Introduce `Split` curve (#143130)

`Split` is a curve that progresses according to `beginCurve` until
`split`, then according to `endCurve`.

This curve is used with bottom sheets to allow linear finger dragging
and non-linear enter/exit animations. This PR cleans up a previously
private class I introduced and replaces it with the more customisable
`Split`.

Fixes https://github.com/flutter/flutter/issues/51627

Diagram to be added with
https://github.com/flutter/assets-for-api-docs/pull/239

## Pre-launch Checklist

- [x] I read the [Contributor Guide] and followed the process outlined
there for submitting PRs.
- [x] I read the [Tree Hygiene] wiki page, which explains my
responsibilities.
- [x] I read and followed the [Flutter Style Guide], including [Features
we expect every widget to implement].
- [x] I signed the [CLA].
- [x] I listed at least one issue that this PR fixes in the description
above.
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] I added new tests to check the change I am making, or this PR is
[test-exempt].
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-new channel
on [Discord].

<!-- Links -->
[Contributor Guide]:
https://github.com/flutter/flutter/wiki/Tree-hygiene#overview
[Tree Hygiene]: https://github.com/flutter/flutter/wiki/Tree-hygiene
[test-exempt]:
https://github.com/flutter/flutter/wiki/Tree-hygiene#tests
[Flutter Style Guide]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo
[Features we expect every widget to implement]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo#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/wiki/Tree-hygiene#handling-breaking-changes
[Discord]: https://github.com/flutter/flutter/wiki/Chat

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

@@ -2,7 +2,6 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
-
 import 'dart:math' as math;
 import 'dart:ui';
 
@@ -193,6 +192,79 @@ class Interval extends Curve {
   }
 }
 
+/// A curve that progresses according to [beginCurve] until [split], then
+/// according to [endCurve].
+///
+/// Split curves are useful in situations where a widget must track the
+/// user's finger (which requires a linear animation), but can also be flung
+/// using a curve specified with the [endCurve] argument, after the finger is
+/// released. In such a case, the value of [split] would be the progress
+/// of the animation at the time when the finger was released.
+///
+/// For example, if [split] is set to 0.5, [beginCurve] is [Curves.linear],
+/// and [endCurve] is [Curves.easeOutCubic], then the bottom-left quarter of the
+/// curve will be a straight line, and the top-right quarter will contain the
+/// entire [Curves.easeOutCubic] curve.
+///
+/// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_split.mp4}
+class Split extends Curve {
+  /// Creates a split curve.
+  const Split(
+    this.split, {
+    this.beginCurve = Curves.linear,
+    this.endCurve = Curves.easeOutCubic,
+  });
+
+  /// The progress value separating [beginCurve] from [endCurve].
+  ///
+  /// The value before which the curve progresses according to [beginCurve] and
+  /// after which the curve progresses according to [endCurve].
+  ///
+  /// When t is exactly `split`, the curve has the value `split`.
+  ///
+  /// Must be between 0 and 1.0, inclusively.
+  final double split;
+
+  /// The curve to use before [split] is reached.
+  ///
+  /// Defaults to [Curves.linear].
+  final Curve beginCurve;
+
+  /// The curve to use after [split] is reached.
+  ///
+  /// Defaults to [Curves.easeOutCubic].
+  final Curve endCurve;
+
+  @override
+  double transform(double t) {
+    assert(t >= 0.0 && t <= 1.0);
+    assert(split >= 0.0 && split <= 1.0);
+
+    if (t == 0.0 || t == 1.0) {
+      return t;
+    }
+
+    if (t == split) {
+      return split;
+    }
+
+    if (t < split) {
+      final double curveProgress = t / split;
+      final double transformed = beginCurve.transform(curveProgress);
+      return lerpDouble(0, split, transformed)!;
+    } else {
+      final double curveProgress = (t - split) / (1 - split);
+      final double transformed = endCurve.transform(curveProgress);
+      return lerpDouble(split, 1, transformed)!;
+    }
+  }
+
+  @override
+  String toString() {
+    return '${describeIdentity(this)}($split, $beginCurve, $endCurve)';
+  }
+}
+
 /// A curve that is 0.0 until it hits the threshold, then it jumps to 1.0.
 ///
 /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_threshold.mp4}

packages/flutter/lib/src/material/bottom_sheet.dart

@@ -2,9 +2,6 @@
 // Use of this source code is governed by a BSD-style license that can be
 // found in the LICENSE file.
 
