## Sunday, 31 August 2008

### Adventures in 3D: Part V - Law and Z-Order

At the end of Part IV, we finally had a rotating sphere that had some nice lighting from one side. But there was a problem. If you turned the sphere, you'd almost certainly see sections where it looked like you were looking through the sphere at the surfaces on the back side.

There's a simple reason for this, and a simple fix. The problem is that we're just drawing polygons relatively willy nilly to the screen - the order in which they appear in the ArrayList that we use for the scene. So in some cases we draw the front side polygons, but then also draw the back side polygons, which just appears over the top of the front side. What we need to do is make sure that anything at the back is drawn first, then anything in front of it is drawn last. This is z-ordering.

The fact that we've got all our scene objects in an ArrayList is very handy. We can just use Collections.sort() to sort our list into Z-order before we draw the polygons. To ease things along, I'm going to rearrange the class hierarchy sightly (read: the original design wasn't really thought through). I'll implement an abstract superclass SceneObject - anything that is in our scene, whether it be Points, Triangles, Spaceships, whatever, needs to be a) Drawable, and b) Comparable, so we can work out the order to draw it. So our scene now becomes an ArrayList<SceneObject> instead of ArrayList<Drawable>. To make the compareTo() method work, it'll also have an abstract method getZOrder(), which will be used in the comparison. Because it's declared in the superclass, it means I can still compare Points with Triangles and Spaceships with Pineapples, at least as far as Z order is concerned.

`import java.awt.Graphics2D;public abstract class SceneObject implements Drawable, Comparable<SceneObject> { @Override public abstract void draw(Graphics2D g); public abstract double getZOrder();  @Override public int compareTo(SceneObject o) {  double zOrder1 = this.getZOrder();  double zOrder2 = o.getZOrder();  if(zOrder1 == zOrder2){   return 0;  }else{   return (zOrder1 > zOrder2) ? -1 : 1;  } } }`

To keep things simple, we just work out the average z distance for the Triangle and use that value. In more complicated 3D scenes, it is of course possible for triangles to overlap, but we'll assume here that everything tessalates nicely. So implementing the getZOrder() method in our Triangle class is very easy.

` public double getZOrder() {  return (z[0] + z[1] + z[2])/3; }`

Now that all that's done, the panel class just calls Collections.sort(scene) before actually drawing the scene. Note that in terms of performance it's probably hard to do much better than Collections.sort(). As one last change, let's light the sphere from the front, so that you can see the whole thing in all it's glory. That just means changing the light vector from (1,0,0) to (0,0,1). You can also check that your z-ordering is working by moving it to (0,0,-1). If the light is behind the sphere, and your polygons are being painted correctly, you should see nothing.

Yes, you are l33t. If you have failed at being l33t, you can at least pretend by downloading the source. Then you can move on to Part VI - Faster Pussycat! Cull! Cull!