RoundSuperellipse algorithm v3: Ultrawideband heuristic formula #164755

dkwingsmt · 2025-03-07T00:44:21Z

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)

Before PR: (Notice the short wedgy gap at the end of curves)

After PR:

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.

Details

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

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.

The algorithm for paths are also updated in a similar way and approximated the Bezier factors with heuristic formulae for bigger ns. 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.

flutter-dashboard · 2025-03-07T02:52:20Z

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jonahwilliams · 2025-03-07T03:45:04Z

engine/src/flutter/impeller/geometry/path_builder.cc

  typedef std::function<
      void(const Point&, const Point&, const Point&, const Point&)>
      CubicAdder;
+  typedef std::function<void(const Point&)> PointAdder;


Suggested change

typedef std::function<void(const Point&)> PointAdder;

using PointAdder = std::function<void(const Point&)>;

I probably should have caught the previous one, but you can use using instead of typedef

jonahwilliams

LGTM

flutter-dashboard · 2025-03-07T05:19:14Z

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Changes reported for pull request #164755 at sha 8a734a0

mark8044 · 2025-03-07T17:02:26Z

Noob question: How do we implement this superelljpse shape? Is it just part and parcel when we use ContinuousRectangleBorder?

dkwingsmt · 2025-03-07T17:13:35Z

Noob question: How do we implement this superelljpse shape? Is it just part and parcel when we use ContinuousRectangleBorder?

Thanks for asking. Currently it is available as ClipRSuperellipse (on main channel only for now, ofc). See #161111 for an example.

I'm working on providing it as a path and a border decoration shape.

mark8044 · 2025-03-08T05:13:11Z

Noob question: How do we implement this superelljpse shape? Is it just part and parcel when we use ContinuousRectangleBorder?

Thanks for asking. Currently it is available as ClipRSuperellipse (on main channel only for now, ofc). See #161111 for an example.

I'm working on providing it as a path and a border decoration shape.

WOW thanks for the info. If its that easy, I plan to use this extensivly in my app over the next few days. Maybe I can ditch figma squircle

…la (flutter/flutter#164755)

rydmike · 2025-03-08T17:53:53Z

Thanks @dkwingsmt for this awesome work.

Looking forward to seeing this as a paint and ShapeBorder so I can add it to my Flutter Squircle Study to compare it to other attempts at making the Squircle in Flutter.

For the new RoundSuperEllipse ShapeBorder it would be important that it can handle these cases:

Lerp animate on radius change
Lerp animate to other Flutter ShapeBorders
Not break down when using border radius > the shape's stadium radius (= shorter side/2)
Also draw a continuous stadium border, which means handle radius case where the border radius is equal to the stadium border radius (shorter side/2).
Also draw a good super ellipse shape when border radius is large, meaning between 0.5 to 1 of the stadium radius (shorter side/2). Current solutions do not handle this well, they become close to circular at radius > 0.65 of stadium radius or break down.
Handle AR from 1 (circle) to "infinity"
Use strokeAlign correctly in BorderSide

None of the current solutions can handle drawing a correct continuous Stadium (pill/capsule) shape. The dedicated shape SquircleStadiumBorder in the study comes closest, with some minor issues and limitations on shape AR.

https://github.com/rydmike/squircle_study?tab=readme-ov-file#flutter-squircle-status-march-8-2025

Also some other note worthy issues on other Flutter shapes mentioned in the study:

ContinuousRectangleBorder does not support strokeAlign on BorderSide, it does center not matter what you set it to.
BeveledRectangleBorder, does support strokeAlign on BorderSide, but with wrong line width, it is 2x what it should be.

mark8044 · 2025-03-08T23:05:41Z

@rydmike Never knew about this study you have created. This is the document I never knew I needed but now have been studying voraciously. thanks again for putting this together!

…la (flutter/flutter#164755)

bernaferrari · 2025-03-10T02:16:36Z

IMO ContinuousRectangleBorder should probably be deprecated and replaced with superellipse (or however it is called).

In theory IMO it could/should be an attribute in RoundedRectangleBorder, just like in Figma you can go from 0% to 100% and iOS is like 60%.

I think BeveledRectangleBorder only exists for an old deprecated version of material design, it never got traction, but I don't think anyone would want to remove it. I think we can safely ignore it.

