packages/flutter/lib/src/animation/tween.dart - external/github.com/flutter/flutter - Git at Google

 // Copyright 2014 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.

 import 'dart:ui' show Color, Rect, Size;

 import 'package:flutter/foundation.dart';

 import 'animations.dart';

 export 'dart:ui' show Color, Rect, Size;

 export 'animation.dart' show Animation;
 export 'curves.dart' show Curve;

 // Examples can assume:
 // late Animation<Offset> _animation;
 // late AnimationController _controller;

 /// An object that can produce a value of type `T` given an [Animation<double>]
 /// as input.
 ///
 /// Typically, the values of the input animation are nominally in the range 0.0
 /// to 1.0. In principle, however, any value could be provided.
 ///
 /// The main subclass of [Animatable] is [Tween].
 abstract class Animatable<T> {
   /// Abstract const constructor. This constructor enables subclasses to provide
   /// const constructors so that they can be used in const expressions.
   const Animatable();

   /// Returns the value of the object at point `t`.
   ///
   /// The value of `t` is nominally a fraction in the range 0.0 to 1.0, though
   /// in practice it may extend outside this range.
   ///
   /// See also:
   ///
   ///  * [evaluate], which is a shorthand for applying [transform] to the value
   ///    of an [Animation].
   ///  * [Curve.transform], a similar method for easing curves.
   T transform(double t);

   /// The current value of this object for the given [Animation].
   ///
   /// This function is implemented by deferring to [transform]. Subclasses that
   /// want to provide custom behavior should override [transform], not
   /// [evaluate].
   ///
   /// See also:
   ///
   ///  * [transform], which is similar but takes a `t` value directly instead of
   ///    an [Animation].
   ///  * [animate], which creates an [Animation] out of this object, continually
   ///    applying [evaluate].
   T evaluate(Animation<double> animation) => transform(animation.value);

   /// Returns a new [Animation] that is driven by the given animation but that
   /// takes on values determined by this object.
   ///
   /// Essentially this returns an [Animation] that automatically applies the
   /// [evaluate] method to the parent's value.
   ///
   /// See also:
   ///
   ///  * [AnimationController.drive], which does the same thing from the
   ///    opposite starting point.
   Animation<T> animate(Animation<double> parent) {
     return _AnimatedEvaluation<T>(parent, this);
   }

   /// Returns a new [Animatable] whose value is determined by first evaluating
   /// the given parent and then evaluating this object.
   ///
   /// This allows [Tween]s to be chained before obtaining an [Animation].
   Animatable<T> chain(Animatable<double> parent) {
     return _ChainedEvaluation<T>(parent, this);
   }
 }

 class _AnimatedEvaluation<T> extends Animation<T> with AnimationWithParentMixin<double> {
   _AnimatedEvaluation(this.parent, this._evaluatable);

   @override
   final Animation<double> parent;

   final Animatable<T> _evaluatable;

   @override
   T get value => _evaluatable.evaluate(parent);

   @override
   String toString() {
     return '$parent\u27A9$_evaluatable\u27A9$value';
   }

   @override
   String toStringDetails() {
     return '${super.toStringDetails()} $_evaluatable';
   }
 }

 class _ChainedEvaluation<T> extends Animatable<T> {
   _ChainedEvaluation(this._parent, this._evaluatable);

   final Animatable<double> _parent;
   final Animatable<T> _evaluatable;

   @override
   T transform(double t) {
     return _evaluatable.transform(_parent.transform(t));
   }

   @override
   String toString() {
     return '$_parent\u27A9$_evaluatable';
   }
 }

