moving the vector examples and adding comments

java/examples/Topics/Simulate/GravitationalAttraction3D/GravitationalAttraction3D.pde

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+/**
+ * Gravitational Attraction (3D) 
+ * by Daniel Shiffman.  
+ * 
+ * Simulating gravitational attraction 
+ * G ---> universal gravitational constant
+ * m1 --> mass of object #1
+ * m2 --> mass of object #2
+ * d ---> distance between objects
+ * F = (G*m1*m2)/(d*d)
+ *
+ * For the basics of working with PVector, see
+ * http://processing.org/learning/pvector/
+ * as well as examples in Topics/Vectors/
+ * 
+ */
+
+// A bunch of planets
+Planet[] planets = new Planet[10];
+// One sun (note sun is not attracted to planets (violation of Newton's 3rd Law)
+Sun s;
+
+// An angle to rotate around the scene
+float angle = 0;
+
+void setup() {
+  size(640, 360, P3D);
+  smooth();
+  // Some random planets
+  for (int i = 0; i < planets.length; i++) {
+    planets[i] = new Planet(random(0.1, 2), random(-width/2, width/2), random(-height/2, height/2), random(-100, 100));
+  }
+  // A single sun
+  s = new Sun();
+}
+
+void draw() {
+  background(0);
+  // Setup the scene
+  sphereDetail(8);
+  lights();
+  translate(width/2, height/2);
+  rotateY(angle);
+
+
+  // Display the Sun
+  s.display();
+
+  // All the Planets
+  for (int i = 0; i < planets.length; i++) {
+    // Sun attracts Planets
+    PVector force = s.attract(planets[i]);
+    planets[i].applyForce(force);
+    // Update and draw Planets
+    planets[i].update();
+    planets[i].display();
+  }
+
+  // Rotate around the scene
+  angle += 0.003;
+}
+
+
+
+
+
+
+
+
+
+

java/examples/Topics/Simulate/GravitationalAttraction3D/Planet.pde

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+// Gravitational Attraction (3D) 
+// Daniel Shiffman <http://www.shiffman.net>
+
+// A class for an orbiting Planet
+
+class Planet {
+  
+  // Basic physics model (location, velocity, acceleration, mass)
+  PVector location;
+  PVector velocity;
+  PVector acceleration;
+  float mass;
+
+  Planet(float m, float x, float y, float z) {
+    mass = m;
+    location = new PVector(x,y,z);
+    velocity = new PVector(1,0);   // Arbitrary starting velocity
+    acceleration = new PVector(0,0);
+  }
+  
+  // Newton's 2nd Law (F = M*A) applied
+  void applyForce(PVector force) {
+    PVector f = PVector.div(force,mass);
+    acceleration.add(f);
+  }
+
+  // Our motion algorithm (aka Euler Integration)
+  void update() {
+    velocity.add(acceleration); // Velocity changes according to acceleration
+    location.add(velocity);     // Location changes according to velocity
+    acceleration.mult(0);
+  }
+
+  // Draw the Planet
+  void display() {
+    noStroke();
+    fill(255);
+    pushMatrix();
+    translate(location.x,location.y,location.z);
+    sphere(mass*8);
+    popMatrix();
+  }
+}
+
+

java/examples/Topics/Simulate/GravitationalAttraction3D/Sun.pde

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+// Gravitational Attraction (3D) 
+// Daniel Shiffman <http://www.shiffman.net>
+
+// A class for an attractive body in our world
+
+class Sun {
+  float mass;         // Mass, tied to size
+  PVector location;   // Location
+  float G;            // Universal gravitational constant (arbitrary value)
+
+  Sun() {
+    location = new PVector(0,0);
+    mass = 20;
+    G = 0.4;
+  }
+
+
+  PVector attract(Planet m) {
+    PVector force = PVector.sub(location,m.location);    // Calculate direction of force
+    float d = force.mag();                               // Distance between objects
+    d = constrain(d,5.0,25.0);                    // Limiting the distance to eliminate "extreme" results for very close or very far objects
+    force.normalize();                                   // Normalize vector (distance doesn't matter here, we just want this vector for direction)
+    float strength = (G * mass * m.mass) / (d * d);      // Calculate gravitional force magnitude
+    force.mult(strength);                                // Get force vector --> magnitude * direction
+    return force;
+  }
+
+  // Draw Sun
+  void display() {
+    stroke(255);
+    noFill();
+    pushMatrix();
+    translate(location.x,location.y,location.z);
+    sphere(mass*2);
+    popMatrix();
+  }
+}
+
+