Lecture 17 – Physics 4

1. Lecture 17 – Physics 4 Wesley Kerr CS 490/590

2. Lecture Acknowledgements • Physics for Game Programmers: Problem Overview • GDC 2008 Physics Tutorial • Squirrel Eiserloh • Physics for Game Programmers: Reframing the Problem • GDC 2008 Physics Tutorial • Squirrel Eiserloh • Both Available • http://www.essentialmath.com/tutorial.html

3. Types of Problems • Knowing when to cheat • Simplifying things • Giving shape to things • Moving things around • Discussed on Monday • Simulation Baggage • Detecting (and resolving) collisions • Sustained interactions • Dealing with the impossible • Making it fast enough

4. Knowing When to Cheat • “Real” physics is prohibitively expensive… • … so we cheat • Keeps the computation running in real time • Cheats have to be carefully selected • Cannot break in jarring noticeable ways • Cannot result in unrecoverable physics • The challenge is really knowing how and when to cheat

5. Knowing When to Cheat • Ask the following questions: • “Will the player notice?” • “Will the player care?” • “Will the results be predictable?” • “Are we at least cheating in a consistent way?” • “Will the simulation break?” • If the simulation breaks, they will notice and they will care • Some crimes are greater than others

6. Simplifying Things • Simplified bodies • Collisions require geometry • Moving point masses is not enough • Must know where objects meet • Typically use convex shapes • Lines remain inside shape • Mathematically the easiest shapes to compute with • Assumed by most algorithms • Historical research performed on convex shapes • What do you do if the shape is not convex? • Break it up into several primitives

7. Primitives • Axis Aligned Bounding-Box (AABB) • Intersection is very cheap • Project rectangle onto axes • Two intervals per box • Check both intervals overlap • Poor fit for most objects • Super Mario Bros. – works great • Diagonal boxes – not so great • False positives are likely

8. Primitives • Axis Aligned Bounding-Box (AABB) • Intersection is very cheap • Project rectangle onto axes • Two intervals per box • Check both intervals overlap • Poor fit for most objects • Super Mario Bros. – works great • Diagonal boxes – not so great • False positives are likely

9. Primitives • Axis Aligned Bounding-Box (AABB) • Oriented Bounding Box (OBB) • Tighter fit than AABB • Intersection more expensive • Must check 4 edges for overlap

10. Primitives • Axis Aligned Bounding-Box (AABB) • Oriented Bounding Box (OBB) • Discrete Oriented Polytope (DOP) • Captures almost all convex shapes • Intersection is more expensive • O(n2), n = number of edges

11. Primitives • Axis Aligned Bounding-Box (AABB) • Oriented Bounding Box (OBB) • Discrete Oriented Polytope (DOP) • Capsule • An OBB with rounded ends • Intersection cost is roughly the same • Efficient for swept shapes (circles)

12. Primitives • Axis Aligned Bounding-Box (AABB) • Oriented Bounding Box (OBB) • Discrete Oriented Polytope (DOP) • Capsule • Circles/Disks • Not cheaper than AABB • Poor fit for approximating anything other than a circle

13. Collision Detection • Question: • Do objects A and B intersect

14. Collision Detection • Question: • Do objects A and B intersect • Challenge: • Can be in motion

15. Collision Detection • Question: • Do objects A and B intersect • Challenge: • Can be in motion • Bigger Challenge: • Need to know when they collided. • Realistic physics needs the exact point of collision • Necessary for contact resolution

16. Tunneling

17. Tunneling

18. Tunneling

19. Tunneling

20. Tunneling • Small objects tunnel more easily

21. Tunneling • Possible solutions • Minimum size requirement? • Inadequate; fast objects can still tunnel

22. Tunneling • Possible solutions • Minimum size requirement? • Inadequate; fast objects can still tunnel • Maximum speed limit? • Inadequate; speed limit is a function of object size, so small and fast objects (bullets) wouldn’t be allowed • Smaller time step? • Helpful but inadequate; essentially the same as a speed limit

23. Tunneling • Why this is important! • Things can fall through the world • Bullets pass through people or walls • Players getting places they shouldn’t • Players missing trigger boundaries • Tunneling is a false negative • So what can we do about it?