 /// A linear interpolation between a beginning and ending value.
 ///
 /// [Tween] is useful if you want to interpolate across a range.
 ///
 /// To use a [Tween] object with an animation, call the [Tween] object's
 /// [animate] method and pass it the [Animation] object that you want to
 /// modify.
 ///
 /// You can chain [Tween] objects together using the [chain] method, so that a
 /// single [Animation] object is configured by multiple [Tween] objects called
 /// in succession. This is different than calling the [animate] method twice,
 /// which results in two separate [Animation] objects, each configured with a
 /// single [Tween].
 ///
 /// {@tool snippet}
 ///
 /// Suppose `_controller` is an [AnimationController], and we want to create an
 /// [Animation<Offset>] that is controlled by that controller, and save it in
 /// `_animation`. Here are two possible ways of expressing this:
 ///
 /// ```dart
 /// _animation = _controller.drive(
 ///   Tween<Offset>(
 ///     begin: const Offset(100.0, 50.0),
 ///     end: const Offset(200.0, 300.0),
 ///   ),
 /// );
 /// ```
 /// {@end-tool}
 /// {@tool snippet}
 ///
 /// ```dart
 /// _animation = Tween<Offset>(
 ///   begin: const Offset(100.0, 50.0),
 ///   end: const Offset(200.0, 300.0),
 /// ).animate(_controller);
 /// ```
 /// {@end-tool}
 ///
 /// In both cases, the `_animation` variable holds an object that, over the
 /// lifetime of the `_controller`'s animation, returns a value
 /// (`_animation.value`) that depicts a point along the line between the two
 /// offsets above. If we used a [MaterialPointArcTween] instead of a
 /// [Tween<Offset>] in the code above, the points would follow a pleasing curve
 /// instead of a straight line, with no other changes necessary.
 ///
 /// ## Performance optimizations
 ///
 /// Tweens are mutable; specifically, their [begin] and [end] values can be
 /// changed at runtime. An object created with [Animation.drive] using a [Tween]
 /// will immediately honor changes to that underlying [Tween] (though the
 /// listeners will only be triggered if the [Animation] is actively animating).
 /// This can be used to change an animation on the fly without having to
 /// recreate all the objects in the chain from the [AnimationController] to the
 /// final [Tween].
 ///
 /// If a [Tween]'s values are never changed, however, a further optimization can
 /// be applied: the object can be stored in a `static final` variable, so that
 /// the exact same instance is used whenever the [Tween] is needed. This is
 /// preferable to creating an identical [Tween] afresh each time a [State.build]
 /// method is called, for example.
 ///
 /// ## Types with special considerations
 ///
 /// Classes with [lerp] static methods typically have corresponding dedicated
 /// [Tween] subclasses that call that method. For example, [ColorTween] uses
 /// [Color.lerp] to implement the [ColorTween.lerp] method.
 ///
 /// Types that define `+` and `-` operators to combine values (`T + T → T` and
 /// `T - T → T`) and an `*` operator to scale by multiplying with a double (`T *
 /// double → T`) can be directly used with `Tween<T>`.
 ///
 /// This does not extend to any type with `+`, `-`, and `*` operators. In
 /// particular, [int] does not satisfy this precise contract (`int * double`
 /// actually returns [num], not [int]). There are therefore two specific classes
 /// that can be used to interpolate integers:
 ///
 ///  * [IntTween], which is an approximation of a linear interpolation (using
 ///    [double.round]).
 ///  * [StepTween], which uses [double.floor] to ensure that the result is
 ///    never greater than it would be using if a `Tween<double>`.
 ///
 /// The relevant operators on [Size] also don't fulfill this contract, so
 /// [SizeTween] uses [Size.lerp].
 ///
 /// In addition, some of the types that _do_ have suitable `+`, `-`, and `*`
 /// operators still have dedicated [Tween] subclasses that perform the
 /// interpolation in a more specialized manner. One such class is
 /// [MaterialPointArcTween], which is mentioned above. The [AlignmentTween], and
 /// [AlignmentGeometryTween], and [FractionalOffsetTween] are another group of
 /// [Tween]s that use dedicated `lerp` methods instead of merely relying on the
 /// operators (in particular, this allows them to handle null values in a more
 /// useful manner).
 ///
 /// ## Nullability
 ///
 /// The [begin] and [end] fields are nullable; a [Tween] does not have to
 /// have non-null values specified when it is created.
 ///
 /// If `T` is nullable, then [lerp] and [transform] may return null.
 /// This is typically seen in the case where [begin] is null and `t`
 /// is 0.0, or [end] is null and `t` is 1.0, or both are null (at any
 /// `t` value).
 ///
 /// If `T` is not nullable, then [begin] and [end] must both be set to
 /// non-null values before using [lerp] or [transform], otherwise they
 /// will throw.
 class Tween<T extends Object?> extends Animatable<T> {
   /// Creates a tween.
   ///
   /// The [begin] and [end] properties must be non-null before the tween is
   /// first used, but the arguments can be null if the values are going to be
   /// filled in later.
   Tween({
     this.begin,
     this.end,
   });

   /// The value this variable has at the beginning of the animation.
   ///
   /// See the constructor for details about whether this property may be null
   /// (it varies from subclass to subclass).
   T? begin;

   /// The value this variable has at the end of the animation.
   ///
   /// See the constructor for details about whether this property may be null
   /// (it varies from subclass to subclass).
   T? end;

