A Java class can only use methods which were inherited and/or implemented by itself there.
If you wanna put more things there, you gotta create another class extending the former.
Only then, you can add your own extra methods and/or fields.

I'm not good at it yet, but here's a very basic hijacking of PGraphicsJava2D class,
which is the JAVA2D version of a PGraphics class.

The same trick can be done to the other PGraphics' subclasses as well.

"Hijacked PGraphics.pde":

---

/** 
 * Hijacked PGraphics (v1.0)
 * by GoToLoop (2013/Sep)
 * 
 * http://forum.processing.org/topic/pgraphics-can-use-custom-class-method
 */

void setup() {
  size(150, 150);
  noLoop();

  imageMode(CENTER);
  textAlign(CENTER, CENTER);

  background(0);

  final MyJava2D pg = new MyJava2D(this, 50, 50);

  pg.beginDraw();

  pg.smooth(4);
  pg.background(0300);
  pg.stroke(#0000E0);
  pg.strokeWeight(4);

  pg.line(0, 0, pg.width, pg.height);
  pg.line(0, pg.height, pg.width, 0);

  pg.endDraw();

  image(pg, width>>1, height>>1);

  text(pg.alienMethod(), width>>1, height - 30);
}

---

"MyJava2D.pde":

---

class MyJava2D extends PGraphicsJava2D {
  final PApplet p;

  MyJava2D(PApplet pa, int w, int h) {
    setParent(p = pa);
    setSize(w, h);
  }

  String alienMethod() {
    return "Hijacked!!!";
  }
}

---

You can even redefine existing methods. Stupid example, from the above one:

1. void setup() {
2.   size(300, 300);
3.   noLoop();
4.  
5.   imageMode(CENTER);
6.   textAlign(CENTER, CENTER);
7.  
8.   background(0);
9.  
10.   final MyJava2D pg = new MyJava2D(this, 200, 200);
11.  
12.   pg.beginDraw();
13.  
14.   pg.smooth(4);
15.   pg.background(0300);
16.   pg.stroke(#0000E0);
17.   pg.strokeWeight(4);
18.  
19.   pg.line(0, 0, pg.width, pg.height);
20.   pg.line(0, pg.height, pg.width, 0);
21.   pg.ellipse(pg.width / 2, pg.height / 2, 50, 50);
22.  
23.   pg.endDraw();
24.  
25.   image(pg, width>>1, height>>1);
26.  
27.   text(pg.alienMethod(), width / 2, height - 30);
28. }
29.  
30. class MyJava2D extends PGraphicsJava2D {
31.   final PApplet p;
32.  
33.   MyJava2D(PApplet pa, int w, int h) {
34.     setParent(p = pa);
35.     setSize(w, h);
36.   }
37.  
38.   String alienMethod() {
39.     return "Hijacked!!!";
40.   }
41.  
42.   void ellipse(int x, int y, int w, int h)
43.   {
44.     rect(x, y, w, h);
45.   }
46. }

And for 3D ? 

You can extend PGraphicsOpenGL, for example, if you need 3D.

" So we can't implements directly native Processing classes like PGraphics?"
Not sure what you mean by " directly native".
For more advanced stuff, perhaps you better create a library, like the PGraphicsPDF and similar.