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RandomPolygon.java
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RandomPolygon.java
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package Geometry;
import javax.swing.*;
import java.awt.*;
import java.util.Random;
public class RandomPolygon extends JFrame {
public static int[][] getRandomPolygon(int n, int maxWidth, int maxHeight) {
Random rnd = new Random(1);
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 = n - 1; i2 < n; i1 = i2++)
for (int j2 = 0, j1 = n - 1; j2 < n; 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);
}
// visualization code
public RandomPolygon() {
setContentPane(new JPanel() {
protected void paintComponent(Graphics g) {
super.paintComponent(g);
((Graphics2D) g).setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
((Graphics2D) g).setStroke(new BasicStroke(3));
int[][] xy = getRandomPolygon(new Random().nextInt(100) + 3, getWidth() - 20, getHeight() - 50);
g.setColor(Color.BLUE);
int n = xy[0].length;
for (int i = 0, j = n - 1; i < n; j = i++)
g.drawLine(xy[0][i], xy[1][i], xy[0][j], xy[1][j]);
g.setColor(Color.RED);
for (int i = 0; i < n; i++)
g.drawOval(xy[0][i] - 1, xy[1][i] - 1, 3, 3);
}
});
setSize(new Dimension(600, 600));
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE);
setVisible(true);
new Thread() {
public void run() {
while (true) {
try {
Thread.sleep(200);
} catch (InterruptedException e) {
}
repaint();
}
}
}.start();
}
public static void main(String[] args) {
new RandomPolygon();
}
}