   /// Returns the value this variable has at the given animation clock value.
   ///
   /// The default implementation of this method uses the `+`, `-`, and `*`
   /// operators on `T`. The [begin] and [end] properties must therefore be
   /// non-null by the time this method is called.
   ///
   /// In general, however, it is possible for this to return null, especially
   /// when `t`=0.0 and [begin] is null, or `t`=1.0 and [end] is null.
   @protected
   T lerp(double t) {
     assert(begin != null);
     assert(end != null);
     assert(() {
       // Assertions that attempt to catch common cases of tweening types
       // that do not conform to the Tween requirements.
       dynamic result;
       try {
         // ignore: avoid_dynamic_calls
         result = (begin as dynamic) + ((end as dynamic) - (begin as dynamic)) * t;
         result as T;
         return true;
       } on NoSuchMethodError {
         throw FlutterError.fromParts(<DiagnosticsNode>[
           ErrorSummary('Cannot lerp between "$begin" and "$end".'),
           ErrorDescription(
             'The type ${begin.runtimeType} might not fully implement `+`, `-`, and/or `*`. '
             'See "Types with special considerations" at https://api.flutter.dev/flutter/animation/Tween-class.html '
             'for more information.',
           ),
           if (begin is Color || end is Color)
             ErrorHint('To lerp colors, consider ColorTween instead.')
           else if (begin is Rect || end is Rect)
             ErrorHint('To lerp rects, consider RectTween instead.')
           else
             ErrorHint(
               'There may be a dedicated "${begin.runtimeType}Tween" for this type, '
               'or you may need to create one.',
             ),
         ]);
       } on TypeError {
         throw FlutterError.fromParts(<DiagnosticsNode>[
           ErrorSummary('Cannot lerp between "$begin" and "$end".'),
           ErrorDescription(
             'The type ${begin.runtimeType} returned a ${result.runtimeType} after '
             'multiplication with a double value. '
             'See "Types with special considerations" at https://api.flutter.dev/flutter/animation/Tween-class.html '
             'for more information.',
           ),
           if (begin is int || end is int)
             ErrorHint('To lerp int values, consider IntTween or StepTween instead.')
           else
             ErrorHint(
               'There may be a dedicated "${begin.runtimeType}Tween" for this type, '
               'or you may need to create one.',
             ),
         ]);
       }
     }());
     // ignore: avoid_dynamic_calls
     return (begin as dynamic) + ((end as dynamic) - (begin as dynamic)) * t as T;
   }

   /// Returns the interpolated value for the current value of the given animation.
   ///
   /// This method returns `begin` and `end` when the animation values are 0.0 or
   /// 1.0, respectively.
   ///
   /// This function is implemented by deferring to [lerp]. Subclasses that want
   /// to provide custom behavior should override [lerp], not [transform] (nor
   /// [evaluate]).
   ///
   /// See the constructor for details about whether the [begin] and [end]
   /// properties may be null when this is called. It varies from subclass to
   /// subclass.
   @override
   T transform(double t) {
     if (t == 0.0) {
       return begin as T;
     }
     if (t == 1.0) {
       return end as T;
     }
     return lerp(t);
   }

   @override
   String toString() => '${objectRuntimeType(this, 'Animatable')}($begin \u2192 $end)';
 }

 /// A [Tween] that evaluates its [parent] in reverse.
 class ReverseTween<T extends Object?> extends Tween<T> {
   /// Construct a [Tween] that evaluates its [parent] in reverse.
   ReverseTween(this.parent)
     : assert(parent != null),
       super(begin: parent.end, end: parent.begin);

   /// This tween's value is the same as the parent's value evaluated in reverse.
   ///
   /// This tween's [begin] is the parent's [end] and its [end] is the parent's
   /// [begin]. The [lerp] method returns `parent.lerp(1.0 - t)` and its
   /// [evaluate] method is similar.
   final Tween<T> parent;

   @override
   T lerp(double t) => parent.lerp(1.0 - t);
 }

 /// An interpolation between two colors.
 ///
 /// This class specializes the interpolation of [Tween<Color>] to use
 /// [Color.lerp].
 ///
 /// The values can be null, representing no color (which is distinct to
 /// transparent black, as represented by [Colors.transparent]).
 ///
 /// See [Tween] for a discussion on how to use interpolation objects.
 class ColorTween extends Tween<Color?> {
   /// Creates a [Color] tween.
   ///
   /// The [begin] and [end] properties may be null; the null value
   /// is treated as transparent.
   ///
   /// We recommend that you do not pass [Colors.transparent] as [begin]
   /// or [end] if you want the effect of fading in or out of transparent.
   /// Instead prefer null. [Colors.transparent] refers to black transparent and
   /// thus will fade out of or into black which is likely unwanted.
   ColorTween({ super.begin, super.end });

   /// Returns the value this variable has at the given animation clock value.
   @override
   Color? lerp(double t) => Color.lerp(begin, end, t);
 }

 /// An interpolation between two sizes.
 ///
 /// This class specializes the interpolation of [Tween<Size>] to use
 /// [Size.lerp].
 ///
 /// The values can be null, representing [Size.zero].
 ///
 /// See [Tween] for a discussion on how to use interpolation objects.
 class SizeTween extends Tween<Size?> {
   /// Creates a [Size] tween.
   ///
   /// The [begin] and [end] properties may be null; the null value
   /// is treated as an empty size.
   SizeTween({ super.begin, super.end });

