I believe Processing stores its main graphics window @ variable g.   O_o
Just check this code and see if you can use var g as argument for your graphics functions later:

PGraphics sketch;

void setup() {
    println(g);

    sketch=g;
    println(sketch);

    exit();
}

And here's a method called action() @ class Particle which draws a pixel into a screen buffer.
However, if you call it w/o passing any parameters, its parameterless form calls its parametered one using system variable g!

The effect of passing variable g is that the pixel is plotted directly to the main PGraphics buffer,
which is the visible Processing canvas!

Of course, g can be passed directly to the parametered form as well:

class Particle extends PVector {
    PVector vel;

    Particle(int spd) {
        super( (int) random(width), (int) random(height) );

        vel = new PVector(
        (int) random(2, spd+1) * random(2)<1? -1:1, 
        (int) random(2, spd+1) * random(2)<1? 1:-1);
    }

    void action() {
        action(g);
    }

    void action(PGraphics pg) {
        if (x>width  || x<0)    vel.x *= -1f;
        if (y>height || y<0)    vel.y *= -1f;

        add(vel);

        pg.point(x, y);
    }
}

You can check the whole code at this post -> is-this-a-multythreading-app