First, even at a constant framerate, different players will have different experiences with the game due to different amounts of latency in their peripherals, weird CPU bugs, very very minor floating point behavior deviations, etc. The important part of making something framerate independent is to make the effects of framerate independence /smaller enough/ than other factors that make player experiences.
It's entirely possible to not have gameplay change at different tickrates. There are three usual types of problem that cause gameplay to change at different tickrates:
1) Events that happen at specific times
If events can only happen "in sync" with ticks, then running at different framerates will make them happen at different times. Say you have a machine gun that fires once every 1/10th of a second. If you're running at 24fps, then not only do you need to make sure that you correctly output a bullet every two-or-three frames, you also have to make it so that they /act like/ they came out at a time between frames, presumably by simulating them a little extra bit or a little less depending on what's necessary to make each bullet a fixed distance apart (for example). You could also use a continuous interaction system here but that's really hardcore and doesn't matter in 99.9%+ of cases.
2) Treating curved motions as linear motions
This isn't a problem in 99% of cases, but it ~can~ be a problem. If you can't represent your physics curves in closed form, it's effectively impossible to trace them in a framerate-independent way. The only thing you can do for these things is to "fix your timestep", but "fix your timestep" should be used with extreme caution and not be applied to action games because it adds input latency and hides frame-specific-timing information from players. Recommendation: use simpler game physics. Constant acceleration everywhere you can, special-purpose closed form functions with the right curves where you can't, and avoid tight curves. This makes it less of an issue.
You might also want a collision system that allows curved paths, but if you have enough control over your game's environments, and you don't expect people to run at SUPER low framerates, this isn't an issue.
3) Running different "integral" parts of the simulation out of sync with eachother.
This isn't literally about code order execution, it's about the behavior of different pieces of code that "add up" "over time" (if you're into calculus, think antiderivatives)
If you add n to your position every frame, that's all fine and good, as long as it always starts at exactly the right time. If you add "five pixels per second" to your position, then you need to make sure that always causes the same amount of distance travelled. Quake 3 handles this by giving subframe timings to things like pressing and releasing movement keys.
Another example is gravity. Normally, game code adds a specific amount of gravity every frame, possibly adjusted for time, either before or after motion. This isn't good enough, because if you add gravity after moving, very low framerates will have a higher initial frame of gravitational movement; essentially, low framerates will skip "outside" the ideal jump arc rather than tracing it. If you add gravity before moving, the opposite happens, low framerates trace "inside" the ideal jump arc. The correct thing to do is to calculate motion with around half the added velocity from all accelerations for that frame, which basically means the average of accelerating before or after. You can also trace a hermite spline, which is more flexible (you will have perfect framerate independence for any acceleration values that only change along line segments, i.e. "constant jerk", as long as you handle start/stop conditions for changes in acceleration with a correct continuous interaction simulation), but harder to implement.
The above is only 100% ideally possible for things you can represent closed form, and in practice, people will only implement something correctly if it's not just closed form but /simple/. Many games stop short of correct jump arcs, but it's entirely possible. Gang Garrison 2 was just changed to have a correct framerate-independent jump arc.
I don't know what kind of CPU bugs or float point behaviour deviations you think modern cpus have that will effect a game.. such things would cause most online games to immediately go out-of-sync, and in practice they don't, and while latency might effect player's enjoyment, it won't effect how fast they run / how high they jump.
The hardest part is the curved motions -- and also collision detection. Without ticks it's extremely hard to make collision detection repeatable.
I'm unaware of any recent notable multi-player game which don't run on a tick-based physics engine (I'd be interested if you could point me to some) -- that suggests to me that tick-based is necessary.
Sure, you can get things "closer" in tickless physics, but I've never seen anything non-trivial which can produce exactly the same results, for reasons of floating point: when (A+B)+C isn't the same as A+(B+C), it's very hard to make your game produce exactly the same results.
As you say, with a lot of work, you can get a 95% repeatable result with a tickless engine, but you can easily get 100% repeatable with a fixed time-step engine, and in practice it seems to make things work well enough, and is VASTLY easier.
During development of the game [Prototype] I experimented with a number of game logic update scenarios, including variable timesteps, fixed (potentially multiple per frame) and limited fixed (potentially leading to slow motion), in combination with factors like enabling and disabling vsync, taking into account camera movement (speed, mostly horizontal or mostly vertical?), amount of explosions and debris going off, etc. To try and find the best experience for the player at each moment.
But we always had physics running at a fixed update rate (always receiving a constant delta time) regardless of any of the above. Trying variable rates there will ruin the stability of your movement, collisions, platforming, etc in any system that is complex or requires precision and predictability.
Online games avoid that problem by having an authoritative networking architecture, not by avoiding minor deviations in CPU behavior between players. Games that use synchronized lockstep that use floating point math always desync, because floating point math differs slightly between different processors.
