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Discretization can cause fast-moving objects to travel through walls. Another big source of artifacts is the linearization that most physics engines employ—the assumption that during the time step everything travels in a linear motion.
Consider the ball joint illustrated in Figure 2. The two bodies are rotating in opposite directions. At this parti cular point in time, the two bodies are lined up as shown.
Even if the solver manages to entirely solve the relative velocity at the joint-attachment point to zero, as soon as time is advanced, no matter how small the amount, the two attachment points will drift apart.
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This is the fundamental of linearizat ion, which makes it impossible to create an accurat e physics engine by solving just for relative linear velocities at discrete points in time. Even though linearization and discretization are two different approximations, they are somewhat interconnected.
Lowering the step size increasing the number of substeps will always make linearization less problematic, since any nonlinear motion will appear more and more linear the shorter the time span. The ambitious reader can make a parallel here to the Heisenberg principle of uncertainty!
The major takeaway here is that as long as a physics engine employs discretization and linearization, which all modern physics engines and all algorithms 1 2 Figure 2.
Even if relative linear velocity at the joint attachme nt is zero, objects can separate during integration due to rotation.
Time Stepping and the Well of Despair 31 and examples in this book do, there will always be artifacts. These artifacts are not results of a problem with the physics engine itself, but the assumptions and approximations the engin e is built upon.
This is important to realize, because once you accept the artifacts and understand their underlying causes, it makes them easier to deal with and work around. This is a common source of confusion whe n integrating a physic s engine, since you probably want the motion in your game to be independent of frame rate.
On a slow machine, or in the occasion of your modern operating system going off to index the quicksearch database in the middle of a mission, the graphical update might not keep up with the desired frequency.
There are several different strategies for how to handle such a scenario from a physics perspective. You can ignore the fact that a frame was dropped and keep stepping the normal step length, which will create a slow-motion effect that is usually highly undesirable.
Another option is to take a larger time ste p, which will creat e a more realistic path of motion but may introduce jerkiness due to the variation in discretization. The third option is to take several, equally sized physics steps. If physics is the bottleneck, the update frequency will go into the well of despair, meaning every subsequent frame needs more physics updates, causing a slower update frequency, resulting in even more physics updates the next frame, and so on.
There is unfortunatel y no way to solve this problem other than to optimize the physics engine or simplify the problem, so what most people do is put a cap on the number of physics updates per frame, above which the simulation will simply run in slow motion. Actually, it will not only run in slow motion but it will run in slow motion at a lower-thannecessary frame rate, since most of what the physics engine computes is never even shown!
A more sophisticated solution is to measure the time of the physics update, compare it to the overall frame time, and only make subsequent steps if we can avoid the well of despai r.
UnderstandingGamePhysicsArtifacts The Curse of Rotations Since rotation is the mother of most linearization problems, it deserves some special atte ntion. You will be surprised how stable those stacks become and how nicely most scenarios just work. Dialogue between Beccaria, Lombroso and Durkheim Student’s name Institutional Affiliation Dialogue between Beccaria, Lombroso and Durkheim Criminology, as every science, relies on facts and evidence.
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is and in to a was not you i of it the be he his but for are this that by on at they with which she or from had we will have an what been one if would who has her. The current GUI is like a flight simulator whose camera points fixedly at right angle to the document, thus preventing users from looking ahead while navigating.
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