-import 'dart:ui' show lerpDouble;
-
-import 'package:flutter/foundation.dart';
 import 'package:flutter/gestures.dart';
 import 'package:flutter/rendering.dart';
 import 'package:flutter/widgets.dart';
@@ -705,9 +702,9 @@ class _ModalBottomSheetState<T> extends State<_ModalBottomSheet<T>> {
 
   void handleDragEnd(DragEndDetails details, {bool? isClosing}) {
     // Allow the bottom sheet to animate smoothly from its current position.
-    animationCurve = _BottomSheetSuspendedCurve(
+    animationCurve = Split(
       widget.route.animation!.value,
-      curve: _modalBottomSheetCurve,
+      endCurve: _modalBottomSheetCurve,
     );
   }
 
@@ -1124,61 +1121,6 @@ class ModalBottomSheetRoute<T> extends PopupRoute<T> {
   }
 }
 
-// TODO(guidezpl): Look into making this public. A copy of this class is in
-//  scaffold.dart, for now, https://github.com/flutter/flutter/issues/51627
-/// A curve that progresses linearly until a specified [startingPoint], at which
-/// point [curve] will begin. Unlike [Interval], [curve] will not start at zero,
-/// but will use [startingPoint] as the Y position.
-///
-/// For example, if [startingPoint] is set to `0.5`, and [curve] is set to
-/// [Curves.easeOut], then the bottom-left quarter of the curve will be a
-/// straight line, and the top-right quarter will contain the entire contents of
-/// [Curves.easeOut].
-///
-/// This is useful in situations where a widget must track the user's finger
-/// (which requires a linear animation), and afterwards can be flung using a
-/// curve specified with the [curve] argument, after the finger is released. In
-/// such a case, the value of [startingPoint] would be the progress of the
-/// animation at the time when the finger was released.
-class _BottomSheetSuspendedCurve extends ParametricCurve<double> {
-  /// Creates a suspended curve.
-  const _BottomSheetSuspendedCurve(
-    this.startingPoint, {
-    this.curve = Curves.easeOutCubic,
-  });
-
-  /// The progress value at which [curve] should begin.
-  final double startingPoint;
-
-  /// The curve to use when [startingPoint] is reached.
-  ///
-  /// This defaults to [Curves.easeOutCubic].
-  final Curve curve;
-
-  @override
-  double transform(double t) {
-    assert(t >= 0.0 && t <= 1.0);
-    assert(startingPoint >= 0.0 && startingPoint <= 1.0);
-
-    if (t < startingPoint) {
-      return t;
-    }
-
-    if (t == 1.0) {
-      return t;
-    }
-
-    final double curveProgress = (t - startingPoint) / (1 - startingPoint);
-    final double transformed = curve.transform(curveProgress);
-    return lerpDouble(startingPoint, 1, transformed)!;
-  }
-
-  @override
-  String toString() {
-    return '${describeIdentity(this)}($startingPoint, $curve)';
-  }
-}
-
 /// Shows a modal Material Design bottom sheet.
 ///
 /// {@macro flutter.material.ModalBottomSheetRoute}

packages/flutter/lib/src/material/scaffold.dart

@@ -5,7 +5,6 @@
 import 'dart:async';
 import 'dart:collection';
 import 'dart:math' as math;
-import 'dart:ui' show lerpDouble;
 
 import 'package:flutter/foundation.dart';
 import 'package:flutter/gestures.dart' show DragStartBehavior;
@@ -3119,61 +3118,6 @@ class ScaffoldFeatureController<T extends Widget, U> {
   final StateSetter? setState;
 }
 