   /// Returns the value this variable has at the given animation clock value.
   @override
   Size? lerp(double t) => Size.lerp(begin, end, t);
 }

 /// An interpolation between two rectangles.
 ///
 /// This class specializes the interpolation of [Tween<Rect>] to use
 /// [Rect.lerp].
 ///
 /// The values can be null, representing a zero-sized rectangle at the
 /// origin ([Rect.zero]).
 ///
 /// See [Tween] for a discussion on how to use interpolation objects.
 class RectTween extends Tween<Rect?> {
   /// Creates a [Rect] tween.
   ///
   /// The [begin] and [end] properties may be null; the null value
   /// is treated as an empty rect at the top left corner.
   RectTween({ super.begin, super.end });

   /// Returns the value this variable has at the given animation clock value.
   @override
   Rect? lerp(double t) => Rect.lerp(begin, end, t);
 }

 /// An interpolation between two integers that rounds.
 ///
 /// This class specializes the interpolation of [Tween<int>] to be
 /// appropriate for integers by interpolating between the given begin
 /// and end values and then rounding the result to the nearest
 /// integer.
 ///
 /// This is the closest approximation to a linear tween that is possible with an
 /// integer. Compare to [StepTween] and [Tween<double>].
 ///
 /// The [begin] and [end] values must be set to non-null values before
 /// calling [lerp] or [transform].
 ///
 /// See [Tween] for a discussion on how to use interpolation objects.
 class IntTween extends Tween<int> {
   /// Creates an int tween.
   ///
   /// The [begin] and [end] properties must be non-null before the tween is
   /// first used, but the arguments can be null if the values are going to be
   /// filled in later.
   IntTween({ super.begin, super.end });

   // The inherited lerp() function doesn't work with ints because it multiplies
   // the begin and end types by a double, and int * double returns a double.
   @override
   int lerp(double t) => (begin! + (end! - begin!) * t).round();
 }

 /// An interpolation between two integers that floors.
 ///
 /// This class specializes the interpolation of [Tween<int>] to be
 /// appropriate for integers by interpolating between the given begin
 /// and end values and then using [double.floor] to return the current
 /// integer component, dropping the fractional component.
 ///
 /// This results in a value that is never greater than the equivalent
 /// value from a linear double interpolation. Compare to [IntTween].
 ///
 /// The [begin] and [end] values must be set to non-null values before
 /// calling [lerp] or [transform].
 ///
 /// See [Tween] for a discussion on how to use interpolation objects.
 class StepTween extends Tween<int> {
   /// Creates an [int] tween that floors.
   ///
   /// The [begin] and [end] properties must be non-null before the tween is
   /// first used, but the arguments can be null if the values are going to be
   /// filled in later.
   StepTween({ super.begin, super.end });

   // The inherited lerp() function doesn't work with ints because it multiplies
   // the begin and end types by a double, and int * double returns a double.
   @override
   int lerp(double t) => (begin! + (end! - begin!) * t).floor();
 }

 /// A tween with a constant value.
 class ConstantTween<T> extends Tween<T> {
   /// Create a tween whose [begin] and [end] values equal [value].
   ConstantTween(T value) : super(begin: value, end: value);

   /// This tween doesn't interpolate, it always returns the same value.
   @override
   T lerp(double t) => begin as T;

   @override
   String toString() => '${objectRuntimeType(this, 'ConstantTween')}(value: $begin)';
 }

 /// Transforms the value of the given animation by the given curve.
 ///
 /// This class differs from [CurvedAnimation] in that [CurvedAnimation] applies
 /// a curve to an existing [Animation] object whereas [CurveTween] can be
 /// chained with another [Tween] prior to receiving the underlying [Animation].
 /// ([CurvedAnimation] also has the additional ability of having different
 /// curves when the animation is going forward vs when it is going backward,
 /// which can be useful in some scenarios.)
 ///
 /// {@tool snippet}
 ///
 /// The following code snippet shows how you can apply a curve to a linear
 /// animation produced by an [AnimationController] `controller`:
 ///
 /// ```dart
 /// final Animation<double> animation = _controller.drive(
 ///   CurveTween(curve: Curves.ease),
 /// );
 /// ```
 /// {@end-tool}
 ///
 /// See also:
 ///
 ///  * [CurvedAnimation], for an alternative way of expressing the sample above.
 ///  * [AnimationController], for examples of creating and disposing of an
 ///    [AnimationController].
 class CurveTween extends Animatable<double> {
   /// Creates a curve tween.
   ///
   /// The [curve] argument must not be null.
   CurveTween({ required this.curve })
     : assert(curve != null);

   /// The curve to use when transforming the value of the animation.
   Curve curve;

   @override
   double transform(double t) {
     if (t == 0.0 || t == 1.0) {
       assert(curve.transform(t).round() == t);
       return t;
     }
     return curve.transform(t);
   }

