[Impeller] add support for superellipse. (flutter/engine#54562)

This is an entity testing only implementation of a superellipse. rectellipse is a special case where degree = 4.

Part of https://github.com/flutter/flutter/issues/139321

engine/src/flutter/ci/licenses_golden/licenses_flutter

@@ -42862,6 +42862,8 @@ ORIGIN: ../../../flutter/impeller/entity/geometry/round_rect_geometry.cc + ../..
 ORIGIN: ../../../flutter/impeller/entity/geometry/round_rect_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
+ORIGIN: ../../../flutter/impeller/entity/geometry/superellipse_geometry.h + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/geometry/vertices_geometry.cc + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/geometry/vertices_geometry.h + ../../../flutter/LICENSE
 ORIGIN: ../../../flutter/impeller/entity/inline_pass_context.cc + ../../../flutter/LICENSE
@@ -45739,6 +45741,8 @@ FILE: ../../../flutter/impeller/entity/geometry/round_rect_geometry.cc
 FILE: ../../../flutter/impeller/entity/geometry/round_rect_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
+FILE: ../../../flutter/impeller/entity/geometry/superellipse_geometry.h
 FILE: ../../../flutter/impeller/entity/geometry/vertices_geometry.cc
 FILE: ../../../flutter/impeller/entity/geometry/vertices_geometry.h
 FILE: ../../../flutter/impeller/entity/inline_pass_context.cc

engine/src/flutter/impeller/aiks/canvas.cc

@@ -23,6 +23,7 @@
 #include "impeller/entity/contents/texture_contents.h"
 #include "impeller/entity/contents/vertices_contents.h"
 #include "impeller/entity/geometry/geometry.h"
+#include "impeller/entity/geometry/superellipse_geometry.h"
 #include "impeller/geometry/color.h"
 #include "impeller/geometry/constants.h"
 #include "impeller/geometry/path_builder.h"

engine/src/flutter/impeller/entity/BUILD.gn

@@ -196,6 +196,8 @@ impeller_component("entity") {
     "geometry/round_rect_geometry.h",
     "geometry/stroke_path_geometry.cc",
     "geometry/stroke_path_geometry.h",
+    "geometry/superellipse_geometry.cc",
+    "geometry/superellipse_geometry.h",
     "geometry/vertices_geometry.cc",
     "geometry/vertices_geometry.h",
     "inline_pass_context.cc",

engine/src/flutter/impeller/entity/entity_unittests.cc

@@ -39,6 +39,7 @@
 #include "impeller/entity/geometry/geometry.h"
 #include "impeller/entity/geometry/point_field_geometry.h"
 #include "impeller/entity/geometry/stroke_path_geometry.h"
+#include "impeller/entity/geometry/superellipse_geometry.h"
 #include "impeller/entity/render_target_cache.h"
 #include "impeller/geometry/color.h"
 #include "impeller/geometry/geometry_asserts.h"
@@ -2587,6 +2588,37 @@ TEST_P(EntityTest, CanRenderEmptyPathsWithoutCrashing) {
   ASSERT_TRUE(OpenPlaygroundHere(std::move(entity)));
 }
 
+TEST_P(EntityTest, DrawSuperEllipse) {
+  auto callback = [&](ContentContext& context, RenderPass& pass) -> bool {
+    // UI state.
+    static float alpha = 10;
+    static float beta = 10;
+    static float radius = 40;
+    static int degree = 4;
+    static Color color = Color::Red();
+
+    ImGui::Begin("Controls", nullptr, ImGuiWindowFlags_AlwaysAutoResize);
+    ImGui::SliderFloat("Alpha", &alpha, 0, 100);
+    ImGui::SliderFloat("Beta", &beta, 0, 100);
+    ImGui::SliderInt("Degreee", &degree, 1, 20);
+    ImGui::SliderFloat("Radius", &radius, 0, 400);
+    ImGui::ColorEdit4("Color", reinterpret_cast<float*>(&color));
+    ImGui::End();
+
+    auto contents = std::make_shared<SolidColorContents>();
+    contents->SetColor(color);
+    contents->SetGeometry(std::make_shared<SuperellipseGeometry>(
+        Point{400, 400}, radius, degree, alpha, beta));
+
+    Entity entity;
+    entity.SetContents(contents);
+
+    return entity.Render(context, pass);
+  };
+
+  ASSERT_TRUE(OpenPlaygroundHere(callback));
+}
+
 }  // namespace testing
 }  // namespace impeller
 

