RoundSuperellipse algorithm v3: Ultrawideband heuristic formula (#164755)

This PR revises the algorithm for RoundSuperellipses, replacing the
current "max ratio" approximation with an algorithm that works for
ratios from 2.0 to infinity.

The previous "max ratio" approximation, which replaces the middle of
edges with straight lines when the ratio is above 2.3, turns out to
produce results too close to classic RRects. After reexamining the
shapes and more calculation, I discovered that the max-ratio
approximation is flawed. Even squircles with with really high ratios
(~100) have a significant part of the edges that must not be
approximated by straight lines.

The new version is much closer to native.

### Comparison
Native: (Notice the long wedgy gap at the end of curves)
<img
src="https://github.com/user-attachments/assets/61b60191-7d45-4c49-9e09-b0422243cd8c"
width="400"/>

Before PR: (Notice the short wedgy gap at the end of curves)
<img
src="https://github.com/user-attachments/assets/15ea374b-4b16-4187-aaa4-94f432fbb61e"
width="400"/>

After PR:
<img
src="https://github.com/user-attachments/assets/973ef4d1-7c26-44a9-b45e-10d109d5618b"
width="400"/>

Another example (after PR). Even though the rectangular RSE has ratios
of around 4, there are still curvature near the middle section of edges,
which can be identified with the help of antialias pixels.
<img width="838" alt="image"
src="https://github.com/user-attachments/assets/5078d098-c582-48a8-81e5-615909def675"
/>

### Details

I found that `n` has really good linearity towards larger ratios.

<img width="844" alt="image"
src="https://github.com/user-attachments/assets/73e99e45-a0f0-450b-8e2b-f6fd97082958"
/>

I also found a good candidate for the precomputed unknown (called
`k_xJ`), which has a smooth curve at the beginning and almost straight
line towards larger `n`, removing the need to cap the scope of
application of the formula.

<img width="1203" alt="image"
src="https://github.com/user-attachments/assets/67664898-2dbd-4f00-a9ba-d76030cf3742"
/>

The algorithm for paths are also updated in a similar way and
approximated the Bezier factors with heuristic formulae for bigger `n`s.
I've also verified that the path deviates from the geometry by no more
than 0.01% over the range of n [15, 100]

Theoretically removing "stretch" should simplify the algorithms.
Unfortunately I had to spend more lines to process cases of zero radii,
which were conveniently handled by stretches.

## 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].

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[Tree Hygiene]:
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[CLA]: https://cla.developers.google.com/
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https://dart.googlesource.com/external/github.com/flutter/flutter/+/83781ae65c67f81cf16ce15209788fb3e5d00060
2 files changed
tree: d260e17bb42a84077b5917931c04cc571aa652a9
  1. ci/
  2. tools/
  3. .gitignore
  4. commits.json
  5. DEPS
  6. OWNERS
  7. README.md
README.md

Monorepo

A gclient solution for checking out Dart and Flutter source trees

Monorepo is:

  • Optimized for Tip-of-Tree testing: The Monorepo DEPS used to check out Dart and Flutter dependencies comes from the Flutter engine DEPS with updated dependencies from Dart.

Checking out Monorepo

With depot_tools installed and on your path, create a directory for your monorepo checkout and run these commands to create a gclient solution in that directory:

mkdir monorepo
cd monorepo
gclient config --unmanaged https://dart.googlesource.com/monorepo
gclient sync -D

This gives you a checkout in the monorepo directory that contains:

monorepo/
  DEPS - the DEPS used for this gclient checkout
  commits.json - the pinned commits for Dart, flutter/engine,
                 and flutter/flutter
  tools/ - scripts used to create monorepo DEPS
engine/src/ - the flutter/buildroot repo
    flutter/ - the flutter/engine repo
    out/ - the build directory, where Flutter engine builds are created
    third_party/ - Flutter dependencies checked out by DEPS
      dart/ - the Dart SDK checkout.
        third_party - Dart dependencies, also used by Flutter
flutter/ - the flutter/flutter repo

Building Flutter engine

Flutter's instructions for building the engine are at Compiling the engine

They can be followed closely, with a few changes:

  • Googlers working on Dart do not need to switch to Fuchsia's Goma RBE, except for Windows. The GOMA_DIR enviroment variable can just point to the .cipd_bin directory in a depot_tools installation, and just goma_ctl ensure_start is sufficient.
  • The --no-prebuilt-dart-sdk option has to be added to every gn command, so that the build is set up to build and use a local Dart SDK.
  • The --full-dart-sdk option must be added to gn for the host build target if you will be building web or desktop apps.

Example build commands that work on linux:

MONOREPO_PATH=$PWD
if [[ ! $PATH =~ (^|:)$MONOREPO_PATH/flutter/bin(:|$) ]]; then
  PATH=$MONOREPO_PATH/flutter/bin:$PATH
fi

export GOMA_DIR=$(dirname $(command -v gclient))/.cipd_bin
goma_ctl ensure_start

pushd engine/src
flutter/tools/gn --goma --no-prebuilt-dart-sdk --unoptimized --full-dart-sdk
autoninja -C out/host_debug_unopt
popd

Building Flutter apps

The Flutter commands used to build and run apps will use the locally built Flutter engine and Dart SDK, instead of the one downloaded by the Flutter tool, if the --local-engine option is provided.

For example, to build and run the Flutter spinning square sample on the web platform,

MONOREPO_PATH=$PWD
cd flutter/examples/layers
flutter --local-engine=host_debug_unopt \
  -d chrome run widgets/spinning_square.dart
cd $MONOREPO_PATH

To build for desktop, specify the desktop platform device in flutter run as -d macos or -d linux or -d windows. You may also need to run the command

flutter create --platforms=windows,macos,linux

on existing apps, such as sample apps. New apps created with flutter create already include these support files. Details of desktop support are at Desktop Support for Flutter

Testing

Tests in the Flutter source tree can be run with the flutter test command, run in the directory of a package containing tests. For example:

MONOREPO_PATH=$PWD
cd flutter/packages/flutter
flutter test --local-engine=host_debug_unopt
cd $MONOREPO_PATH

Troubleshooting

Please file an issue or email the dart-engprod team with any problems with or questions about using monorepo.

We will update this documentation to address them.

  • flutter commands may download the engine and Dart SDK files for the configured channel, even though they will be using the local engine and its SDK.

Windows

  • On Windows, gclient sync needs to be run in an administrator session, because some installed dependencies create symlinks.