Curved motions are easy as long as you have simple polygons and only one of them is accelerating and is accelerating in a simple way. You remove the acceleration by skewing the polygon you're going to collide with and then you have a linear path of motion again. (if the acceleration is not constant for the duration of that frame, then skewing doesn't give the right result; as long as you have a closed form representation, though, it's entirely possible to get it right)
"Don't run on a tick-based physics engine" is a misconception. Interactions are the borders between ticks. It's just dynamic. As long as your tick doesn't contain interaction changes inside it, you can simulate that tick with 100% tickrate independence with 100% certainty.
Floating point differences between cpus are Much Larger, especially if your code uses hardware-accelerated trig at all. Games networking is authoritative for this reason.
You can get a 100% repeatable result with a tickless engine.
Fixed timestep doesn't solve the problem. If the user can't run the simulation at 60 ticks per second, they're still going to slow down, period. All you're doing is separating simulation from rendering, which basically every modern FPS under the sun already tries to do in a different way than fixed timestep does. If you run the simulation slow enough that nobody will have performance problems with it, you just added tons of input latency. Thanks a lot, sincerely, someone with dysgraphia.
> because floating point math differs slightly between different processors.
I don't know why you keep saying this. If I compile a program which uses floating point for (say) x64, it will produce the same results on every machine. Can you give any example where the same executable will produce different results on different machines?
Now, you may get different answers on ARM, or 32-bit, but almost no games (I'm having trouble thinking of any) try to do cross-CPU networking, so the (extremely) minor differences doesn't make any difference. Most games don't sync between users, they trust each user to run the game engine -- you can't afford to send the total state of the world to users, it would take far too much network traffic.
Can you point me to a physics engine which gives 100% repeatable results with tickless? I'm genuinely interested, I didn't know of any that claim they achieve that, the common ones (box2d, unity and havok for example) certainly don't.
Because it's true. The same operation on the same data may give different results on different CPUs, even if you're operating at the machine code level (no implementation-specific optimizations).
>Can you point me to a physics engine which gives 100% repeatable results with tickless? I'm genuinely interested, I didn't know of any that claim they achieve that, the common ones (box2d, unity and havok for example) certainly don't.
box2d is sufficiently low level that it gives programmers the tools necessary to do this.
Most notably, box2d provides the following:
>Continuous physics with time of impact solver
This directly allows developers to create a "tickless" physics simulation by breaking up the simulation into the timespans between interactions, as long as pathological situations aren't introduced (like the quake 3 ledge climbing bug). That doesn't mean that the developer will actually do so, and if the gameplay logic interacts with physics in framerate-dependent ways the result will still be wrong. It just means that the possibility is there.
Of course, this doesn't solve game logic issues with things happening only at the moment that a frame happens. That's entirely on the developer, even if they use an ideal physics engine.
At the end of this, I'll repeat that fixed timestep doesn't actually solve the problem, all it does is allow you to output higher graphical framerates than the physics simulation is running at. If the physics simulation itself can't run at full speed, you still need a way to adapt to longer frametimes, and you have to do so correctly. And if you run the physics simulation so slowly that it won't slow down on any reasonable PC, you either have a very simple game or you just added tons of input latency.
The reason why you don't see an issue while using Box2D is because its integration methods are low-error. A simple platform game using Euler style integration of the type
each step, add forces from input and gravity. add the resulting acceleration multiplied by time to my position.
will trivially produce jump heights of 50% variation when subjected to a variable timestep. On a quick search, Box2D uses semi-implicit Euler [0], which much more accurately fits the curve. It does not guarantee zero error: to do that you have to have an analytic method, which isn't applicable to a general-purpose physics simulation.
I covered integration error in my first post here, point 3. The thing I was calling Box2D out for is the fact that it doesn't use a hacky way of rectifying collisions. It seeks out the point in time that they occur.
>It does not guarantee zero error: to do that you have to have an analytic method, which isn't applicable to a general-purpose physics simulation.
If you have constant acceleration, the analytic way to get the point you want to be at at the end of the frame is simple: just pretend your current frame is using half the added speed from the acceleration that you're going to undergo this frame. Or you could use a hermite curve or something.
Those are the integration methods I was talking about. An analytic method without error is one which can describe the curve at any moment in time, not "constant acceleration per frame".
Box2d's continuous physics does not allow for a tickless simulation as I understand the term, because continuous interactions (stacking, sliding, rolling, etc.) are not reduced to discrete time-of-impact calculations. Joints are also in that category. If you run the testbed and crank the timestep way up, you'll definitely see problems with things like ragdolls.
Continuous collision detection definitely makes it easier to handle high velocities and bigger timesteps, but it's not a panacea.
By "continuous physics", it doesn't mean the "objects don't go through walls" thing (that's easy), it means that it actually finds the times that interactions happen. Box2d isn't able to use that in all cases, but it does allow it to act the same way as a tickless simulation if your game's physics is simple enough, like 2d platformers.