   @override
   String toString() => '${objectRuntimeType(this, 'CurveTween')}(curve: $curve)';
 }
	// Copyright 2014 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.

	import 'dart:ui' show Color, Rect, Size;

	import 'package:flutter/foundation.dart';

	import 'animations.dart';

	export 'dart:ui' show Color, Rect, Size;

	export 'animation.dart' show Animation;
	export 'curves.dart' show Curve;

	// Examples can assume:
	// late Animation<Offset> _animation;
	// late AnimationController _controller;

	/// An object that can produce a value of type `T` given an [Animation<double>]
	/// as input.
	///
	/// Typically, the values of the input animation are nominally in the range 0.0
	/// to 1.0. In principle, however, any value could be provided.
	///
	/// The main subclass of [Animatable] is [Tween].
	abstract class Animatable<T> {
	/// Abstract const constructor. This constructor enables subclasses to provide
	/// const constructors so that they can be used in const expressions.
	const Animatable();

	/// Returns the value of the object at point `t`.
	///
	/// The value of `t` is nominally a fraction in the range 0.0 to 1.0, though
	/// in practice it may extend outside this range.
	///
	/// See also:
	///
	/// * [evaluate], which is a shorthand for applying [transform] to the value
	/// of an [Animation].
	/// * [Curve.transform], a similar method for easing curves.
	T transform(double t);

	/// The current value of this object for the given [Animation].
	///
	/// This function is implemented by deferring to [transform]. Subclasses that
	/// want to provide custom behavior should override [transform], not
	/// [evaluate].
	///
	/// See also:
	///
	/// * [transform], which is similar but takes a `t` value directly instead of
	/// an [Animation].
	/// * [animate], which creates an [Animation] out of this object, continually
	/// applying [evaluate].
	T evaluate(Animation<double> animation) => transform(animation.value);

	/// Returns a new [Animation] that is driven by the given animation but that
	/// takes on values determined by this object.
	///
	/// Essentially this returns an [Animation] that automatically applies the
	/// [evaluate] method to the parent's value.
	///
	/// See also:
	///
	/// * [AnimationController.drive], which does the same thing from the
	/// opposite starting point.
	Animation<T> animate(Animation<double> parent) {
	return _AnimatedEvaluation<T>(parent, this);
	}

	/// Returns a new [Animatable] whose value is determined by first evaluating
	/// the given parent and then evaluating this object.
	///
	/// This allows [Tween]s to be chained before obtaining an [Animation].
	Animatable<T> chain(Animatable<double> parent) {
	return _ChainedEvaluation<T>(parent, this);
	}
	}

	class _AnimatedEvaluation<T> extends Animation<T> with AnimationWithParentMixin<double> {
	_AnimatedEvaluation(this.parent, this._evaluatable);

	@override
	final Animation<double> parent;

	final Animatable<T> _evaluatable;

	@override
	T get value => _evaluatable.evaluate(parent);

	@override
	String toString() {
	return '$parent\u27A9$_evaluatable\u27A9$value';
	}

	@override
	String toStringDetails() {
	return '${super.toStringDetails()} $_evaluatable';
	}
	}

	class _ChainedEvaluation<T> extends Animatable<T> {
	_ChainedEvaluation(this._parent, this._evaluatable);

	final Animatable<double> _parent;
	final Animatable<T> _evaluatable;

	@override
	T transform(double t) {
	return _evaluatable.transform(_parent.transform(t));
	}