-// TODO(guidezpl): Look into making this public. A copy of this class is in
-//  bottom_sheet.dart, for now, https://github.com/flutter/flutter/issues/51627
-/// A curve that progresses linearly until a specified [startingPoint], at which
-/// point [curve] will begin. Unlike [Interval], [curve] will not start at zero,
-/// but will use [startingPoint] as the Y position.
-///
-/// For example, if [startingPoint] is set to `0.5`, and [curve] is set to
-/// [Curves.easeOut], then the bottom-left quarter of the curve will be a
-/// straight line, and the top-right quarter will contain the entire contents of
-/// [Curves.easeOut].
-///
-/// This is useful in situations where a widget must track the user's finger
-/// (which requires a linear animation), and afterwards can be flung using a
-/// curve specified with the [curve] argument, after the finger is released. In
-/// such a case, the value of [startingPoint] would be the progress of the
-/// animation at the time when the finger was released.
-class _BottomSheetSuspendedCurve extends ParametricCurve<double> {
-  /// Creates a suspended curve.
-  const _BottomSheetSuspendedCurve(
-      this.startingPoint, {
-        this.curve = Curves.easeOutCubic,
-      });
-
-  /// The progress value at which [curve] should begin.
-  ///
-  /// This defaults to [Curves.easeOutCubic].
-  final double startingPoint;
-
-  /// The curve to use when [startingPoint] is reached.
-  final Curve curve;
-
-  @override
-  double transform(double t) {
-    assert(t >= 0.0 && t <= 1.0);
-    assert(startingPoint >= 0.0 && startingPoint <= 1.0);
-
-    if (t < startingPoint) {
-      return t;
-    }
-
-    if (t == 1.0) {
-      return t;
-    }
-
-    final double curveProgress = (t - startingPoint) / (1 - startingPoint);
-    final double transformed = curve.transform(curveProgress);
-    return lerpDouble(startingPoint, 1, transformed)!;
-  }
-
-  @override
-  String toString() {
-    return '${describeIdentity(this)}($startingPoint, $curve)';
-  }
-}
-
 class _StandardBottomSheet extends StatefulWidget {
   const _StandardBottomSheet({
     super.key,
@@ -3247,9 +3191,9 @@ class _StandardBottomSheetState extends State<_StandardBottomSheet> {
 
   void _handleDragEnd(DragEndDetails details, { bool? isClosing }) {
     // Allow the bottom sheet to animate smoothly from its current position.
-    animationCurve = _BottomSheetSuspendedCurve(
+    animationCurve = Split(
       widget.animationController.value,
-      curve: _standardBottomSheetCurve,
+      endCurve: _standardBottomSheetCurve,
     );
   }
 

packages/flutter/test/animation/curves_test.dart

@@ -13,6 +13,7 @@ void main() {
     expect(const SawTooth(3), hasOneLineDescription);
     expect(const Interval(0.25, 0.75), hasOneLineDescription);
     expect(const Interval(0.25, 0.75, curve: Curves.ease), hasOneLineDescription);
+    expect(const Split(0.25, beginCurve: Curves.ease), hasOneLineDescription);
   });
 
   test('Curve flipped control test', () {
@@ -187,6 +188,9 @@ void main() {
     expect(() => const Interval(0.0, 1.0).transform(-0.0001), throwsAssertionError);
     expect(() => const Interval(0.0, 1.0).transform(1.0001), throwsAssertionError);
 
+    expect(() => const Split(0.0).transform(-0.0001), throwsAssertionError);
+    expect(() => const Split(0.0).transform(1.0001), throwsAssertionError);
+
     expect(() => const Threshold(0.5).transform(-0.0001), throwsAssertionError);
     expect(() => const Threshold(0.5).transform(1.0001), throwsAssertionError);
 
@@ -222,6 +226,9 @@ void main() {
     expect(const Interval(0, 1).transform(0), 0);
     expect(const Interval(0, 1).transform(1), 1);
 
+    expect(const Split(0.5).transform(0), 0);
+    expect(const Split(0.5).transform(1), 1);
+
     expect(const Threshold(0.5).transform(0), 0);
     expect(const Threshold(0.5).transform(1), 1);
 
@@ -259,6 +266,19 @@ void main() {
     expect(Curves.bounceInOut.transform(1), 1);
   });
 
+  test('Split interpolates values properly', () {
+    const Split curve = Split(0.3);
+
+    const double tolerance = 1e-6;
+    expect(curve.transform(0.0), equals(0.0));
+    expect(curve.transform(0.1), equals(0.1));
+    expect(curve.transform(0.25), equals(0.25));
+    expect(curve.transform(0.3), equals(0.3));
+    expect(curve.transform(0.5), moreOrLessEquals(0.760461, epsilon: tolerance));
+    expect(curve.transform(0.75), moreOrLessEquals(0.962055, epsilon: tolerance));
+    expect(curve.transform(1.0), equals(1.0));
+  });
+
   test('CatmullRomSpline interpolates values properly', () {
     final CatmullRomSpline curve = CatmullRomSpline(
       const <Offset>[