engine/src/flutter/impeller/entity/geometry/superellipse_geometry.cc

@@ -0,0 +1,111 @@
+// Copyright 2013 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include <vector>
+
+#include "flutter/impeller/entity/geometry/superellipse_geometry.h"
+
+#include "impeller/geometry/constants.h"
+
+namespace impeller {
+
+SuperellipseGeometry::SuperellipseGeometry(const Point& center,
+                                           Scalar radius,
+                                           Scalar degree,
+                                           Scalar alpha,
+                                           Scalar beta)
+    : center_(center),
+      degree_(degree),
+      radius_(radius),
+      alpha_(alpha),
+      beta_(beta) {}
+
+GeometryResult SuperellipseGeometry::GetPositionBuffer(
+    const ContentContext& renderer,
+    const Entity& entity,
+    RenderPass& pass) const {
+  // https://math.stackexchange.com/questions/2573746/superellipse-parametric-equation
+  Scalar a = alpha_;
+  Scalar b = beta_;
+  Scalar n = degree_;
+
+  // TODO(jonahwilliams): determine parameter values based on scaling factor.
+  Scalar step = kPi / 80;
+
+  // Generate the points for the top left quadrant, and then mirror to the other
+  // quadrants.
+  std::vector<Point> points;
+  points.reserve(41);
+  for (int i = 0; i <= 40; i++) {
+    Scalar t = i * step;
+    Scalar x = a * pow(abs(cos(t)), 2 / n);
+    Scalar y = b * pow(abs(sin(t)), 2 / n);
+    points.emplace_back(x * radius_, y * radius_);
+  }
+
+  static constexpr Point reflection[4] = {{1, 1}, {-1, 1}, {-1, -1}, {1, -1}};
+
+  // Reflect into the 4 quadrants and generate the tessellated mesh. The
+  // iteration order is reversed so that the trianges are continuous from
+  // quadrant to quadrant.
+  std::vector<Point> geometry;
+  geometry.reserve(1 + 4 * points.size());
+  geometry.push_back(center_);
+  for (auto i = 0u; i < points.size(); i++) {
+    geometry.push_back(center_ + (reflection[0] * points[i]));
+  }
+  for (auto i = 0u; i < points.size(); i++) {
+    geometry.push_back(center_ +
+                       (reflection[1] * points[points.size() - i - 1]));
+  }
+  for (auto i = 0u; i < points.size(); i++) {
+    geometry.push_back(center_ + (reflection[2] * points[i]));
+  }
+  for (auto i = 0u; i < points.size(); i++) {
+    geometry.push_back(center_ +
+                       (reflection[3] * points[points.size() - i - 1]));
+  }
+
+  std::vector<uint16_t> indices;
+  indices.reserve(geometry.size() * 3);
+  for (auto i = 2u; i < geometry.size(); i++) {
+    indices.push_back(0);
+    indices.push_back(i - 1);
+    indices.push_back(i);
+  }
+
+  auto& host_buffer = renderer.GetTransientsBuffer();
+  return GeometryResult{
+      .type = PrimitiveType::kTriangle,
+      .vertex_buffer =
+          {
+              .vertex_buffer = host_buffer.Emplace(
+                  geometry.data(), geometry.size() * sizeof(Point),
+                  alignof(Point)),
+              .index_buffer = host_buffer.Emplace(
+                  indices.data(), indices.size() * sizeof(uint16_t),
+                  alignof(uint16_t)),
+              .vertex_count = indices.size(),
+              .index_type = IndexType::k16bit,
+          },
+      .transform = entity.GetShaderTransform(pass),
+  };
+}
+
+std::optional<Rect> SuperellipseGeometry::GetCoverage(
+    const Matrix& transform) const {
+  return Rect::MakeOriginSize(center_ - Point(radius_, radius_),
+                              Size(radius_ * 2, radius_ * 2));
+}
+
+bool SuperellipseGeometry::CoversArea(const Matrix& transform,
+                                      const Rect& rect) const {
+  return false;
+}
+
+bool SuperellipseGeometry::IsAxisAlignedRect() const {
+  return false;
+}
+
+}  // namespace impeller

engine/src/flutter/impeller/entity/geometry/superellipse_geometry.h

@@ -0,0 +1,62 @@
+// Copyright 2013 The Flutter Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#ifndef FLUTTER_IMPELLER_ENTITY_GEOMETRY_SUPERELLIPSE_GEOMETRY_H_
+#define FLUTTER_IMPELLER_ENTITY_GEOMETRY_SUPERELLIPSE_GEOMETRY_H_
+
+#include "impeller/entity/geometry/geometry.h"
+
+namespace impeller {
+
+/// Geometry class that can generate vertices for a superellipse.
+///
+/// A Superellipse is an ellipse-like shape that is defined by the parameters N,
+/// alpha, and beta:
+///
+///  1 = |x / b| ^n + |y / a| ^n
+///
+/// The radius and center apply a uniform scaling and offset that is separate
+/// from alpha or beta. When n = 4, the shape is referred to as a rectellipse.
+///
+/// See also: https://en.wikipedia.org/wiki/Superellipse
+class SuperellipseGeometry final : public Geometry {
+ public:
+  explicit SuperellipseGeometry(const Point& center,
+                                Scalar radius,
+                                Scalar degree,
+                                Scalar alpha,
+                                Scalar beta);
+
+  ~SuperellipseGeometry() = default;
+
+  // |Geometry|
+  bool CoversArea(const Matrix& transform, const Rect& rect) const override;
+
+  // |Geometry|
+  bool IsAxisAlignedRect() const override;
+
+ private:
+  // |Geometry|
+  GeometryResult GetPositionBuffer(const ContentContext& renderer,
+                                   const Entity& entity,
+                                   RenderPass& pass) const override;
+
+  // |Geometry|
+  std::optional<Rect> GetCoverage(const Matrix& transform) const override;
+
+  Point center_;
+  // 4 is a rectellipse
+  Scalar degree_;
+  Scalar radius_;
+  Scalar alpha_;
+  Scalar beta_;
+
+  SuperellipseGeometry(const SuperellipseGeometry&) = delete;
+
+  SuperellipseGeometry& operator=(const SuperellipseGeometry&) = delete;
+};
+
+}  // namespace impeller
+
+#endif  // FLUTTER_IMPELLER_ENTITY_GEOMETRY_SUPERELLIPSE_GEOMETRY_H_