How to avoid overlapping polygon

Question

I created a program to draw many polygons automatically everytimes user presses a button. The points of the polygon are generated automatically using the random function. The problem is that, since the points of the polygon were randomly generated, some of the polygon are overlap with other polygon. How can I avoid this, so that every polygon shown without being overlapped?

.....
List<Polygon> triangles = new LinkedList<Polygon>(); 
Random generator = new Random();

public void paintComponent(Graphics g) {

   for(int i = 0; i < 10; i++) {
      double xWidth = generator.nextDouble() * 40.0 + 10.0;
      double yHeight = generator.nextDouble() * 40.0 + 10.0;

      xCoord[0] = generator.nextInt(MAX_WIDTH);
      yCoord[0] = generator.nextInt(MAX_HEIGHT); 

      xCoord[1] = (int) (xCoord[0] - xWidth);
      xCoord[2] = (int) (xCoord[1] + (xWidth/2));       

      yCoord[1] = yCoord[0];
      yCoord[2] = (int) (yCoord[1] - yHeight);     

      triangles.add( new Polygon(xCoord,yCoord, 3));          
   }

   Graphics2D g2 = (Graphics2D) g;
   g2.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
   g2.setStroke(new BasicStroke(1)); 
   g2.setComposite(AlphaComposite.getInstance(AlphaComposite.SRC_OVER, 1.00f));
   g2.setPaint(Color.black);//set the polygon line 

   for (Polygon triangle : triangles)  g2.drawPolygon(triangle);

   Polygon[] triArray = triangles.toArray(new Polygon[triangles.size()]);
   for (Polygon p:triArray) triangles.remove (p);

}

Answer 1

Check out the game programming wiki on Polygon Collision:

http://gpwiki.org/index.php/Polygon%5FCollision

Answer 2

You could implement a method Polycon.containsPoint( x, y ) and repeat your random generation until this method returns false for all drawn Polygons.

Answer 3

You could break your canvas into 10 regions and constrain your polygons each to their own region. To do this, you could use your i value and a %100 (or other suitable magnitude) of your randomly generated value and apply them to your x coordinates and y coordinates as applicable. The result would be a grid of similarly constrained(no larger than the grid cell), but randomly shaped, Polygons.

EDIT:

Taking another look and fooling around a bit, I took the general concept as I described above and made a stab at an implementation:

public void paintComponent(Graphics g) {
    int[] xCoord = new int[3];
    int[] yCoord = new int[3];
    int colCnt = 5;
    int rowCnt = 2;
    int maxCellWidth = getWidth() / colCnt;
    int maxCellHeight = getHeight() / rowCnt;

    for (int i = 0; i < (colCnt * rowCnt); i++) {
        int xMultiple = i % colCnt;
        int yMultiple = i / colCnt;
        for (int j = 0; j < 3; j++) {
         xCoord[j] = generator.nextInt(maxCellWidth)
                   + (maxCellWidth * xMultiple);
             yCoord[j] = generator.nextInt(maxCellHeight)
                   + (maxCellHeight * yMultiple);
        }
        triangles.add(new Polygon(xCoord, yCoord, 3));
    }
    //... the rest of your method
}

As you can see, all of the Polygons have all points randomly generated, as opposed to your method of generating the first point and then making the rest relative to the first. There is a sense of randomness that is lost, however, as the Polygons are laid out in a grid-like pattern.

Answer 4

Create Area objects from your new polygon as well as for all existing polygons. Subtract the new polygon's area from the existing ones. If the subtract changed the area, the polygons overlap.

Area newArea = new Area(newPolygon);
Area existingArea = new Area(existingPolygon);
Area existingAreaSub = new Area(existingPolygon); existingAreaSub.subtract(newArea);
boolean intersects = existingAreaSub.equals(existingArea);