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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