OffRoad Racing Physics,

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Off-Road Racing Physics,

• Indie Style

Jim Buck Twitchy Thumbs Entertainment,
Inc. jbuck_at_twitchythumbs.com August 19, 2009
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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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Why?

• Yesterdays next-gen technology is todays
• 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
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What is Rally Cross?
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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

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What is Rally Cross?

• Demo

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Rally Cross physics history

• Chris Hecker physics articles too late (October
  1996 - June 1997)
• SGI 4Dgifts newton demo
• Robert Sheehans bouncer simulation

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Physics Primer

• F ma
• v at (F/m)t
• p vt

All math is 1.19.12 fixed-point!
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What is Rally Cross physics?
Springs!
(well, actually, damped springs)
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Damped spring physics
v0
t 0
Spring at rest
v1
t 1
x
F kx cv1
Hookes law
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Rally Cross physics components

• Vehicle box
• Box collision with ground
• Box collision with track boundaries
• Box collision with another box (vehicle)
• Vehicle-specific physics

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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

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Vehicle Box
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Vehicle Box

• For each spring
• x length(p1 p0) - at_rest_length
• v dot(v1 v0, unit(p1 p0))
• F ( kx cv) unit(p1 p0)
• F1 F, F0 F

v1
v0
p1
p0
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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

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Box Collision with Ground

• Ground is a height-mapped grid
• Gravity constantly affects point masses
• F mG

m
G
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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 ( kxn cvn) normal_map(p.x, p.z)
• Formula is for a damped spring!

n
xn
x
height_map
p
vn
v
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Sidebar Friction

• Static Fmax fsN
• Kinetic F fkN

v 0
v
N
N
F
fsN
fkN
mG
mG
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Box Collision with Ground

• Friction
• Viscous F fvvo
• Static/kinetic
• If vo 0
• If Fo lt fsxn, Fo 0
• Else Fo fkxn
• Else if length(vo (Fo/m)t) lt (fkxn)t, vo
  0
• Else F unit(vo) fkxn

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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
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Box Collision with Another Box

• Sphere test for each car pair
• If succeeds, ray-through-box test

F ( kx cvn) normal
(Formula look familiar?)
x
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Box Collision with Another Box

• If ray-through-box fails, test each cars points
  against others box

x
n
Again, F ( kx cvn) normal
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Vehicle-specific Physics

• For steering, F kvvx (viscous friction!)
• For acceleration in Z, that would require a
  separate presentation ?

X
X
Z
Z
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But briefly
engine axle
gear ratio
wheel axle
fsN or fkN
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Physics ? Rendering

• Points time-stepped v (F/m)t, p vt
• Display matrix
• Car position top_center box_height
• Wheel position based on shock length

X
Top face
Z
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Physics Demo
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Problems

• Box freaking out
• Stuck on track boundaries

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Box Freaking Out

• Check crossbars dot product is in safe range
• Check upper points are above lower points

Lower points

Upper points
bad!
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Stuck on Track Boundaries

• Stuck if 2 adjacent points such that dot(n0b,
  n1b) lt 0
• Find boundary intersected by center of box to
  center of the 2 points
• Push out with spring equation

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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

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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

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QA
Contact jbuck_at_twitchythumbs.com