1. Background Shapes & Collision Resolution (Top-down and Side-scrolling)
CS 134
Background Shapes &
Collision Resolution
(Top-down and Side-scrolling)

2. Today in Video Games

3. Physics Update Overview
So far:
Collision Detection
(sprite / sprite)
To cover:
Collision Detection
(sprite / background)
Collision Resolution
Advanced Actor Motion

4. Backgrounds Recall how we stored the tile positions in an array?
int[] bg;
Collision can go there too!

5. Backgrounds class Tile { int image; boolean coll; }; Tile[] bg;
Other information can go in a tile as well!

6. Backgrounds
As the player moves, you will need to collide against all the background shapes.
AABB / AABB
Use the camera drawing optimization
Start: pX / tileW
End: (pX + pW) / tileW
Similar in Y

7. Questions? (Remember, this is just for DETECTING collisions)
Backgrounds
Questions?
(Remember, this is just for
DETECTING collisions)

8. Collision Resolution
The job of collision resolution is to “fix” the simulation state so that it is accurate again.

9. Collision Resolution For now, assume a simple top down game
Up / Down / Left / Right move player
Background is “block shaped”

10. Collision Resolution
Simplest possible collision resolution is with bullets
Deal damage to player
Remove bullet
Check if player is dead

11. Collision Resolution For colliding with walls
Simple solution: Back up player to prev position
More complex: Back up player to when the collision starts
This may be enough for some games!

12. Collision Resolution Best feeling solution: Back up on each axis
Back up on X axis by overlap with wall tile
Back up on Y axis by overlap with ceiling tile
This allows smooth sliding along walls
Also, can do things like wall jumps, pushing, etc. by remembering which axes you collided with prev frame
More state for a player!

13. Collision Resolution How do you know the overlap?
Collision is just returning true / false!
right1 < left2 is false, return right1 – left2
Similar for other sides

14. Collision Resolution
Questions?

15. Actor Motion Basic actor motion isn't enough for many games
In maze games, the player should be given some give to going around corners
In platformers, the player should be affected by gravity
One way walls are a common thing too

16. Actor Motion Maze edge motion:
When moving, if you are just barely colliding, fix the motion to a tile boundary
Here, pressing up will still get Link into the fortune teller's house

17. Actor Motion Add new state, set during motion to detect near misses
When you release pressing the direction, clear the near miss state.
If in a near miss state, move in the near miss direction instead

18. Actor Motion
Frame 1:
Link would collides with statue, set near miss left, moves right
Frame 2:
Still in near miss state, move right
Frame 3:
No longer in near miss state, move up

19. Actor Motion

20. Raycasting Recall: Physics is running at a fixed rate
Collision is only checked AFTER objects move
Problem:
Fast moving objects can jump past an object
Raycasts shoot an
infinitely long ray to
collide with AABB /
Circles

21. WARNING! WARNING! INCOMING MATH
Raycasting
WARNING! WARNING!
INCOMING MATH

22. Ray / Circle Ray formula: Circle formula: 𝑝=𝐀+𝑡𝐁 𝑡≥0
𝑟=∣𝑝−𝐎∣ 𝑟= 𝑝−𝐎 ⋅ 𝑝−𝐎

23. Ray / Circle
Plug ray into circle formula and simplify:

24. Ray / Circle Three possibilities (solutions for t): t has no solutions
Ray does not intersect the circle
t has one negative, one positive solution
Ray starts inside the circle, collides at positive solution
t has two positive solutions
Ray hits circle, use the lesser solution

25. Ray / Circle Optimization
Remember, we don't care if ray starts inside of circle!
Calculate t via:
Collision is only when t is positive.
𝑡= −𝑏− 𝑏 2 −4𝑎𝑐 2a

26. Ray / AABB
Intersect ray with all sides, choose earliest intersection that is inside box
Four sides of of AABB are:
x = left
x = right
y = left
y = right

27. Ray / AABB Plug into side formula and simplify:
A_x + t B_x = left → t = (left – A_x) / B_x
A_x + t B_x = right → t = (right – A_x) / B_x
Solve for t
Given t, check if specified point is in box edge
Top < A_y + t B_y < bottom
Then do same thing for y, and choose earliest t

28. Ray / AABB Optimization
For any particular direction, only two sides could be the earliest
Unless the ray is exactly parallel to X or Y, only the later of the two times can be inside the box

29. Homework 3 Some sort of projectile with “enemies” to hit.
When the projectile hits the enemy, the projectile goes away.
Enemies can have health, so they need to be hit multiple times.
Extra credit:
Enemies can shoot projectiles too!
Raycast-style instant shots