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This PR makes `TransitionRoute` support driving the animation with `Simulation`. This is needed for Cupertino widgets, since iOS use "spring simulations" for a majority of their animations. This PR also applies the standard spring animation to `CupertinoDialogRoute` (alert dialogs) and `CupertinoModalPopupRoute` (action sheets). (This PR does not yet support customizing the spring parameters or conveniently using the springs for custom routes, which are left for future PRs.) ### Comparison I tried to create a comparison video for action sheets, however the difference is far less noticeable than I expected. (All clips are precisely aligned at the moment the pointer is lifted.) I guess the original curve _is_ good enough. Nevertheless, the spring simulation is the correct one and we should support it. Edit: [The comment](https://github.com/flutter/flutter/pull/155575#issuecomment-2489303282) below also mentioned that supporting spring animation will improve the fidelity when the animation is caused by a user gesture. I assume this requires initial speed, which is not supported by this PR but we can add it in the future. https://github.com/user-attachments/assets/06d2f684-ad1c-4a4d-8663-a561895f45e9 Also, Flutter's response seems to be always a moment slower than SwiftUI, possibly because Flutter requiring two frames to start the animation (one frame to add the transition widget, one frame for the animation to actually progress.) We probably want to solve it in the future. ## Pre-launch Checklist - [ ] I read the [Contributor Guide] and followed the process outlined there for submitting PRs. - [ ] I read the [Tree Hygiene] wiki page, which explains my responsibilities. - [ ] I read and followed the [Flutter Style Guide], including [Features we expect every widget to implement]. - [ ] I signed the [CLA]. - [ ] I listed at least one issue that this PR fixes in the description above. - [ ] I updated/added relevant documentation (doc comments with `///`). - [ ] I added new tests to check the change I am making, or this PR is [test-exempt]. - [ ] I followed the [breaking change policy] and added [Data Driven Fixes] where supported. - [ ] All existing and new tests are passing. If you need help, consider asking for advice on the #hackers-new channel on [Discord]. <!-- Links --> [Contributor Guide]: https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#overview [Tree Hygiene]: https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md [test-exempt]: https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#tests [Flutter Style Guide]: https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md [Features we expect every widget to implement]: https://github.com/flutter/flutter/blob/main/docs/contributing/Style-guide-for-Flutter-repo.md#features-we-expect-every-widget-to-implement [CLA]: https://cla.developers.google.com/ [flutter/tests]: https://github.com/flutter/tests [breaking change policy]: https://github.com/flutter/flutter/blob/main/docs/contributing/Tree-hygiene.md#handling-breaking-changes [Discord]: https://github.com/flutter/flutter/blob/main/docs/contributing/Chat.md [Data Driven Fixes]: https://github.com/flutter/flutter/blob/main/docs/contributing/Data-driven-Fixes.md