- Collsion Resolution / Physics
  - The way you resolve collisions is very game dependant.  Every game I've worked on had a different way resolving collisions
  - One Extreme -- Mathmatically Correct Physics
    - Simulate based on applying forces
      - F = ma, so you end up setting acceleration
      - From acceleration, you can calculate velocity, position
        - v' = v + a dt, p' = p + v dt
    - Common forces: Friction, Gravity
    - Enforce Conservation of (linear + angular) momentum 
  - Other Extreme -- "Game" physics
    - Simulate by setting velocities
    - No conservation of momentum
    - Can be thought of as modelling Mathematically correct physics with a super huge friction that would always stop you instantly.
  - The usual solution is somewhere in the middle.  Where depends on the type of game.

- Examples that would be relevant to your projects:    
  - Adventure game physics (for Blind Samurai, Excitement Challenge)
    - Commonly used in top-down adventure games, like Legend of Zelda or God of War.
    - Usually velocity based
      - Sometimes the velocity is smoothed, so that you do not stop instantly
    - No state machine needed; you are always on the ground
    - How does it handle Collision Resolution w/ Background?
      - Just disallow player from entering cell.  Algorithm is:
        - Look at direction of movement and figure out where you would be at the time of collision, see what edges are touching
        - If you cap velocity low enough, you could also just look at where your AABB/Capsule/Circle is in the tile.

      - Velocity usually has a very low max, so the previous simplification is quite doable. :)
      - Often you will want to add a "buffer zone" to the corners of the tiles where the player will be snapped around the tile (perpendicular to velocity) so the player can get around tiles.
    - How does it handle Collision Resolution w/ Objects?
      - Usually by cheating - if you would collide, take damage and get pushed back
        - The push back prevents the player from colliding next frame
      - Often the player becomes invincible so that you don't collide again.
        - Also helps avoid colliding next frame
      - If you collide with an item, pick it up and remove it from the physics
      
  - Platformer physics (MOD Shell)
    - Mario, Sonic, even modern games like Batman: Arkham Asylum
    - Simulation is Psuedo-acceleration based
    - Physics tends to stateful -- Common states are "On_Platform", "In_Freefall", and "Jumping_Freefall"
      - Each state has different behavior for physics.
    - How does "On_Platform" work?
      - Player is glued to ground.  He will follow the path of the ground, even if it has inclines.
      - Conservation of momentum is commonly simulated in different ways
        - Keep constant magnitude (walking up a hill slows you down based on the steepness) -- Sonic style
        - Keep axial component (walking up a hill does not slow you down much, if at all) -- Mario style
      - Gravity / Friction
        - Gravity is *not* simulated
        - Friction is simulated by a drag velocity that slows you down if you are not pressing a direction.
    - How does "In_Freefall" work?
      - Acceleration based physics with a gravity accel added each frame.
      - Some terminal velocity; clamp the player's fall speed to never be more than this.
    - How does "Jumping_Freefall" work?
      - Set upward velocity until button is released or time runs out
        - "Up" could be normal to the plane of ground where jumping -- Sonic style
        - "Up" is always straight up -- Mario style
        
    - How do all the prior states support collision resolution w/ background?
      - Just like Adventure Game Physics
      - Also, you may want to think about being nice and letting the player land on the platform as often as possible
    - How do all the prior states support collision resolution w/ objects?
      - Often cheated -- if you would collide, just don't move in X/Y and adjust your velocity to "bounce"
        - Ensures you are not colliding next frame!
      - Mario would put you back in the "jumpping" state, with a longer timer, so you can keep jumping over and over again.