java.lang.Object
  ⇒ java.awt.Polygon

public class Polygon extends Object implements Shape, Serializable

Polygon
public Polygon(int[] xpoints,
               int[] ypoints,
               int npoints)

int[] xpoints = {30, 150, 170, 120, 30};
int[] ypoints = {20, 40, 140, 110, 80};
int npoints = xpoints.length;
Polygon polygon = new Polygon(xpoints, ypoints, npoints);

サンプルプログラム

/**
 * Polygonクラス
 */
import javax.swing.*;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.geom.*;
import java.awt.Polygon;

public class PolygonTest1 extends JPanel{
  public static void main(String[] args){
    JFrame frame = new JFrame();

    PolygonTest1 app = new PolygonTest1();
    frame.getContentPane().add(app);

    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.setBounds(10, 10, 300, 200);
    frame.setTitle("タイトル");
    frame.setVisible(true);
  }

  public void paintComponent(Graphics g){
    Graphics2D g2 = (Graphics2D)g;

    g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, 
                        RenderingHints.VALUE_ANTIALIAS_ON);

    int[] xpoints = {30, 150, 170, 80, 30};
    int[] ypoints = {20, 40, 120, 140, 80};
    int npoints = xpoints.length;
    Polygon polygon = new Polygon(xpoints, ypoints, npoints);

    g2.draw(polygon);
  }
}

addPoint
public void addPoint(int x,
                     int y)

int[] xpoints = {30, 150, 170, 120, 30};
int[] ypoints = {20, 40, 140, 110, 80};
int npoints = xpoints.length;
Polygon polygon = new Polygon(xpoints, ypoints, npoints);

polygon.addPoint(40, 50);

サンプルプログラム

/**
 * 頂点を追加する
 */
import javax.swing.*;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.geom.*;
import java.awt.Polygon;
import java.awt.Color;

public class PolygonTest2 extends JPanel{
  public static void main(String[] args){
    JFrame frame = new JFrame();

    PolygonTest2 app = new PolygonTest2();
    frame.getContentPane().add(app);

    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.setBounds(10, 10, 300, 200);
    frame.setTitle("タイトル");
    frame.setVisible(true);
  }

  public void paintComponent(Graphics g){
    Graphics2D g2 = (Graphics2D)g;

    g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, 
                        RenderingHints.VALUE_ANTIALIAS_ON);

    int[] xpoints = {60, 180, 200, 130, 60};
    int[] ypoints = {20, 40, 120, 140, 110};
    int npoints = xpoints.length;
    Polygon polygon = new Polygon(xpoints, ypoints, npoints);

    g2.draw(polygon);

    polygon.addPoint(40, 70);

    g2.setPaint(Color.PINK);
    g2.draw(polygon);
  }
}

translate
public void translate(int deltaX,
                      int deltaY)

int[] xpoints = {30, 150, 170, 120, 30};
int[] ypoints = {20, 40, 140, 110, 80};
int npoints = xpoints.length;
Polygon polygon = new Polygon(xpoints, ypoints, npoints);

polygon.translate(10, 20);

サンプルプログラム

/**
 * 位置を移動する
 */
import javax.swing.*;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import java.awt.geom.*;
import java.awt.Polygon;
import java.awt.Color;

public class PolygonTest3 extends JPanel{
  public static void main(String[] args){
    JFrame frame = new JFrame();

    PolygonTest3 app = new PolygonTest3();
    frame.getContentPane().add(app);

    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.setBounds(10, 10, 300, 200);
    frame.setTitle("タイトル");
    frame.setVisible(true);
  }

  public void paintComponent(Graphics g){
    Graphics2D g2 = (Graphics2D)g;

    g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, 
                        RenderingHints.VALUE_ANTIALIAS_ON);

    int[] xpoints = {60, 180, 200, 130, 60};
    int[] ypoints = {20, 40, 120, 140, 110};
    int npoints = xpoints.length;
    Polygon polygon = new Polygon(xpoints, ypoints, npoints);

    g2.draw(polygon);

    polygon.translate(30, 20);

    g2.setPaint(Color.PINK);
    g2.draw(polygon);
  }
}