1. 1 KIPA Game Engine Seminars Jonathan Blow Ajou University December 6, 2002 Day 10

2. 2 Collision Detection Methods Early today I’ll overview some of the simpler methods and talk about real-world issues about integrating them in games –bounding spheres, boxes, bsp –find time of collision, prevent tunneling Later we’ll go to some of the more advanced collision detection schemes –GJK algorithm –Lin/Canny Closest Features

3. 3 Bounding Spheres Simplest, fastest bounding volume Least information to store Isotropic –Means it may be a poor fit Better fit: perhaps use the centroid, not the origin (or find the two furthest points) –But this takes more information per sphere

4. 4 Bounding Boxes: Axis Aligned Don’t take much information to store May be a poor fit for “diagonal” data Easy to test them against each other for intersection Abbreviated “AABB” –(“Axis-Aligned Bounding Box”)

5. 5 Bounding Boxes: Oriented Better fit than AABB –But a little more complicated to compute More complicated intersection detection –See Gottschalk’s 1998 paper I will include this in the course notes Unclear in the end whether it’s better than AABB or spheres –Probably depends on the nature of your data Abbreviated “OBB” –(“Oriented Bounding Box”) Software toolkit “RAPID”

6. 6 Bounding Volume Hierarchies Method of saving computation time –It costs memory, though Form volumes around pieces of a mesh so that you can “early-reject”

7. 7 BSP Tree Can be viewed as a hierarchical bounding volume system The split planes are spheres with infinite radius So an individual sphere has poor spatial locality, but the hierarchy makes up for that

8. 8 BSP Tree What might a BSP tree be like that didn’t use planes as its splitting surface? –Spheres of finite radius? –Other curved surfaces?

9. 9 Animated Meshes How are we to adapt hierarchical bounding volumes to animated meshes? –Fully recompute every time –Try to do an incremental update, but quality will decay Always slow!

10. 10 Animated Mesh Example In Barbaric Smackdown I made a set of spheres that track the skeleton (not the mesh) The spheres animate with the mesh, and we collide against the spheres This is faster than colliding against the mesh Also faster than building spheres from the mesh vertices each frame

11. 11 Intersection Primitives Box/box, sphere/sphere, etc What kind of information do they return? What kind of information do we get from a triangle vs. triangle intersection routine?

12. 12 Finding the time of intersection Necessary for good physics? How do you do it given a triangle/triangle intersection style primitive? –Move through time in very small samples and interpolate? –Binary search through time

13. 13 Preventing “tunneling” When long frame times happen, objects might pass through each other What do we do here? –Raycasting solution –Analytic method?

14. 14 Closed-form intersection test for spheres Without acceleration With acceleration (constant over time period)

15. 15 Separating Axis Theorem Convex objects and separating planes But we want non-convex objects! –Model them as unions of convex objects and do separate collision tests Still very difficult (Maya is not a solid modeling program) –BSP the thing? This can be harder than you would think Also it produces a lot of pieces –Try to re-join the pieces?

16. 16 Algorithms that help us estimate collision times Maybe tell us how much two entities are colliding, so that we can better guide our search for the collision time Example of two spheres, or sphere vs plane

17. 17 GJK Collision Detection Algorithm “Gilbert-Johnson-Keerthi” Operates on convex solids –Again, that’s a problem! Uses Minkowski sums

18. 18 Minkowski Sum / Minkowski Difference (examples on whiteboard)

19. 19 Lin-Canny Closest Feature Tracking Tells you the closest “features” between two objects –A feature can be a point, line segment, or face Relies on frame coherence (example on whiteboard)

20. 20 Hierarchical Bounding Volume Quantization/Packing Sphere tree, bounding box tree –Exploit multiscale nature of hierarchy BSP Tree –Exploit recurrence of plane equations

21. 21 AI, A* search, and “speculative collision detection” (discussion)

22. 22 Higher-Level Scene Management Indoor shooter level –BSP –Portals Terrain Flight / Space Sim / Heavily occupied environment