Just like CircleBorder with eccentricity = 1 => OvalBorder, IMO RoundedRectangleBorder with cornerSmoothing = 60% => SuperEllipseBorder (or CupertinoBorder).

bernaferrari · 2025-03-10T02:19:33Z

If @dkwingsmt agrees on my idea/proposal, and it ends up being similar to Figma (corner smoothing in rounded rectangle border), I can implement it with lerp and everything super quickly. The only thing I need is the superellipse path it is going to be drawn.

dkwingsmt · 2025-03-10T02:50:00Z

IMO ContinuousRectangleBorder should probably be deprecated and replaced with superellipse (or however it is called).

I would agree, although we don't have to. We don't need the name anyway since there will be a RoundedSuperellipseBorder (which is a more natural name given how I call this shape.)

In theory IMO it could/should be an attribute in RoundedRectangleBorder, just like in Figma you can go from 0% to 100% and iOS is like 60%.

This I can't. My algorithm is completely based on iOS's .continuous shape and is not adjustable. In fact my doc (flutter.dev/go/apple-squircles) described the set of equations, which has 4 unknowns for 3 equations, leaving perfectly one unknown to be mapped from corner radius. There is no room for variants.

bernaferrari · 2025-03-10T03:05:50Z

we don't have to

Yeah, but from my understanding it exists to make the iOS border, so with super ellipse it wouldn't have a reason to exist.

This I can't

Ok, I didn't know that.

dkwingsmt · 2025-03-10T06:55:58Z

Yeah, but from my understanding it exists to make the iOS border, so with super ellipse it wouldn't have a reason to exist.

I completely agree with you (AFAIK). But there can always be apps that still use this API, and removing it will disturb them, and a library should not pay this cost without good benefits. And just because it no longer serves the original purpose we designed them for is not a sufficient benefit.

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flutter/flutter@6b93cf9...b16430b 2025-03-10 [email protected] [macOS] Enable Impeller by default on macOS. (flutter/flutter#164572) 2025-03-10 [email protected] Roll Packages from 4c5a7ed to 464cea5 (5 revisions) (flutter/flutter#164904) 2025-03-10 [email protected] Roll Skia from f17d37ee0ac6 to 4ac86f17f2d4 (1 revision) (flutter/flutter#164893) 2025-03-10 [email protected] Roll Skia from 0f53870c7449 to f17d37ee0ac6 (1 revision) (flutter/flutter#164887) 2025-03-09 [email protected] Roll Fuchsia Linux SDK from 6tAcm4hdtXPE55GJP... to U-zlyIZrZRbr9I6gv... (flutter/flutter#164868) 2025-03-09 [email protected] Roll Skia from 345dc2d05dcd to 0f53870c7449 (1 revision) (flutter/flutter#164865) 2025-03-08 [email protected] Roll Skia from 916caa2f0102 to 345dc2d05dcd (1 revision) (flutter/flutter#164843) 2025-03-08 [email protected] Roll Fuchsia Linux SDK from ixl5bKWCqsRiYGvps... to 6tAcm4hdtXPE55GJP... (flutter/flutter#164838) 2025-03-08 [email protected] Roll Skia from b29851b2ada6 to 916caa2f0102 (1 revision) (flutter/flutter#164835) 2025-03-08 [email protected] [Impeller] add capability check for extended range formats. (flutter/flutter#164817) 2025-03-08 [email protected] Added calendar delegate to support custom calendar systems (flutter/flutter#161874) 2025-03-08 [email protected] RoundSuperellipse algorithm v3: Ultrawideband heuristic formula (flutter/flutter#164755) 2025-03-08 [email protected] Merge CHANGELOG for 3.29.1 stable release (flutter/flutter#164743) 2025-03-08 [email protected] Add and link to `Infra-Triage.md`. (flutter/flutter#164673) 2025-03-07 [email protected] Roll Skia from cbc7e99d6c2f to b29851b2ada6 (10 revisions) (flutter/flutter#164812) 2025-03-07 [email protected] [Impeller] dont redundantly set stencil reference on vulkan backend. (flutter/flutter#164763) 2025-03-07 [email protected] content-aware-hash experiment update (flutter/flutter#164803) 2025-03-07 [email protected] [Widget Inspector] Handle null exceptions calling `renderObject` (flutter/flutter#163642) 2025-03-07 [email protected] Use Python 3.12 to run the yapf formatter if no lower version is available (flutter/flutter#164807) 2025-03-07 [email protected] Roll gn to 7a8aa3a08a13521336853a28c46537ec04338a2d (flutter/flutter#164806) 2025-03-07 [email protected] [Impeller] Store the TextureGLES cached framebuffer object as a reactor handle (flutter/flutter#164761) If this roll has caused a breakage, revert this CL and stop the roller using the controls here: https://autoroll.skia.org/r/flutter-packages Please CC [email protected],[email protected] on the revert to ensure that a human is aware of the problem. To file a bug in Packages: https://github.com/flutter/flutter/issues/new/choose To report a problem with the AutoRoller itself, please file a bug: https://issues.skia.org/issues/new?component=1389291&template=1850622 Documentation for the AutoRoller is here: https://skia.googlesource.com/buildbot/+doc/main/autoroll/README.md

