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Squirrel Eiserloh. Technical Director. MumboJumbo Games. squirrel ... Or confusing. 112. Questions? Feel free to reach me by email at: squirrel@eiserloh.net ...

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  1. Physics for Games Programmers Reframing the Problem Squirrel EiserlohTechnical DirectorMumboJumbo Gamessquirrel@eiserloh.netwww.algds.org

  2. Physics for Games Programmers Reframing the Problema.k.a. “It’s All Relative” Squirrel EiserlohTechnical DirectorMumboJumbo Gamessquirrel@eiserloh.netwww.algds.org

  3. Overview • Tunneling • Movement Bounds • Swept Shapes • Einstein Says... • Minkowski Says... • Rotation

  4. Tunneling (Sucks)

  5. Tunneling • Question #1: Do objects A and B overlap? • Plenty of reference material to help solve this, but... • ...this is often the wrong question to ask (begs tunneling).

  6. Tunneling

  7. Tunneling

  8. Tunneling

  9. Tunneling

  10. Tunneling (cont’d) • Tunneling is very, very bad – this is not a “mundane detail” • Things falling through world • Bullets passing through people or walls • Players getting places they shouldn’t • Players missing a trigger boundary • Tunneling is a false negative • Okay, so tunneling really sucks. What can we do about it?

  11. Movement Bounds

  12. Movement Bounds • Disc / Sphere

  13. Movement Bounds • Disc / Sphere • AABB (Axis-Aligned Bounding Box)

  14. Movement Bounds • Disc / Sphere • AABB (Axis-Aligned Bounding Box) • OBB (Oriented Bounding Box)

  15. Movement Bounds • Question #2: Could A and B have collided during the frame? • Better than Question #1 (solves tunneling!), but...

  16. Movement Bounds • Question #2: Could A and B have collided during the frame? • Better than Question #1 (solves tunneling!), but... • ...even if the answer is “yes”, we still don’t know for sure (false positive).

  17. Movement Bounds • Conclusion • Good: They prevent tunneling! (i.e. no false negatives) • Bad: They don’t actually tell us whether A and B collided (still have false positives). • Good: They can be used as a cheap, effective early rejection test.

  18. Swept Shapes

  19. Swept Shapes • Swept disc / sphere (n-sphere): capsule

  20. Swept Shapes • Swept disc / sphere (n-sphere): capsule • Swept AABB: convexpolytope (polygon in 2d, polyhedron in 3d)

  21. Swept Shapes • Swept disc / sphere (n-sphere): capsule • Swept AABB: convex polytope (polygon in 2d, polyhedron in 3d) • Swept triangle / tetrahedron (simplex): convex polytope

  22. Swept Shapes • Swept disc / sphere (n-sphere): capsule • Swept AABB: convex polytope (polygon in 2d, polyhedron in 3d) • Swept triangle / tetrahedron (simplex): convex polytope • Swept polytope: convexpolytope

  23. Swept Shapes (cont’d) • Like movement bounds, only with a perfect fit!

  24. Swept Shapes (cont’d) • Like movement bounds, only with a perfect fit! • Still no false negatives (tunneling).

  25. Swept Shapes (cont’d) • Like movement bounds, only with a perfect fit! • Still no false negatives (tunneling). • Finally, no false positives, either!

  26. Swept Shapes (cont’d) • Like movement bounds, only with a perfect fit! • Still no false negatives (tunneling). • Finally, no false positives, either! • No, wait, nevermind. Still have ‘em. Rats.

  27. Swept Shapes (cont’d) • Like movement bounds, only with a perfect fit! • Still no false negatives (tunneling). • Finally, no false positives, either! • No, wait, nevermind. Still have ‘em. Rats.

  28. Swept Shapes (cont’d) • Like movement bounds, only with a perfect fit! • Still no false negatives (tunneling). • Finally, no false positives, either! • No, wait, nevermind. Still have ‘em. Rats.

  29. Swept Shapes (cont’d) • Conclusion • Suck? • Can be used as early rejection test, but... • ...movement bounds are better for that. • If you’re not too picky... • ...they DO solve a large number of nasty problems (especially tunneling) • ...and can serve as a poor man’s continuous collision detection for a basic engine.

  30. Einstein Says... • Coordinate systems are relative

  31. Relative Coordinate Systems

  32. Relative Coordinate Systems • World coordinates

  33. Relative Coordinate Systems • World coordinates • A’s local coordinates

  34. Relative Coordinate Systems • World coordinates • A’s local coordinates • B’s local coordinates

  35. Relative Coordinate Systems • World coordinates • A’s local coordinates • B’s local coordinates • Many others (e.g. origin at point of impact)

  36. Relative Coordinate Systems (cont’d) • Ball vs. world...

  37. Relative Coordinate Systems (cont’d) • Ball vs. world... • in world coordinates

  38. Relative Coordinate Systems (cont’d) • Ball vs. world... • in world coordinates • x component • y component

  39. Relative Coordinate Systems (cont’d) • Ball vs. world... • in world coordinates • x component • y component • in impact coordinates

  40. Relative Coordinate Systems (cont’d) • Ball vs. world... • in world coordinates • x component • y component • in impact coordinates • parallel component • perpendicular component

  41. Relative Coordinate Systems (cont’d) • Ball vs. world... • in world coordinates • x component • y component • in impact coordinates • parallel component • perpendicular component • Change in motion happens along the perpendicular axis

  42. Relative Coordinate Systems (cont’d) • Ball vs. ball...

  43. Relative Coordinate Systems (cont’d) • Ball vs. ball... • in world coordinates

  44. Relative Coordinate Systems (cont’d) • Ball vs. ball... • in world coordinates • x component • y component

  45. Relative Coordinate Systems (cont’d) • Ball vs. ball... • in world coordinates • x component • y component • in impact coordinates

  46. Relative Coordinate Systems (cont’d) • Ball vs. ball... • in world coordinates • x component • y component • in impact coordinates • parallel component • perpendicular component • Energy is exchanged along the perpendicular axis

  47. Relative Coordinate Systems (cont’d) Also, math is often nicer at the origin. x2 - 2xh + h2 + y2 - 2yk + k2 = r2 x2 + y2 = r2

  48. Einstein Says... • Coordinate systems are relative • Motion is relative

  49. Relative Motion

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