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Off-Road Racing Physics,

Off-Road Racing Physics,. Indie Style. Jim Buck Twitchy Thumbs Entertainment, Inc. jbuck@twitchythumbs.com August 19, 2009. Who is this dude??. 1996 – 2000 : 989 Studios, programmer 2000 – 2003 : DepthQ, founder 2003 – 2005 : SCEA, programmer 2005 – present : Twitchy Thumbs, founder.

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Off-Road Racing Physics,

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  1. Off-Road Racing Physics, Indie Style Jim Buck Twitchy Thumbs Entertainment, Inc. jbuck@twitchythumbs.com August 19, 2009

  2. Who is this dude?? • 1996 – 2000 : 989 Studios, programmer • 2000 – 2003 : DepthQ, founder • 2003 – 2005 : SCEA, programmer • 2005 – present : Twitchy Thumbs, founder

  3. Why? Yesterday’s next-gen technology is today’s: • achievability by indie developers • handheld technology • next-gen effects during spare CPU time “Doing a lot with a little is something we can't forget how to do.” – Mike Acton, Insomniac Studios

  4. What is Rally Cross?

  5. What is Rally Cross? • PlayStation off-road racing • Sony-developed/published • February ‘97 in N. America • 200,000 sold in N. America • Japanese/PAL releases • Considered “cult” classic • One of first for PS1-on-PSP

  6. What is Rally Cross? Demo

  7. Rally Cross physics history • Chris Hecker physics articles too late (October 1996 - June 1997) • SGI 4Dgifts newton demo • Robert Sheehan’s bouncer simulation

  8. Physics Primer • F = m*a • v += a*t = (F/m)*t • p += v*t All math is 1.19.12 fixed-point!

  9. What is Rally Cross physics? Springs! (well, actually, damped springs)

  10. Damped spring physics v0 t = 0 Spring at rest v1 t = 1 x F = – k*x – c*v1 Hooke’s law

  11. Rally Cross physics components • Vehicle box • Box collision with ground • Box collision with track boundaries • Box collision with another box (vehicle) • Vehicle-specific physics

  12. Vehicle Box • 8 points, or point masses, representing box corners • Each point accumulates forces (F) and gets time-stepped at bottom of loop • 28 damped springs from each point to every other point

  13. Vehicle Box

  14. Vehicle Box For each spring: • x = length(p1 – p0) - at_rest_length • v = dot(v1 – v0, unit(p1 – p0)) • F = (– k*x – c*v) * unit(p1 – p0) • F1 += F, F0 += –F v1 v0 p1 p0

  15. Vehicle Box • “Shock” springs are special • Separated into Y and ortho-Y vectors • “Softer” in Y than in ortho-Y • Ortho-Y treated same as other springs

  16. Box Collision with Ground • Ground is a height-mapped grid • Gravity constantly affects point masses: F = m*G m G

  17. Box Collision with Ground • For each point mass, if under height-map: • xn = (height_map(p.x, p.z) – p.y) * normal_map(p.x, p.z).y • vn = dot(v, normal_map(p.x, p.z) • F = (– k*xn – c*vn) * normal_map(p.x, p.z) • Formula is for a damped spring! n xn x height_map p vn v

  18. Sidebar: Friction • Static: Fmax = fs*N • Kinetic: F = fk*N v = 0 v N N F fs*N fk*N m*G m*G

  19. Box Collision with Ground Friction • Viscous: F = –fv*vo • Static/kinetic • If vo == 0 • If Fo <= fs*xn, Fo = 0 • Else Fo –= fk*xn • Else if length(vo + (Fo/m)*t) <= (fk*xn)*t, vo = 0 • Else F = –unit(vo) * fk*xn

  20. Box Collision with Boundaries • 2d (infinite height) line segments surrounding the track • Physics is same as for hitting the ground • Damped spring pushing back along normal • Friction applied ortho to the normal n In bounds xn Out of bounds p vn v

  21. Box Collision with Another Box • Sphere test for each car pair • If succeeds, ray-through-box test F = (– k*x – c*vn) * normal (Formula look familiar?) x

  22. Box Collision with Another Box • If ray-through-box fails, test each car’s points against other’s box x n Again, F = (– k*x – c*vn) * normal

  23. Vehicle-specific Physics • For steering, F = –kv*vx (viscous friction!) • For acceleration in Z, that would require a separate presentation  X X Z Z

  24. But briefly… engine axle gear ratio wheel axle fs*N or fk*N

  25. Physics  Rendering • Points time-stepped: v += (F/m)*t, p += v*t • Display matrix: • Car position = top_center – box_height • Wheel position = based on shock length X Top face Z

  26. Physics Demo

  27. Problems • Box freaking out • Stuck on track boundaries

  28. Box Freaking Out • Check “crossbars” dot product is in safe range • Check upper points are “above” lower points Lower points + Upper points = bad!

  29. Stuck on Track Boundaries • Stuck if 2 adjacent points such that: dot(n0b, n1b) < 0 • Find boundary intersected by center of box to center of the 2 points • Push out with spring equation

  30. Optimizations • Constants mostly power-of-2 • Cached calculations (ex. 1/mass * time) • Local variables to avoid aliasing • 64-bit MIPS multiplications • Assembly language for key math functions and height-map lookup

  31. Evolution of Physics CART World Series • correct wheel friction Twisted Metal 3 • 3d poly collision with no penetration (no height-map) Twisted Metal 4 • car-to-car collision with 3d boolean intersection

  32. Q&A Contact: jbuck@twitchythumbs.com

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