Timing in Real Time Simulations

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Timing in Real Time Simulations

• 11/11/09
• Kevin Dressel
• dressel3

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Moving an Object

• Update()
• obj.pos obj.vel

On your machine
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Moving an Object

• Update()
• obj.pos obj.vel

On an older machine
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Moving an Object

• Update()
• obj.pos obj.vel

On machine in future
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Common Way to Do It

• Update(float dt)
• obj.pos (obj.vel dt)

• dt is the time since the last update (variable)
• Change position in proportion to the speed the
  simulation is running at

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Common Way to Do It

• Incrementally integrate over time
• (Euler method)
• Variable time steps
• Like Riemann Sum

Update(float dt) obj.pos (obj.vel dt)
Velocity
dt
Position
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Stability

• This is an estimation
• Variable time steps
• Large dt makes incremental integration inaccurate
• Complex physics tends to be very sensitive to
  this

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Solutions

• Find better integration method
• Ignore large jumps in dt
• Go back to fixed time step
• Ignore it
• One common way to fix this
• Use fixed time step for physics
• If running too quickly, wait until fixed time
  passed to update
• Or, do as many physics steps needed to catch up
  to current time

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Example
Running too slow Do as many physics steps as
needed to catch up to current time. Running too
fast Dont update physics until FIXED_DT time
has actually passed

• define FIXED_DT (0.017f)
• float remainder 0.0f
• Update(float dt)
• remainder dt
• while(remainder gt FIXED_DT)
• obj.vel obj.acc FIXED_DT
• obj.pos obj.vel FIXED_DT
• remainder - FIXED_DT

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Example

• define FIXED_DT (0.017f)
• define MAX_DT (2.0f)
• float remainder 0.0f
• Update(float dt)
• if(dt gt MAX_DT) return
• remainder dt
• while(remainder gt FIXED_DT)
• obj.vel obj.acc FIXED_DT
• obj.pos obj.vel FIXED_DT
• remainder - FIXED_DT

To avoid getting stuck in the while loop, skip
this update if dt is too big.
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What Does it Look Like?
Physics Timeline
0 steps
1 step
2 steps
3 steps
4 steps
Simulation Timeline
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Update 0
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Update 1
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Update 2
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Update 3
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Update 4
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Update 5
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Update 6
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Example

• define FIXED_DT (0.017f)
• define MAX_DT (2.0f)
• float remainder 0.0f
• Update(float dt)
• if(dt gt MAX_DT) return
• remainder dt
• while(remainder gt FIXED_DT)
• obj.old.pos obj.curr.pos
• obj.old.vel obj.curr.vel
• obj.curr.vel obj.curr.acc FIXED_DT
• obj.curr.pos obj.curr.vel FIXED_DT
• remainder - FIXED_DT

• Keep previous physics state and a current physics
  state.
• Interpolate between them based on how far into
  the next physics state we are

Linear interpolation
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Update 0 with Interpolation
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Update 1 with Interpolation
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Update 2 with Interpolation
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Update 3 with Interpolation
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Update 4 with Interpolation
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Update 5 with Interpolation
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Update 6 with Interpolation
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Timer Resolution

• Time between updates is extremely small
• Real time requires high resolution time queries
• time() 1 second resolution
• GetTickCount() clock() 25-60 millisecond
  resolution
• timeGetTime() 15-30 millisecond resolution
• Microsecond resolution (run in separate thread)
• X86 rdtsc instruction
• QueryPerformanceCounter on Windows
• gettimeofday() (µs) and clock_gettime() (ns) on
  Linux

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From SDL for Linux
void SDL_StartTicks(void) / Set first ticks
value / if HAVE_CLOCK_GETTIME clock_gettime(CLO
CK_MONOTONIC,start) else gettimeofday(start,
NULL) endif Uint32 SDL_GetTicks (void) if
HAVE_CLOCK_GETTIME Uint32 ticks struct
timespec now clock_gettime(CLOCK_MONOTONIC,now)
ticks(now.tv_sec-start.tv_sec)1000(now.tv_ns
ec-start.tv_nsec)/1000000 return(ticks) else
Uint32 ticks struct timeval now gettimeofday(
now, NULL) ticks(now.tv_sec-start.tv_sec)1000
(now.tv_usec-start.tv_usec)/1000 return(ticks)
endif
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From SDL for Windows
void SDL_StartTicks(void) / Set first ticks
value / ifdef USE_GETTICKCOUNT start
GetTickCount() else if (QueryPerformanceFrequen
cy(hires_ticks_per_second) TRUE) hires_ti
mer_available TRUE QueryPerformanceCounter(h
ires_start_ticks) else hires_timer_avail
able FALSE timeBeginPeriod(1) / use 1 ms
timer precision / start timeGetTime() en
dif
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From SDL for Windows
Uint32 SDL_GetTicks(void) DWORD now,
ticks ifndef USE_GETTICKCOUNT LARGE_INTEGER
hires_now endif ifdef USE_GETTICKCOUNT now
GetTickCount() else if (hires_timer_available)
QueryPerformanceCounter(hires_now) hires_
now.QuadPart - hires_start_ticks.QuadPart hire
s_now.QuadPart 1000 hires_now.QuadPart /
hires_ticks_per_second.QuadPart return
(DWORD)hires_now.QuadPart else now
timeGetTime() endif if ( now lt start )
ticks (TIME_WRAP_VALUE-start) now
else ticks (now - start) return(ticks)

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Conclusion

• We want simulations to run predictably on any
  machine
• Integrators are sensitive to large/variable dt
• Physics is sensitive to inaccurate integration
• Need to make sure timer can update fast enough