1. CSE 380 – Computer Game Programming Collision Detection & Response Erin Catto’s Box2D

2. Collision Detection Calculations What data are we looking for? 1.Do these two objects potentially collide? 2.Do these two objects collide? 3.When did these two objects collide? 4.Where did these two objects collide? where on geometry of objects, points of impact These 4 questions get progressively: –more computationally expensive to implement –more complex to implement (more math)

3. Phases of Collision Detection Spatial Partitioning Algorithms –problem reduction –only perform additional phases on pairs of object on same “islands” Broad Phase – early rejection tests –Do the coarse Bounding Volumes of two objects collide? Narrow Phase –Do the tight bounding volumes of two objects collide? –What are the contact points on object geometries? Done down to the last triangle in 3D games

4. Common Bounding Volumes Note that the space craft has been rotated Ref: [1], Figure 4.2 This semester, we like AABBs –axis-aligned bounding boxes

5. Bounding Volumes The base geometry used for all collision tests –instead of the shape’s geometry, which is too expensive Properties of desirable BVs: –inexpensive intersection tests –tight fitting –inexpensive to compute –easy to rotate and transform –use little memory Ref: [1]

6. Assumptions for this semester All sprites & game objects: –have rectangular Bounding Volumes (AABBs) –don’t rotate, or –if they do rotate, we don’t care about them colliding with stuff Thus: –no polytope collision detection equations –no rotation equations –this makes life much easier

7. How about a big, complicated object? We can have 2 AABBs –Don’t test them against each other

8. Spatial Partitioning First, reduce the problem only perform additional phases on pairs of object on same “islands” Common Solutions: –Octree Algorithms (quadtrees for 2D) –Uniform Grid Algorithms –also: Portals (ala Quake), BSP trees (Binary Space Partitions), Spatial Hashing, etc.

9. Octrees Used to divide a 3D world into “islands” –2D divided via Quadtrees Why? –to make rendering more efficient –to make collision detection more efficient What would be the data for these nodes? –region coordinates for cell though a smart implementation might eliminate this too –AABBs

10. Octree Source: http://en.wikipedia.org/wiki/Image:Octree2.pnghttp://en.wikipedia.org/wiki/Image:Octree2.png

11. Octree Drawbacks Objects cross islands –octree has to be constantly updated –not so bad Objects straddle islands –collision detection may involve objects from multiple islands –can be a headache

12. Uniform Grids Fast mechanism for reducing the problem –used for 2D & 3D games Steps: –divide the world into a grid of equal sized cells –associate each object with the cells it overlaps –only objects sharing a cell are compared Serves 2 purposes: –reduces the problem for sprite-sprite collision detection –provides solution for easy sprite-world collision detection

13. Calculating Grid Position What cells does our sprite currently occupy? How would you calculate that? –For min/max tile rows/columns: sprite.X/tileWidth sprite.Y/tileHeight (sprite.X+sprite.Width)/tileWidth (sprite.Y+sprite.Height)/tileHeight –For this guy, cells (0,0), (0,1), (1,0), & (1,1) only test against: –other objects in those cells –collidable tiles in those cells (treat like objects) »don’t let sprites occupy “collidable cells”

14. Side-scrollers simulate gravity –not necessarily accelerated (constant velocity) –move all affected sprites down by dY This way, characters can fall We must detect when sprites are colliding with a floor/platform Easy solution: make a tile with a walkable surface at the very top of the image Collision system will handle response Grid Cell Collision & Walkable Surfaces

15. Grid Cell Collision Advantages/Disadvantages Advantages –easy to implement –very fast (computationally inexpensive) Disadvantages –constrains look of game to grid-like world Action Game alternative: –use this algorithm for some board collision detection –use other algorithms for other collisions i.e. inclines

16. Object Tests Premise Think of all collision tests as between pairs of collidable objects In our games this means: –sprite object – to – game tile object –sprite object – to – sprite object In a single game loop, for each sprite, we may have to check against –many other sprites –many other tiles

