Hi guys,
I am trying to understand what is wrong with the cross product. It is giving me some funky result when I normalize it. I guess its a simple one...really thankful if somebody could help. Here is the code:
Thanks a lot :)
buzz

// peasyCam library
import peasy.*;
// orbit
PeasyCam cam;

void setup()
{
  size(600, 600, P3D);
  smooth();
  colorMode(HSB, 6, 100, 100); // mode, rangeHue, rangeSat, rangeBright

  cam = new PeasyCam(this, 100); // qto maior menor o obj
  cam.setMinimumDistance(10); // close zoom
  cam.setMaximumDistance(10000); // far zoom
}

void draw()
{
  background(6);
  //translate(width/2, height/2, 0);
  //rotateY(frameCount*0.01);

  PVector a =  new PVector(100, 100, 0);
  PVector b =  new PVector(150, 100, 0);
  PVector c =  new PVector(200, 200, 0);
  strokeWeight(5);
  stroke(0);
  point(a.x, a.y, a.z);
  point(b.x, b.y, b.z);
  point(c.x, c.y, c.z);

  // 1. calculate the cross product
//  PVector n = new PVector((a.y * b.z) - (a.z * b.y), (a.z * b.x) - (a.x * b.z), (a.x * b.y) - (a.y * b.x));
//  stroke(0, 100, 100);
//  strokeWeight(5);
//  point(n.x, n.y, n.z);

  // 1.1 cross product check
  PVector n = a.cross(b);
  //n.normalize(); ?????????????????????????????????
  println(n);
  stroke(0, 100, 100);
  strokeWeight(15);
  point(n.x, n.y, n.z);

  // 2. find the centroid
  PVector g = new PVector( (a.x+b.x+c.x)/3, (a.y+b.y+c.y)/3, (a.z+b.z+c.z)/3 );
  stroke(2, 100, 100);     
  strokeWeight(5);
  point(g.x, g.y, g.z);
 
  float d = g.dist(n);
  println(d); 

  // 3. draw the normal
  strokeWeight(1);
  stroke(0, 100, 100);
//  line(g.x, g.y, g.z, n.x, n.y, n.z);
  line(g.x, g.y, g.z, n.x, n.y, n.z);

  // 4. pvector that follows the mouse - will be replaced by the sun
  PVector m = new PVector(mouseX, mouseY, 300);
  stroke(0);
  line(g.x, g.y, g.z, m.x, m.y, m.z); 

  // 5. calcullate the angle between sun and normal vector
  float angle = PVector.angleBetween(n, m);
  //println(degrees(angle));

  // 6. map the angle to a color value anf fill the triangle to that value
  float mapping = map(angle, 0, 180, 0, 255); //possible angles to possible colours
  //println(mapping);
  strokeWeight(1);
  stroke(0);
  fill(mapping, 100, 100);
  beginShape(TRIANGLES);
  vertex(a.x, a.y, a.z);
  vertex(b.x, b.y, b.z);
  vertex(c.x, c.y, c.z);
  endShape(); 
}