Ten Minute Physics
Ten Minute Physics is a great resource! Matthias Mueller makes concise demos and explains them really well. (Though I think it would take someone without existing familiarity with the subject matter a lot longer than 10 minutes to digest the results. Lots of rewatching!)<p>A really interesting results that&#x27;s come out of Matthias and co.&#x27;s research in the last few years that is still percolating its way through the realtime physics community is the so called &quot;small step&quot; technique. Explained at a really high level: integrating a physical system requires solving large sparse systems of nonlinear equations. Traditionally, the equations would be solved once a frame with iterative methods (often with a fixed number of iterations, such as 10 or 20 per frame). It turns out it&#x27;s massively more efficient for accurate results to just run a single iteration of the solver, but increase the physics framerate by 10 or 20 times (or actually, since there&#x27;s a tiny bit of overhead to process a physics frame, for equivalent computational load, you can usually only increase the framerate 9-18 times). The intuition here is that even though 1 iteration of the solver is much less accurate than 20, by only taking a small step forward in time the error drift in the physical system is even lower. It&#x27;s only somewhat handwavy to say solver iterations reduce error at a linear rate, but decreasing physics frame time reduces error at an O(n^2) rate.<p>While almost all engines have added an option to use the small step technique, one issue slowing down adoption is that it is <i>too</i> accurate! The old way of solving the nonlinear equations once a frame introduced a huge amount of numerical damping. That greatly reduced accuracy, but did serve to stabilize simulations, in a way. With the small step technique, numerical damping is greatly reduced, so intentional physical models of damping need to be added back in and tuned by hand. People aren&#x27;t used to working this way, so designers are still toggling back to the &quot;large step&quot; method. It&#x27;s likely once people figure out how to properly use this new technique, you&#x27;ll see a noticeable uptick in the fidelity of physics in games.