• What kinds of games need physics? What games have physics that you know of?
  • Angry Birds, Tower/World of Goo, Crayon Physics, platformers
• Assume fixed discrete simulation (constant time step).
• Approximation (This isn't climate modeling or rocket science or something.)
  • “If You Can Get Away With it, Fake it” (From "How to Prototype a Game in Under 7 Days")
• Working with a 2D coordinate system.
• If you need a formula (e.g., that involves forces or mass), look it up.
• Keep it as simple as possible.
• Use the metric system (e.g., m, m/s)

• Question: Where is the object at time t?
• Velocity - “The rate of change of position along a straight line with respect to time”
• Speed and velocity are not the same; velocity is a vector quantity (has direction) while speed is a scalar quantity.
• Given variables: object_x, object_y, speed, angle
• Calculation of an object's next x and y coordinates (in your game loop):
  • scale_x = cos(angle)
  • scale_y = sin(angle)
  • velocity_x = (speed * scale_x)
  • velocity_y = (speed * scale_y)
  • object_x = object_x + velocity_x
  • object_y = object_y + velocity_y

• Acceleration - “The rate of change of velocity with respect to time”
• When an object moves along at a certain velocity, an amount of acceleration is continuously added to the velocity.
• Given variables: object_x, object_y, speed, acceleration, angle
• Calculation of an object's next x and y coordinates (in your game loop):
  • scale_x = cos(angle)
  • scale_y = sin(angle)
  • speed = speed + acceleration
  • velocity_x = (speed * scale_x)
  • velocity_y = (speed * scale_y)
  • object_x = object_x + velocity_x
  • object_y = object_y + velocity_y

• acceleration that only acts downward in the game window
• Earth's gravity constant = 9.81 meters per second squared
• In a game world, the gravity constant will be different, depending on the frame rate.
• Given variables: object_x, object_y
• Calculation of an object's next x and y coordinates (in your game loop; assuming that the object is moving):
  • velocity_y = velocity_y - gravity (gravity is a drag on vertical velocity)
  • object_y = object_y + velocity_y (if the object has not hit the ground yet)
  • object_x = object_x + velocity_x
• Where gravity computation might be useful
  • a character jumping in a sidescroller (a “platformer”), games that involve firing projectiles

• Problem: often have irregularly shaped objects (thus wasted space).
  • However, empirically, less space will be wasted using the bounding box method over bounding sphere method.

• 1. if (object.x >= box.min_x && object.x < = box.max_x && object.y >= box.min_y && object.y < = box.max_y) then collision occurred
  • Use same approach for mouse choosing in game menus.
    • In your mouseClicked() or equivalent method, check to see if the object was picked via x-y coordinates.
• 2. Use shapes in Graphics or Graphics2D and see if two intersect. Example:

                 public boolean collidesWith (Entity other) 
                 {
                    if (other instanceof RectEntity) {
                       Rectangle him = new Rectangle();
                       me.setBounds((int) x, (int) y, sprite.getWidth(), sprite.getHeight());
                       him.setBounds((int) other.x, (int) other.y, other.sprite.getWidth(), other.sprite.getHeight());
                       return me.intersects(him);
                    }
                    else if (other instanceof CircleEntity) {
                       Ellipse2D him = new Ellipse2D.Double();
                       me.setBounds((int) x, (int) y, sprite.getWidth(), sprite.getHeight());
                       him.setFrame((int) other.x, (int) other.y, other.sprite.getWidth(), other.sprite.getHeight());
                       return him.intersects(me);
                    }
                    else if (other instanceof TriangleEntity) {
                       boolean collided = false;
                       Point2D p1 = ((TriangleEntity)other).p1;
                       Point2D p2 = ((TriangleEntity)other).p2;
                       Point2D p3 = ((TriangleEntity)other).p3;
                       collided = me.intersectsLine(p1.getX(), p1.getY(), p2.getX(), p2.getY()) || 
                        me.intersectsLine(p2.getX(), p2.getY(), p3.getX(), p3.getY()) ||
                        me.intersectsLine(p3.getX(), p3.getY(), p1.getX(), p1.getY());
                       return collided;
                    }
                    else {
                       System.out.println("Other Entity's shape is ambiguous!");
                       return false;
                    }
                 }

• Different objects respond differently to collisions
• Some collisions will resemble that of balls on a billiards table (elastic collision).
• Angle of incidence - The angle between the ball movement vector and the plane of the billiards rail that it strikes when the ball moving in a straight line collides with it.
  • Remember, when the ball hits the rail, it will bounce away from the rail at the same angle that it strikes the rail. (assumes no spin on ball)
  • In other words, the angle of reflection = angle of incidence
• Calculation (adapted from GameSprite.java):

              if ((ballPoint.x + ballSpeed.x) <= plane.x) {
                  ballSpeed.x = (ballSpeed.x * -1);
              }
              
              if ((ballPoint.x + ballSpeed.x) >= (plane.width)) {
                  ballSpeed.x = (ballSpeed.x * -1);
              }
              
              if ((ballPoint.y + ballSpeed.y) <= plane.y) {
                  ballSpeed.y = (ballSpeed.y * -1);
              }
              
              if ((ballPoint.y + ballSpeed.y) >= (plane.height)) {
                  ballSpeed.y = (ballSpeed.y * -1);
              }

• Gravity and collision example: CannonFireTest
• Gravity example: Lander
• Collision example: Pong
• Get all 3 Eclipse projects at https://cssegit.monmouth.edu:2443/jchung/JavaPhysicsCollisionExamples.git