Update CupertinoPageRoute transition animation curves (#122275)

Update `CupertinoPageRoute` transition animation curves

dev/integration_tests/flutter_gallery/test/demo/cupertino/cupertino_navigation_demo_test.dart

@@ -32,7 +32,7 @@ void main() {
     // Tap some row to go to the next page.
     await tester.tap(find.text('Buy this cool color').first);
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
 
     await expectLater(
       find.byType(CupertinoNavigationDemo),

packages/flutter/lib/src/animation/curves.dart

@@ -6,6 +6,7 @@
 import 'dart:math' as math;
 import 'dart:ui';
 
+import 'package:flutter/cupertino.dart';
 import 'package:flutter/foundation.dart';
 
 export 'dart:ui' show Offset;
@@ -1381,6 +1382,26 @@ abstract final class Curves {
   /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_fast_linear_to_slow_ease_in.mp4}
   static const Cubic fastLinearToSlowEaseIn = Cubic(0.18, 1.0, 0.04, 1.0);
 
+  /// A curve that starts slowly, speeds up very quickly, and then ends slowly.
+  ///
+  /// This curve is used by default to animate page transitions used by
+  /// [CupertinoPageRoute].
+  ///
+  /// It has been derived from plots of native iOS 16.3
+  /// animation frames on iPhone 14 Pro Max.
+  /// Specifically, transition animation positions were measured
+  /// every frame and plotted against time. Then, a cubic curve was
+  /// strictly fit to the measured data points.
+  ///
+  /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_fast_ease_in_to_slow_ease_out.mp4}
+  static const ThreePointCubic fastEaseInToSlowEaseOut = ThreePointCubic(
+    Offset(0.056, 0.024),
+    Offset(0.108, 0.3085),
+    Offset(0.198, 0.541),
+    Offset(0.3655, 1.0),
+    Offset(0.5465, 0.989),
+  );
+
   /// A cubic animation curve that speeds up quickly and ends slowly.
   ///
   /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease.mp4}

packages/flutter/lib/src/cupertino/route.dart

@@ -136,7 +136,7 @@ mixin CupertinoRouteTransitionMixin<T> on PageRoute<T> {
 
   @override
   // A relatively rigorous eyeball estimation.
-  Duration get transitionDuration => const Duration(milliseconds: 400);
+  Duration get transitionDuration => const Duration(milliseconds: 500);
 
   @override
   Color? get barrierColor => fullscreenDialog ? null : _kCupertinoPageTransitionBarrierColor;
@@ -457,15 +457,9 @@ class CupertinoPageTransition extends StatelessWidget {
            (linearTransition
              ? primaryRouteAnimation
              : CurvedAnimation(
-                 // The curves below have been rigorously derived from plots of native
-                 // iOS animation frames. Specifically, a video was taken of a page
-                 // transition animation and the distance in each frame that the page
-                 // moved was measured. A best fit bezier curve was the fitted to the
-                 // point set, which is linearToEaseIn. Conversely, easeInToLinear is the
-                 // reflection over the origin of linearToEaseIn.
                  parent: primaryRouteAnimation,
-                 curve: Curves.linearToEaseOut,
-                 reverseCurve: Curves.easeInToLinear,
+                 curve: Curves.fastEaseInToSlowEaseOut,
+                 reverseCurve: Curves.fastEaseInToSlowEaseOut.flipped,
                )
            ).drive(_kRightMiddleTween),
        _secondaryPositionAnimation =

packages/flutter/test/cupertino/nav_bar_test.dart

@@ -53,7 +53,7 @@ void main() {
     ));
 
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
 
     // Expect the middle of the title to be exactly in the middle of the screen.
     expect(tester.getCenter(find.text('Page 2')).dx, 400.0);
@@ -673,7 +673,7 @@ void main() {
     ));
 
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
 
     expect(find.byType(CupertinoButton), findsOneWidget);
     expect(find.text(String.fromCharCode(CupertinoIcons.back.codePoint)), findsOneWidget);
@@ -688,22 +688,22 @@ void main() {
     ));
 
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
 
     expect(find.widgetWithText(CupertinoButton, 'Close'), findsOneWidget);
 
     // Test popping goes back correctly.
     await tester.tap(find.text('Close'));
 
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
 
     expect(find.text('Page 2'), findsOneWidget);
 
     await tester.tap(find.text(String.fromCharCode(CupertinoIcons.back.codePoint)));
 
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
 
     expect(find.text('Home page'), findsOneWidget);
   });
@@ -1157,7 +1157,7 @@ void main() {
       );
 
       await tester.pump();
-      await tester.pump(const Duration(milliseconds: 500));
+      await tester.pump(const Duration(milliseconds: 600));
 
       tester.state<NavigatorState>(find.byType(Navigator)).push(
         CupertinoPageRoute<void>(
@@ -1176,11 +1176,11 @@ void main() {
       );
 
       await tester.pump();
-      await tester.pump(const Duration(milliseconds: 500));
+      await tester.pump(const Duration(milliseconds: 600));
 
       await tester.tap(find.byType(CupertinoNavigationBarBackButton));
       await tester.pump();
-      await tester.pump(const Duration(milliseconds: 500));
+      await tester.pump(const Duration(milliseconds: 600));
 
       // The second page is still on top and didn't pop.
       expect(find.text('A Phone'), findsOneWidget);
@@ -1406,13 +1406,13 @@ void main() {
     );
 
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
     expect(find.text('Page 1'), findsNothing);
     expect(find.text('Page 2'), findsOneWidget);
 
     await tester.tap(find.text(String.fromCharCode(CupertinoIcons.back.codePoint)));
     await tester.pump();
-    await tester.pump(const Duration(milliseconds: 500));
+    await tester.pump(const Duration(milliseconds: 600));
     expect(find.text('Page 1'), findsOneWidget);
     expect(find.text('Page 2'), findsNothing);
   });