	@override
	String toString() {
	return '$_parent\u27A9$_evaluatable';
	}
	}

	/// A linear interpolation between a beginning and ending value.
	///
	/// [Tween] is useful if you want to interpolate across a range.
	///
	/// To use a [Tween] object with an animation, call the [Tween] object's
	/// [animate] method and pass it the [Animation] object that you want to
	/// modify.
	///
	/// You can chain [Tween] objects together using the [chain] method, so that a
	/// single [Animation] object is configured by multiple [Tween] objects called
	/// in succession. This is different than calling the [animate] method twice,
	/// which results in two separate [Animation] objects, each configured with a
	/// single [Tween].
	///
	/// {@tool snippet}
	///
	/// Suppose `_controller` is an [AnimationController], and we want to create an
	/// [Animation<Offset>] that is controlled by that controller, and save it in
	/// `_animation`. Here are two possible ways of expressing this:
	///
	/// ```dart
	/// _animation = _controller.drive(
	/// Tween<Offset>(
	/// begin: const Offset(100.0, 50.0),
	/// end: const Offset(200.0, 300.0),
	/// ),
	/// );
	/// ```
	/// {@end-tool}
	/// {@tool snippet}
	///
	/// ```dart
	/// _animation = Tween<Offset>(
	/// begin: const Offset(100.0, 50.0),
	/// end: const Offset(200.0, 300.0),
	/// ).animate(_controller);
	/// ```
	/// {@end-tool}
	///
	/// In both cases, the `_animation` variable holds an object that, over the
	/// lifetime of the `_controller`'s animation, returns a value
	/// (`_animation.value`) that depicts a point along the line between the two
	/// offsets above. If we used a [MaterialPointArcTween] instead of a
	/// [Tween<Offset>] in the code above, the points would follow a pleasing curve
	/// instead of a straight line, with no other changes necessary.
	///
	/// ## Performance optimizations
	///
	/// Tweens are mutable; specifically, their [begin] and [end] values can be
	/// changed at runtime. An object created with [Animation.drive] using a [Tween]
	/// will immediately honor changes to that underlying [Tween] (though the
	/// listeners will only be triggered if the [Animation] is actively animating).
	/// This can be used to change an animation on the fly without having to
	/// recreate all the objects in the chain from the [AnimationController] to the
	/// final [Tween].
	///
	/// If a [Tween]'s values are never changed, however, a further optimization can
	/// be applied: the object can be stored in a `static final` variable, so that
	/// the exact same instance is used whenever the [Tween] is needed. This is
	/// preferable to creating an identical [Tween] afresh each time a [State.build]
	/// method is called, for example.
	///
	/// ## Types with special considerations
	///
	/// Classes with [lerp] static methods typically have corresponding dedicated
	/// [Tween] subclasses that call that method. For example, [ColorTween] uses
	/// [Color.lerp] to implement the [ColorTween.lerp] method.
	///
	/// Types that define `+` and `-` operators to combine values (`T + T → T` and
	/// `T - T → T`) and an `` operator to scale by multiplying with a double (`T
	/// double → T`) can be directly used with `Tween<T>`.
	///
	/// This does not extend to any type with `+`, `-`, and `*` operators. In
	/// particular, [int] does not satisfy this precise contract (`int * double`
	/// actually returns [num], not [int]). There are therefore two specific classes
	/// that can be used to interpolate integers:
	///
	/// * [IntTween], which is an approximation of a linear interpolation (using
	/// [double.round]).
	/// * [StepTween], which uses [double.floor] to ensure that the result is
	/// never greater than it would be using if a `Tween<double>`.
	///
	/// The relevant operators on [Size] also don't fulfill this contract, so
	/// [SizeTween] uses [Size.lerp].
	///
	/// In addition, some of the types that _do_ have suitable `+`, `-`, and `*`
	/// operators still have dedicated [Tween] subclasses that perform the
	/// interpolation in a more specialized manner. One such class is
	/// [MaterialPointArcTween], which is mentioned above. The [AlignmentTween], and
	/// [AlignmentGeometryTween], and [FractionalOffsetTween] are another group of
	/// [Tween]s that use dedicated `lerp` methods instead of merely relying on the
	/// operators (in particular, this allows them to handle null values in a more
	/// useful manner).
	///
	/// ## Nullability
	///
	/// The [begin] and [end] fields are nullable; a [Tween] does not have to
	/// have non-null values specified when it is created.
	///
	/// If `T` is nullable, then [lerp] and [transform] may return null.
	/// This is typically seen in the case where [begin] is null and `t`
	/// is 0.0, or [end] is null and `t` is 1.0, or both are null (at any
	/// `t` value).
	///
	/// If `T` is not nullable, then [begin] and [end] must both be set to
	/// non-null values before using [lerp] or [transform], otherwise they
	/// will throw.
	class Tween<T extends Object?> extends Animatable<T> {
	/// Creates a tween.
	///
	/// The [begin] and [end] properties must be non-null before the tween is
	/// first used, but the arguments can be null if the values are going to be
	/// filled in later.
	Tween({
	this.begin,
	this.end,
	});

	/// The value this variable has at the beginning of the animation.
	///
	/// See the constructor for details about whether this property may be null
	/// (it varies from subclass to subclass).
	T? begin;

	/// The value this variable has at the end of the animation.
	///
	/// See the constructor for details about whether this property may be null
	/// (it varies from subclass to subclass).
	T? end;

