (y[j] > y[i]))
					++cnt;
			}
		}
		return cnt % 2 == 0 ? -1 /* exterior */ : 1 /* interior */;
	}

	static int pointInPolygon2(int qx, int qy, int[] x, int[] y) {
		double sumAngles = 0;
		for (int i = 0, j = x.length - 1; i < x.length; j = i++) {
			if (isCrossOrTouchIntersect(qx, qy, qx, qy, x[i], y[i], x[j], y[j]))
				return 0;
			long x1 = x[j] - qx;
			long y1 = y[j] - qy;
			long x2 = x[i] - qx;
			long y2 = y[i] - qy;
			sumAngles += Math.atan2(x1 * y2 - y1 * x2, x1 * x2 + y1 * y2);
		}
		return Math.abs(sumAngles) < 1e-9 ? -1 : 1;
	}

	static int pointInPolygon3(int qx, int qy, int[] x, int[] y) {
		Random rnd = new Random();
		long x2 = rnd.nextInt(100_000_000) + 100_000_000;
		long y2 = rnd.nextInt(100_000_000) + 100_000_000;
		int cnt = 0;
		for (int i = 0, j = x.length - 1; i < x.length; j = i++) {
			if (isCrossOrTouchIntersect(qx, qy, qx, qy, x[i], y[i], x[j], y[j]))
				return 0;
			if (isCrossIntersect(qx, qy, x2, y2, x[i], y[i], x[j], y[j]))
				++cnt;
		}
		return cnt % 2 == 0 ? -1 : 1;
	}

	// random test
	public static void main(String[] args) {
		for (int step = 0; step < 10_000; step++) {
			int n = rnd.nextInt(10) + 3;
			int range = 10;
			int[][] xy = getRandomPolygon(n, range, range);
			int[] x = xy[0];
			int[] y = xy[1];
			int qx = rnd.nextInt(3 * range) - range;
			int qy = rnd.nextInt(3 * range) - range;
			boolean res = new Polygon(x, y, n).contains(qx, qy);
			for (int i = 0, j = n - 1; i < n; j = i++)
				res |= isCrossOrTouchIntersect(qx, qy, qx, qy, x[i], y[i], x[j], y[j]); // apply fix
			int res1 = pointInPolygon(qx, qy, x, y);
			int res2 = pointInPolygon2(qx, qy, x, y);
			int res3 = pointInPolygon3(qx, qy, x, y);
			if (res == (res1 == -1) || res1 != res2 || res1 != res3)
				throw new RuntimeException();
		}
	}

	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);
	}

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