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# Objective Almost all of the `*InOut` easing functions are not actually smooth (`SineInOut` is the one exception). Because they're defined piecewise, they jump from accelerating upwards to accelerating downwards, causing infinite jerk at t=½. ## Solution This PR adds the well-known [smoothstep](https://registry.khronos.org/OpenGL-Refpages/gl4/html/smoothstep.xhtml), as well as its higher-degree version [smootherstep](https://en.wikipedia.org/wiki/Smoothstep#Variations), as easing functions. Mathematically, these are the classic [Hermite interpolation](https://en.wikipedia.org/wiki/Hermite_interpolation) results: - for smoothstep, the cubic with velocity zero at both ends - for smootherstep, the quintic with velocity zero *and acceleration zero* at both ends And because they're simple polynomials, there's no branching and thus they don't have the acceleration jump in the middle. I also added some more information and cross-linking to the documentation for these and some of the other easing functions, to help clarify why one might want to use these over other existing ones. In particular, I suspect that if people are willing to pay for a quintic they might prefer `SmootherStep` to `QuinticInOut`. For consistency with how everything else has triples, I added `Smooth(er)Step{In,Out}` as well, in case people want to run the `In` and `Out` versions separately for some reason. Qualitatively they're not hugely different from `Quadratic{In,Out}` or `Cubic{In,Out}`, though, so could be removed if you'd rather. They're low cost to keep, though, and convenient for testing. ## Testing These are simple polynomials, so their coefficients can be read directly from the Horner's method implementation and compared to the reference materials. The tests from #16910 were updated to also test these 6 new easing functions, ensuring basic behaviour, plus one was updated to better check that the InOut versions of things match their rescaled In and Out versions. Even small changes like ```diff - (((2.5 + (-1.875 + 0.375*t) * t) * t) * t) * t + (((2.5 + (-1.85 + 0.375*t) * t) * t) * t) * t ``` are caught by multiple tests this way. If you want to confirm them visually, here are the 6 new ones graphed: <https://www.desmos.com/calculator/2d3ofujhry>  --- ## Migration Guide This version of bevy marks `EaseFunction` as `#[non_exhaustive]` to that future changes to add more easing functions will be non-breaking. If you were exhaustively matching that enum -- which you probably weren't -- you'll need to add a catch-all (`_ =>`) arm to cover unknown easing functions. |
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Bevy Math