24. Movement Bounds • Disc / Sphere

25. Movement Bounds • Disc / Sphere • AABB

26. Movement Bounds • Disc / Sphere • AABB • OBB

27. Movement Bounds • Question: • Could A and B have collided during the frame? • Better than our earlier question because it handles tunneling, but…

28. Movement Bounds • Question: • Could A and B have collided during the frame? • Better than our earlier question because it handles tunneling, but… • … even if the answer is “yes”, we still don’t know for sure • false positives

29. Movement Bounds • Conclusion • Good: they prevent tunneling • Bad: they produce false positives • Good: cheap, effective early rejection test

30. Swept Shapes • Swept disc: capsule

31. Swept Shapes • Swept disc: capsule • Swept AABB: polygon

32. Swept Shapes • Swept disc: capsule • Swept AABB: polygon • Swept triangle: polygon

33. Swept Shapes • Swept disc: capsule • Swept AABB: polygon • Swept triangle: polygon • Swept polytope: polygon

34. Swept Shapes • Better fit than movement bounds

35. Swept Shapes • Better fit than movement bounds • No false negatives (tunneling)

36. Swept Shapes • Better fit than movement bounds • No false negatives (tunneling) • No false positives either!

37. Swept Shapes • Better fit than movement bounds • No false negatives (tunneling) • No false positives either! • Nope! False positives still exist

38. Swept Shapes • Better fit than movement bounds • No false negatives (tunneling) • No false positives either! • Nope! False positives still exist

39. Collision Detection • Occurs in three phases • Broad Phase • Determine all pairs of objects that potentially collide • Sweep and Prune or Spatial Hashing • Mid phase • Determine potentially colliding primitives • Movement Bounds using AABBs • Narrow phase • Determine exact contact between two shapes • The Gilbert-Johnson-Keerthi (GJK) algorithm

40. Collision Resolution • What happens once we finally find the collision? • Two types of collisions elastic and inelastic • Inelastic collisions • No energy preserved in collision • Ensure objects do not overlap • Extremely easy to implement • Elastic collisions • 100% energy preserved • More complicated to implement

41. Simple Case: Circles • Simple collisions • Single point of contact • Impact coordinates • Point of contact is origin

42. Simple Case: Circles • Simple collisions • Single point of contact • Impact coordinates • Point of contact is origin

43. Simple Case: Circles • Simple collisions • Single point of contact • Impact coordinates • Point of contact is origin • Perpendicular component • Parallel component

44. Simple Case: Circles • Simple collisions • Single point of contact • Impact coordinates • Point of contact is origin • Perpendicular component • Parallel component • Change in motion happens along the perpendicular axis

45. Simple Case: Circles • Simple collisions • Single point of contact • Impact coordinates • Point of contact is origin • Perpendicular component • Parallel component • Exchange in energy happens along the perpendicular axis

46. Complex Case • With complex shapes, the point of contact is more complex • Could be a single point • Could be an edge • Solution: • Break object into several points • Connect the points by constraints • Apply forces to each of the points • Transfer forces to other points while obeying constraints • Requires constraint solver

47. Complex Case • With complex shapes, the point of contact is more complex • Could be a single point • Could be an edge • Solution: • Break object into several points • Connect the points by constraints • Apply forces to each of the points • Transfer forces to other points while obeying constraints • Requires constraint solver

48. Summary • Accurate physics is challenging • We didn’t even cover rotational motion! • Accurate collision detection is challenging • We’ve seen the problems that a physics engine must solve • Tips for moving ahead • Structure game to make collision detection easy • Use circles, AABBs, grids, etc. • Kinematic dynamics is straightforward and may produce “good enough” results • Use a physics engine rather than writing your own.