	/// Returns the value this variable has at the given animation clock value.
	///
	/// The default implementation of this method uses the `+`, `-`, and `*`
	/// operators on `T`. The [begin] and [end] properties must therefore be
	/// non-null by the time this method is called.
	///
	/// In general, however, it is possible for this to return null, especially
	/// when `t`=0.0 and [begin] is null, or `t`=1.0 and [end] is null.
	@protected
	T lerp(double t) {
	assert(begin != null);
	assert(end != null);
	assert(() {
	// Assertions that attempt to catch common cases of tweening types
	// that do not conform to the Tween requirements.
	dynamic result;
	try {
	// ignore: avoid_dynamic_calls
	result = (begin as dynamic) + ((end as dynamic) - (begin as dynamic)) * t;
	result as T;
	return true;
	} on NoSuchMethodError {
	throw FlutterError.fromParts(<DiagnosticsNode>[
	ErrorSummary('Cannot lerp between "$begin" and "$end".'),
	ErrorDescription(
	'The type ${begin.runtimeType} might not fully implement `+`, `-`, and/or `*`. '
	'See "Types with special considerations" at https://api.flutter.dev/flutter/animation/Tween-class.html '
	'for more information.',
	),
	if (begin is Color \|\| end is Color)
	ErrorHint('To lerp colors, consider ColorTween instead.')
	else if (begin is Rect \|\| end is Rect)
	ErrorHint('To lerp rects, consider RectTween instead.')
	else
	ErrorHint(
	'There may be a dedicated "${begin.runtimeType}Tween" for this type, '
	'or you may need to create one.',
	),
	]);
	} on TypeError {
	throw FlutterError.fromParts(<DiagnosticsNode>[
	ErrorSummary('Cannot lerp between "$begin" and "$end".'),
	ErrorDescription(
	'The type ${begin.runtimeType} returned a ${result.runtimeType} after '
	'multiplication with a double value. '
	'See "Types with special considerations" at https://api.flutter.dev/flutter/animation/Tween-class.html '
	'for more information.',
	),
	if (begin is int \|\| end is int)
	ErrorHint('To lerp int values, consider IntTween or StepTween instead.')
	else
	ErrorHint(
	'There may be a dedicated "${begin.runtimeType}Tween" for this type, '
	'or you may need to create one.',
	),
	]);
	}
	}());
	// ignore: avoid_dynamic_calls
	return (begin as dynamic) + ((end as dynamic) - (begin as dynamic)) * t as T;
	}

	/// Returns the interpolated value for the current value of the given animation.
	///
	/// This method returns `begin` and `end` when the animation values are 0.0 or
	/// 1.0, respectively.
	///
	/// This function is implemented by deferring to [lerp]. Subclasses that want
	/// to provide custom behavior should override [lerp], not [transform] (nor
	/// [evaluate]).
	///
	/// See the constructor for details about whether the [begin] and [end]
	/// properties may be null when this is called. It varies from subclass to
	/// subclass.
	@override
	T transform(double t) {
	if (t == 0.0) {
	return begin as T;
	}
	if (t == 1.0) {
	return end as T;
	}
	return lerp(t);
	}

	@override
	String toString() => '${objectRuntimeType(this, 'Animatable')}($begin \u2192 $end)';
	}

	/// A [Tween] that evaluates its [parent] in reverse.
	class ReverseTween<T extends Object?> extends Tween<T> {
	/// Construct a [Tween] that evaluates its [parent] in reverse.
	ReverseTween(this.parent)
	: assert(parent != null),
	super(begin: parent.end, end: parent.begin);

	/// This tween's value is the same as the parent's value evaluated in reverse.
	///
	/// This tween's [begin] is the parent's [end] and its [end] is the parent's
	/// [begin]. The [lerp] method returns `parent.lerp(1.0 - t)` and its
	/// [evaluate] method is similar.
	final Tween<T> parent;

	@override
	T lerp(double t) => parent.lerp(1.0 - t);
	}

	/// An interpolation between two colors.
	///
	/// This class specializes the interpolation of [Tween<Color>] to use
	/// [Color.lerp].
	///
	/// The values can be null, representing no color (which is distinct to
	/// transparent black, as represented by [Colors.transparent]).
	///
	/// See [Tween] for a discussion on how to use interpolation objects.
	class ColorTween extends Tween<Color?> {
	/// Creates a [Color] tween.
	///
	/// The [begin] and [end] properties may be null; the null value
	/// is treated as transparent.
	///
	/// We recommend that you do not pass [Colors.transparent] as [begin]
	/// or [end] if you want the effect of fading in or out of transparent.
	/// Instead prefer null. [Colors.transparent] refers to black transparent and
	/// thus will fade out of or into black which is likely unwanted.
	ColorTween({ super.begin, super.end });

	/// Returns the value this variable has at the given animation clock value.
	@override
	Color? lerp(double t) => Color.lerp(begin, end, t);
	}

	/// An interpolation between two sizes.
	///
	/// This class specializes the interpolation of [Tween<Size>] to use
	/// [Size.lerp].
	///
	/// The values can be null, representing [Size.zero].
	///
	/// See [Tween] for a discussion on how to use interpolation objects.
	class SizeTween extends Tween<Size?> {
	/// Creates a [Size] tween.
	///
	/// The [begin] and [end] properties may be null; the null value
	/// is treated as an empty size.
	SizeTween({ super.begin, super.end });

	/// Returns the value this variable has at the given animation clock value.
	@override
	Size? lerp(double t) => Size.lerp(begin, end, t);
	}