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flutter/flutter@6b93cf9...b16430b 2025-03-10 [email protected] [macOS] Enable Impeller by default on macOS. (flutter/flutter#164572) 2025-03-10 [email protected] Roll Packages from 4c5a7ed to 464cea5 (5 revisions) (flutter/flutter#164904) 2025-03-10 [email protected] Roll Skia from f17d37ee0ac6 to 4ac86f17f2d4 (1 revision) (flutter/flutter#164893) 2025-03-10 [email protected] Roll Skia from 0f53870c7449 to f17d37ee0ac6 (1 revision) (flutter/flutter#164887) 2025-03-09 [email protected] Roll Fuchsia Linux SDK from 6tAcm4hdtXPE55GJP... to U-zlyIZrZRbr9I6gv... (flutter/flutter#164868) 2025-03-09 [email protected] Roll Skia from 345dc2d05dcd to 0f53870c7449 (1 revision) (flutter/flutter#164865) 2025-03-08 [email protected] Roll Skia from 916caa2f0102 to 345dc2d05dcd (1 revision) (flutter/flutter#164843) 2025-03-08 [email protected] Roll Fuchsia Linux SDK from ixl5bKWCqsRiYGvps... to 6tAcm4hdtXPE55GJP... (flutter/flutter#164838) 2025-03-08 [email protected] Roll Skia from b29851b2ada6 to 916caa2f0102 (1 revision) (flutter/flutter#164835) 2025-03-08 [email protected] [Impeller] add capability check for extended range formats. (flutter/flutter#164817) 2025-03-08 [email protected] Added calendar delegate to support custom calendar systems (flutter/flutter#161874) 2025-03-08 [email protected] RoundSuperellipse algorithm v3: Ultrawideband heuristic formula (flutter/flutter#164755) 2025-03-08 [email protected] Merge CHANGELOG for 3.29.1 stable release (flutter/flutter#164743) 2025-03-08 [email protected] Add and link to `Infra-Triage.md`. (flutter/flutter#164673) 2025-03-07 [email protected] Roll Skia from cbc7e99d6c2f to b29851b2ada6 (10 revisions) (flutter/flutter#164812) 2025-03-07 [email protected] [Impeller] dont redundantly set stencil reference on vulkan backend. (flutter/flutter#164763) 2025-03-07 [email protected] content-aware-hash experiment update (flutter/flutter#164803) 2025-03-07 [email protected] [Widget Inspector] Handle null exceptions calling `renderObject` (flutter/flutter#163642) 2025-03-07 [email protected] Use Python 3.12 to run the yapf formatter if no lower version is available (flutter/flutter#164807) 2025-03-07 [email protected] Roll gn to 7a8aa3a08a13521336853a28c46537ec04338a2d (flutter/flutter#164806) 2025-03-07 [email protected] [Impeller] Store the TextureGLES cached framebuffer object as a reactor handle (flutter/flutter#164761) If this roll has caused a breakage, revert this CL and stop the roller using the controls here: https://autoroll.skia.org/r/flutter-packages Please CC [email protected],[email protected] on the revert to ensure that a human is aware of the problem. To file a bug in Packages: https://github.com/flutter/flutter/issues/new/choose To report a problem with the AutoRoller itself, please file a bug: https://issues.skia.org/issues/new?component=1389291&template=1850622 Documentation for the AutoRoller is here: https://skia.googlesource.com/buildbot/+doc/main/autoroll/README.md

…ter#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].  [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

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	typedef std::function<void(const Point&)> PointAdder;
	using PointAdder = std::function<void(const Point&)>;

RoundSuperellipse algorithm v3: Ultrawideband heuristic formula #164755

RoundSuperellipse algorithm v3: Ultrawideband heuristic formula #164755

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