[Impeller] Add rounded superellipse (#56726)

Support rounded superellipse.

Part of flutter/flutter#139321 and
flutter/flutter#13914, also related to
flutter/flutter#91523.

### Open questions

* Alternative names:
  * Round**ed**Superellipse
  * Squircle
  * ContinuousBorderRectangle (or something like this...)
* I chose rounded superellipse because this name, albeit its length,
precisely describe this shape. "Squircle" is not strictly defined but
generally refers any shape intermediate between a rectangle and a
circle.
* Alternative definition for `corner_radius`:
* Currently the `corner_radius` corresponds to SwiftUI parameters. To
make the shape definition more generalized, we can instead define the
`corner_radius` to be the radius of the corner circles, and make the
framework do a look up table.
* The down side is, not only the work to re-calculate the table, but
also that it doesn't completely eliminates the relationship with
SwiftUI, since currently the degree of the superellipse (`n`) is also
mapped from the SwiftUI `cornerRadius`, which is not necessary for the
shape per se.
* To some extent it boils down to the question of whether we'd like this
shape to support anything beyond SwiftUI.

### Demo


https://github.com/user-attachments/assets/806ac0e9-d62f-4b04-ab6a-83436a11f6f3

Low ratio: (900, 900, 445)

<img width="520" alt="image"
src="https://github.com/user-attachments/assets/54087467-85cd-4021-91cc-a948866ab5a8">

Mid ratio: (900, 650, 180)

<img width="508" alt="image"
src="https://github.com/user-attachments/assets/460a4927-0396-462b-948d-0846a781c92c">

High ratio: (900, 650, 17)

<img width="490" alt="image"
src="https://github.com/user-attachments/assets/8d7f625d-8a3b-4aba-b3f9-f292b874b606">


## 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] and the [C++,
Objective-C, Java style guides].
- [ ] I listed at least one issue that this PR fixes in the description
above.
- [ ] I added new tests to check the change I am making or feature I am
adding, or the PR is [test-exempt]. See [testing the engine] for
instructions on writing and running engine tests.
- [ ] I updated/added relevant documentation (doc comments with `///`).
- [ ] I signed the [CLA].
- [ ] 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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Author: dkwingsmt

ci/licenses_golden/licenses_flutter

@@ -43161,6 +43161,8 @@ ORIGIN: ../../../flutter/impeller/entity/geometry/rect_geometry.cc + ../../../fl
 ORIGIN: ../../../flutter/impeller/entity/geometry/rect_geometry.h + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/geometry/round_rect_geometry.cc + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/geometry/round_rect_geometry.h + ../../../flutter/LICENSE
+ORIGIN: ../../../flutter/impeller/entity/geometry/round_superellipse_geometry.cc + ../../../flutter/LICENSE
+ORIGIN: ../../../flutter/impeller/entity/geometry/round_superellipse_geometry.h + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/geometry/stroke_path_geometry.cc + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/geometry/stroke_path_geometry.h + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/geometry/superellipse_geometry.cc + ../../../flutter/LICENSE
@@ -46088,6 +46090,8 @@ FILE: ../../../flutter/impeller/entity/geometry/rect_geometry.cc
 FILE: ../../../flutter/impeller/entity/geometry/rect_geometry.h
 FILE: ../../../flutter/impeller/entity/geometry/round_rect_geometry.cc
 FILE: ../../../flutter/impeller/entity/geometry/round_rect_geometry.h
+FILE: ../../../flutter/impeller/entity/geometry/round_superellipse_geometry.cc
+FILE: ../../../flutter/impeller/entity/geometry/round_superellipse_geometry.h
 FILE: ../../../flutter/impeller/entity/geometry/stroke_path_geometry.cc
 FILE: ../../../flutter/impeller/entity/geometry/stroke_path_geometry.h
 FILE: ../../../flutter/impeller/entity/geometry/superellipse_geometry.cc

impeller/display_list/canvas.cc

@@ -37,6 +37,7 @@
 #include "impeller/entity/geometry/point_field_geometry.h"
 #include "impeller/entity/geometry/rect_geometry.h"
 #include "impeller/entity/geometry/round_rect_geometry.h"
+#include "impeller/entity/geometry/round_superellipse_geometry.h"
 #include "impeller/entity/geometry/stroke_path_geometry.h"
 #include "impeller/entity/save_layer_utils.h"
 #include "impeller/geometry/color.h"

impeller/entity/BUILD.gn

@@ -199,6 +199,8 @@ impeller_component("entity") {
     "geometry/rect_geometry.h",
     "geometry/round_rect_geometry.cc",
     "geometry/round_rect_geometry.h",
+    "geometry/round_superellipse_geometry.cc",
+    "geometry/round_superellipse_geometry.h",
     "geometry/stroke_path_geometry.cc",
     "geometry/stroke_path_geometry.h",
     "geometry/superellipse_geometry.cc",

impeller/entity/entity_unittests.cc

@@ -37,6 +37,7 @@
 #include "impeller/entity/entity_playground.h"
 #include "impeller/entity/geometry/geometry.h"
 #include "impeller/entity/geometry/point_field_geometry.h"
+#include "impeller/entity/geometry/round_superellipse_geometry.h"
 #include "impeller/entity/geometry/stroke_path_geometry.h"
 #include "impeller/entity/geometry/superellipse_geometry.h"
 #include "impeller/geometry/color.h"
@@ -2321,6 +2322,41 @@ TEST_P(EntityTest, DrawSuperEllipse) {
   ASSERT_TRUE(OpenPlaygroundHere(callback));
 }
 
+TEST_P(EntityTest, DrawRoundSuperEllipse) {
+  auto callback = [&](ContentContext& context, RenderPass& pass) -> bool {
+    // UI state.
+    static float center_x = 100;
+    static float center_y = 100;
+    static float width = 900;
+    static float height = 900;
+    static float corner_radius = 300;
+    static Color color = Color::Red();
+
+    ImGui::Begin("Controls", nullptr, ImGuiWindowFlags_AlwaysAutoResize);
+    ImGui::SliderFloat("Center X", &center_x, 0, 1000);
+    ImGui::SliderFloat("Center Y", &center_y, 0, 1000);
+    ImGui::SliderFloat("Width", &width, 0, 1000);
+    ImGui::SliderFloat("Height", &height, 0, 1000);
+    ImGui::SliderFloat("Corner radius", &corner_radius, 0, 500);
+    ImGui::End();
+
+    auto contents = std::make_shared<SolidColorContents>();
+    std::unique_ptr<RoundSuperellipseGeometry> geom =
+        std::make_unique<RoundSuperellipseGeometry>(
+            Rect::MakeOriginSize({center_x, center_y}, {width, height}),
+            corner_radius);
+    contents->SetColor(color);
+    contents->SetGeometry(geom.get());
+
+    Entity entity;
+    entity.SetContents(contents);
+
+    return entity.Render(context, pass);
+  };
+
+  ASSERT_TRUE(OpenPlaygroundHere(callback));
+}
+
 TEST_P(EntityTest, SolidColorApplyColorFilter) {
   auto contents = SolidColorContents();
   contents.SetColor(Color::CornflowerBlue().WithAlpha(0.75));