	/// An interpolation between two rectangles.
	///
	/// This class specializes the interpolation of [Tween<Rect>] to use
	/// [Rect.lerp].
	///
	/// The values can be null, representing a zero-sized rectangle at the
	/// origin ([Rect.zero]).
	///
	/// See [Tween] for a discussion on how to use interpolation objects.
	class RectTween extends Tween<Rect?> {
	/// Creates a [Rect] tween.
	///
	/// The [begin] and [end] properties may be null; the null value
	/// is treated as an empty rect at the top left corner.
	RectTween({ super.begin, super.end });

	/// Returns the value this variable has at the given animation clock value.
	@override
	Rect? lerp(double t) => Rect.lerp(begin, end, t);
	}

	/// An interpolation between two integers that rounds.
	///
	/// This class specializes the interpolation of [Tween<int>] to be
	/// appropriate for integers by interpolating between the given begin
	/// and end values and then rounding the result to the nearest
	/// integer.
	///
	/// This is the closest approximation to a linear tween that is possible with an
	/// integer. Compare to [StepTween] and [Tween<double>].
	///
	/// The [begin] and [end] values must be set to non-null values before
	/// calling [lerp] or [transform].
	///
	/// See [Tween] for a discussion on how to use interpolation objects.
	class IntTween extends Tween<int> {
	/// Creates an int tween.
	///
	/// The [begin] and [end] properties must be non-null before the tween is
	/// first used, but the arguments can be null if the values are going to be
	/// filled in later.
	IntTween({ super.begin, super.end });

	// The inherited lerp() function doesn't work with ints because it multiplies
	// the begin and end types by a double, and int * double returns a double.
	@override
	int lerp(double t) => (begin! + (end! - begin!) * t).round();
	}

	/// An interpolation between two integers that floors.
	///
	/// This class specializes the interpolation of [Tween<int>] to be
	/// appropriate for integers by interpolating between the given begin
	/// and end values and then using [double.floor] to return the current
	/// integer component, dropping the fractional component.
	///
	/// This results in a value that is never greater than the equivalent
	/// value from a linear double interpolation. Compare to [IntTween].
	///
	/// The [begin] and [end] values must be set to non-null values before
	/// calling [lerp] or [transform].
	///
	/// See [Tween] for a discussion on how to use interpolation objects.
	class StepTween extends Tween<int> {
	/// Creates an [int] tween that floors.
	///
	/// The [begin] and [end] properties must be non-null before the tween is
	/// first used, but the arguments can be null if the values are going to be
	/// filled in later.
	StepTween({ super.begin, super.end });

	// The inherited lerp() function doesn't work with ints because it multiplies
	// the begin and end types by a double, and int * double returns a double.
	@override
	int lerp(double t) => (begin! + (end! - begin!) * t).floor();
	}

	/// A tween with a constant value.
	class ConstantTween<T> extends Tween<T> {
	/// Create a tween whose [begin] and [end] values equal [value].
	ConstantTween(T value) : super(begin: value, end: value);

	/// This tween doesn't interpolate, it always returns the same value.
	@override
	T lerp(double t) => begin as T;

	@override
	String toString() => '${objectRuntimeType(this, 'ConstantTween')}(value: $begin)';
	}

	/// Transforms the value of the given animation by the given curve.
	///
	/// This class differs from [CurvedAnimation] in that [CurvedAnimation] applies
	/// a curve to an existing [Animation] object whereas [CurveTween] can be
	/// chained with another [Tween] prior to receiving the underlying [Animation].
	/// ([CurvedAnimation] also has the additional ability of having different
	/// curves when the animation is going forward vs when it is going backward,
	/// which can be useful in some scenarios.)
	///
	/// {@tool snippet}
	///
	/// The following code snippet shows how you can apply a curve to a linear
	/// animation produced by an [AnimationController] `controller`:
	///
	/// ```dart
	/// final Animation<double> animation = _controller.drive(
	/// CurveTween(curve: Curves.ease),
	/// );
	/// ```
	/// {@end-tool}
	///
	/// See also:
	///
	/// * [CurvedAnimation], for an alternative way of expressing the sample above.
	/// * [AnimationController], for examples of creating and disposing of an
	/// [AnimationController].
	class CurveTween extends Animatable<double> {
	/// Creates a curve tween.
	///
	/// The [curve] argument must not be null.
	CurveTween({ required this.curve })
	: assert(curve != null);

	/// The curve to use when transforming the value of the animation.
	Curve curve;

	@override
	double transform(double t) {
	if (t == 0.0 \|\| t == 1.0) {
	assert(curve.transform(t).round() == t);
	return t;
	}
	return curve.transform(t);
	}

	@override
	String toString() => '${objectRuntimeType(this, 'CurveTween')}(curve: $curve)';
	}