class Boid
{
  PMatrix3D matrix;
  float speed;
  color colour;
  Boid()
  {
    matrix = new PMatrix3D();
    matrix.translate(random(-width/2,width/2),random(-height/2,height/2),random(-height/2,height/2));
    matrix.rotateY(random(TWO_PI));
    matrix.rotateX(random(TWO_PI));
    // random speed
    speed = random(1.0,2.0);
    // random HSB color
    colour = color(random(0,256),204,204);
  }
  void reset()
  {
    matrix.reset();
    matrix.translate(random(-width/2,width/2),random(-height/2,height/2),random(-height/2,height/2));
    matrix.rotateY(random(TWO_PI));
    matrix.rotateX(random(TWO_PI));
  }
  void move(Boid [] flock)
  {
    // the inverse "undoes" how you would get to this boid:
    // applying it views the world relative to this boid
    PMatrix3D inverse = new PMatrix3D(matrix);
    inverse.invert();
    // look for centre of nearby boids and their average heading
    boolean cohere = false;
    boolean separate = false;
    PVector neighbourcentre = new PVector();
    PVector neighbourdir = new PVector();
    PVector kernelcentre = new PVector();
    for (int i = 0; i < flock.length; i++) {
      if (flock[i] != this) {
        // take the position of the other boid,
        // and then apply the position relative to this boid
        PMatrix3D mat_i = new PMatrix3D(flock[i].matrix);
        mat_i.preApply(inverse);
        // now it is simple to find the position of the other
        // boid relative to this one:
        PVector p_i = pos(mat_i);
        float separation = p_i.mag();
        if (separation < width / 4) { 
          PVector d_i = dir(mat_i);
          // check to see if in field of view
          if (d_i.z > -0.25) {
            neighbourcentre.add(p_i);
            neighbourdir.add(d_i);
            cohere = true;
            if (separation < 10) {
              kernelcentre.add(p_i);
              separate = true;
            }
          }
        }
      }
    }
    // if too close, then fly away from other boids,
    // otherwise fly towards them
    if (separate) {
      if (kernelcentre.x > 0) {
        matrix.rotate(-PI/12,0,1,0);
      }
      else {
        matrix.rotate(PI/12,0,1,0);
      }
    }
    else if (cohere) {
      // find direction to centre (for cohesion)
      neighbourcentre.normalize();
      // find direction of neighbours (for alignment)
      neighbourdir.normalize();
      // now turn to these
      PVector desiredir = new PVector();
      desiredir.add(neighbourcentre);
      desiredir.add(neighbourdir);
      desiredir.normalize();
      //
      float ang = acos(desiredir.z);
      if (ang > 0.01) {
        matrix.rotate(ang*0.1,-desiredir.y,desiredir.x,0.0);
      }
    }
    matrix.translate(0,0,speed);
  }
  void draw()
  {
    fill(colour);
    pushMatrix();
    applyMatrix(matrix);
    beginShape();
    vertex(-6,0,-8);
    vertex(0,0,8);
    vertex(6,0,-8);
    endShape(CLOSE);
    beginShape();
    vertex(0,3,-8);
    vertex(0,0,8);
    vertex(0,0,-8);
    endShape(CLOSE);
    popMatrix();
  }
}

PVector pos(PMatrix3D matrix)
{
  return new PVector(matrix.m03,matrix.m13,matrix.m23);
}
PVector dir(PMatrix3D matrix)
{
  return new PVector(matrix.m02,matrix.m12,matrix.m22);
}