17. Broad Phase Do the coarse AABBs of two objects collide? Common solution: –separating axis algorithms –including temporal coherence More sophisticated solution: –Sweep & Prune –an extension of separating axis, more efficient for many elements

18. Narrow Phase What are the contact points on object geometries? –for 3D might be convex hulls Two Steps 1.determine potentially colliding primitives (ex: triangles) of a pair of objects AABB tree algorithms 2.determine contact between primitives GJK algorithms Ref[3] CSE 381 will cover these things next fall

19. priori vs. posteri Approaches to collision detection & response Priori: check if something is going to collide before moving it, then make the necessary correction Posteri: check if something has collided and make the necessary corrections

20. Discrete vs. Continuous Collision Detection Discrete collision detection –perform collision detection at sampled instances of time (like end of frame) –can lead to tunneling problems –“contact data is obtained by computing the penetration depth of a collision” Continuous collision detection –perform collision detection in continuous space-time –More on this in a moment

21. Time in between frames We will make calculations and update velocities and positions at various times When? In response to: –input at start of frame –AI at start of frame –collisions/physics when they happen likely to be mid-frame

22. Axis Separation Tests How do we know if two AABBs are colliding? –if we can squeeze a plane in between them –i.e. if their projections overlap on all axes A B C D NO COLLISIONCOLLISION

23. Be careful of Tunneling What’s that? An object moves through another object because collision is never detected

24. A note about timing If we are running at 30 fps, we are only rendering 1/30 th of the physical states of objects –Squirrel Eiserloh calls this Flipbook syndrome [2] More things happen that we don’t see than we do We likely won’t see the ball in contact with the ground

25. One way to avoid tunneling Swept shapes Potential problem: false positives –Good really only for early rejection tests

26. Better way to avoid tunneling Calculate first contact times Resolve contacts in order of occurrence

27. Continuous Collision Detection 1.For each moving object, compute what grid cells it occupies and will cross & occupy if its current velocity is added 2.Find the first contact time between each object pair that may occupy the same grid cells 3.Sort the collisions, earliest first 4.Move all objects to time of first collision, updating positions 5.Update velocities of collided objects in pair 6.Go back to 1 for collided objects only 7.If no more collisions, update all objects to end of frame Ref[3]

28. Times as % You might want to think of your times as % of the frame Then correct positions according to this % For example, if I know my object is supposed to move 10 units this frame (we’ve locked the frame rate), if a collision happens ½ way through, move all affected objects ½ distance of their velocity and recompute collisions data for collided data Re-sort collisions and find next contact time

29. % Example A at (1, 5), velocity of (4, -3) B stationary at (4, 4) When will they collide? When A goes one unit to the right How long will that take? If it takes 1 frame to go 4 units, it will take.25 frames to go 1

30. What about 2 moving objects? Solution, give the velocity of one to the other for your calculations –make one of them stationary –then do the calculation as with grid tiles –make sure you move both objects –make sure you update the velocities of both objects

31. So how do we calculate the when? We can do it axis by axis –What’s the first time where there is overlap on all 3 axes? For each axis during a frame, what is the time of first and last contact? –t xf, t xl, t yf, t yl When is the time of collision? –first moment tx and ty overlap

32. What collision system should you use? AABB for each collidable object Velocity vector for each dynamic object Uniform Grids for problem reduction Continuous Collision Detection –using method of separating axis algorithm –momentum equations for collision responses if necessary –pweep and prune for efficiency

33. Physics & Timing Christer Ericson & Erin Catto’s recommendations: –physics frame rate should be higher resolution than rendering –minimum of 60 frames/second for physics calculations –makes for more precise, and so realistic interactions How do we manage this? –tie frame rate to 60 fps, but don’t render every frame –don’t worry about this for now Note: these operations might commonly be done in different threads anyway (have their own frame rates)

34. References [1] Real Time Collision Detection by Christer EricsonReal Time Collision Detection [2] Physics for Game Programmers by Squirrel EiserlohPhysics for Game Programmers [3] Collision Detection in Interactive 3D Environments by Gino van den Bergen