I think theoretically you're correct that the methods underlying Box2d could be used in such a way, but practically I don't think it's there, as that was never one of the engine's goals. Read up on the methods used (for instance, http://twvideo01.ubm-us.net/o1/vault/gdc2013/slides/824737Ca...) for some of the limitations that Erin chose to accept. In particular the fact that it misses multiple roots during the solve means that you can't use if for perfect tickless simulation; there are (were? I'm not sure to what extent they've been addressed since I was deep in that code) also issues with conservation of time that would be a problem, which are discussed elsewhere (for instance http://box2d.org/forum/viewtopic.php?t=154).
I didn't know about the innaccuracies in sin/cos, good to know, I'll remember that, but I usually wouldn't use those in a physics engine (and now I certainly won't).
The other stuff, different compiling levels, changing the floating point rounding mode, does indeed change results, but that wouldn't effect a single compile of a program running on different machines.
I maintain a javascript PRNG which relies on basic floating point math operations, addition and multiplication. Its test page here (https://strainer.github.io/Fdrandom.js/) displays a warning if it doesn't hit expected value 1 million rnds after default seeding. I've not found any computer or phone fail that basic compliance test yet.
Differences in trig functions strikes me as more matter of Math library compliance that floating point unit, im not sure but would be hopeful these are fairly well standardised across javascript engines.
To add to this statement: Input latency is a much broader issue than collision latency - a large scale of collision latency is produced simply by being an online game, regardless of how you're trying to represent the events. So the collision being subject to a tickrate is hardly a dealbreaker. Variable timesteps can be a little bit better at performance or responsiveness, but it comes at the expense of flooding additional concerns about consistency throughout the main loop. The modern fixed timestep treats a tick rate as delta times being partitioned into quantities of ticks, but also passes the time each tick represents into each update as a way to ensure that timers and time-centric physics can exhibit perceptually similar behaviors if the tickrate, and thus the duration of each tick, changes.
Input latency, OTOH, is something that has challenged developers from the earliest days since it has to do with how fast you propagate new input through the main loop to the output device, and the timestep's interaction with input is not straightforward. Arcade games could drastically improve their feel just by capturing and debouncing input multiple times a frame, even with the simple screen-refresh timesteps that were the common practice.
It's entirely possible to not have gameplay change at different tickrates. There are three usual types of problem that cause gameplay to change at different tickrates:
1) Events that happen at specific times
If events can only happen "in sync" with ticks, then running at different framerates will make them happen at different times. Say you have a machine gun that fires once every 1/10th of a second. If you're running at 24fps, then not only do you need to make sure that you correctly output a bullet every two-or-three frames, you also have to make it so that they /act like/ they came out at a time between frames, presumably by simulating them a little extra bit or a little less depending on what's necessary to make each bullet a fixed distance apart (for example). You could also use a continuous interaction system here but that's really hardcore and doesn't matter in 99.9%+ of cases.
2) Treating curved motions as linear motions
This isn't a problem in 99% of cases, but it ~can~ be a problem. If you can't represent your physics curves in closed form, it's effectively impossible to trace them in a framerate-independent way. The only thing you can do for these things is to "fix your timestep", but "fix your timestep" should be used with extreme caution and not be applied to action games because it adds input latency and hides frame-specific-timing information from players. Recommendation: use simpler game physics. Constant acceleration everywhere you can, special-purpose closed form functions with the right curves where you can't, and avoid tight curves. This makes it less of an issue.
You might also want a collision system that allows curved paths, but if you have enough control over your game's environments, and you don't expect people to run at SUPER low framerates, this isn't an issue.
3) Running different "integral" parts of the simulation out of sync with eachother.
This isn't literally about code order execution, it's about the behavior of different pieces of code that "add up" "over time" (if you're into calculus, think antiderivatives)
If you add n to your position every frame, that's all fine and good, as long as it always starts at exactly the right time. If you add "five pixels per second" to your position, then you need to make sure that always causes the same amount of distance travelled. Quake 3 handles this by giving subframe timings to things like pressing and releasing movement keys.
Another example is gravity. Normally, game code adds a specific amount of gravity every frame, possibly adjusted for time, either before or after motion. This isn't good enough, because if you add gravity after moving, very low framerates will have a higher initial frame of gravitational movement; essentially, low framerates will skip "outside" the ideal jump arc rather than tracing it. If you add gravity before moving, the opposite happens, low framerates trace "inside" the ideal jump arc. The correct thing to do is to calculate motion with around half the added velocity from all accelerations for that frame, which basically means the average of accelerating before or after. You can also trace a hermite spline, which is more flexible (you will have perfect framerate independence for any acceleration values that only change along line segments, i.e. "constant jerk", as long as you handle start/stop conditions for changes in acceleration with a correct continuous interaction simulation), but harder to implement.
The above is only 100% ideally possible for things you can represent closed form, and in practice, people will only implement something correctly if it's not just closed form but /simple/. Many games stop short of correct jump arcs, but it's entirely possible. Gang Garrison 2 was just changed to have a correct framerate-independent jump arc.