| // 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:math' as math; |
| import 'dart:ui'; |
| |
| import 'package:flutter/foundation.dart'; |
| |
| export 'dart:ui' show Offset; |
| |
| /// An abstract class providing an interface for evaluating a parametric curve. |
| /// |
| /// A parametric curve transforms a parameter (hence the name) `t` along a curve |
| /// to the value of the curve at that value of `t`. The curve can be of |
| /// arbitrary dimension, but is typically a 1D, 2D, or 3D curve. |
| /// |
| /// See also: |
| /// |
| /// * [Curve], a 1D animation easing curve that starts at 0.0 and ends at 1.0. |
| /// * [Curve2D], a parametric curve that transforms the parameter to a 2D point. |
| abstract class ParametricCurve<T> { |
| /// Abstract const constructor to enable subclasses to provide |
| /// const constructors so that they can be used in const expressions. |
| const ParametricCurve(); |
| |
| /// Returns the value of the curve at point `t`. |
| /// |
| /// This method asserts that t is between 0 and 1 before delegating to |
| /// [transformInternal]. |
| /// |
| /// It is recommended that subclasses override [transformInternal] instead of |
| /// this function, as the above case is already handled in the default |
| /// implementation of [transform], which delegates the remaining logic to |
| /// [transformInternal]. |
| T transform(double t) { |
| assert(t != null); |
| assert(t >= 0.0 && t <= 1.0, 'parametric value $t is outside of [0, 1] range.'); |
| return transformInternal(t); |
| } |
| |
| /// Returns the value of the curve at point `t`. |
| /// |
| /// The given parametric value `t` will be between 0.0 and 1.0, inclusive. |
| @protected |
| T transformInternal(double t) { |
| throw UnimplementedError(); |
| } |
| |
| @override |
| String toString() => objectRuntimeType(this, 'ParametricCurve'); |
| } |
| |
| /// An parametric animation easing curve, i.e. a mapping of the unit interval to |
| /// the unit interval. |
| /// |
| /// Easing curves are used to adjust the rate of change of an animation over |
| /// time, allowing them to speed up and slow down, rather than moving at a |
| /// constant rate. |
| /// |
| /// A [Curve] must map t=0.0 to 0.0 and t=1.0 to 1.0. |
| /// |
| /// See also: |
| /// |
| /// * [Curves], a collection of common animation easing curves. |
| /// * [CurveTween], which can be used to apply a [Curve] to an [Animation]. |
| /// * [Canvas.drawArc], which draws an arc, and has nothing to do with easing |
| /// curves. |
| /// * [Animatable], for a more flexible interface that maps fractions to |
| /// arbitrary values. |
| @immutable |
| abstract class Curve extends ParametricCurve<double> { |
| /// Abstract const constructor to enable subclasses to provide |
| /// const constructors so that they can be used in const expressions. |
| const Curve(); |
| |
| /// Returns the value of the curve at point `t`. |
| /// |
| /// This function must ensure the following: |
| /// - The value of `t` must be between 0.0 and 1.0 |
| /// - Values of `t`=0.0 and `t`=1.0 must be mapped to 0.0 and 1.0, |
| /// respectively. |
| /// |
| /// It is recommended that subclasses override [transformInternal] instead of |
| /// this function, as the above cases are already handled in the default |
| /// implementation of [transform], which delegates the remaining logic to |
| /// [transformInternal]. |
| @override |
| double transform(double t) { |
| if (t == 0.0 || t == 1.0) { |
| return t; |
| } |
| return super.transform(t); |
| } |
| |
| /// Returns a new curve that is the reversed inversion of this one. |
| /// |
| /// This is often useful with [CurvedAnimation.reverseCurve]. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_flipped.mp4} |
| /// |
| /// See also: |
| /// |
| /// * [FlippedCurve], the class that is used to implement this getter. |
| /// * [ReverseAnimation], which reverses an [Animation] rather than a [Curve]. |
| /// * [CurvedAnimation], which can take a separate curve and reverse curve. |
| Curve get flipped => FlippedCurve(this); |
| } |
| |
| /// The identity map over the unit interval. |
| /// |
| /// See [Curves.linear] for an instance of this class. |
| class _Linear extends Curve { |
| const _Linear._(); |
| |
| @override |
| double transformInternal(double t) => t; |
| } |
| |
| /// A sawtooth curve that repeats a given number of times over the unit interval. |
| /// |
| /// The curve rises linearly from 0.0 to 1.0 and then falls discontinuously back |
| /// to 0.0 each iteration. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_sawtooth.mp4} |
| class SawTooth extends Curve { |
| /// Creates a sawtooth curve. |
| /// |
| /// The [count] argument must not be null. |
| const SawTooth(this.count) : assert(count != null); |
| |
| /// The number of repetitions of the sawtooth pattern in the unit interval. |
| final int count; |
| |
| @override |
| double transformInternal(double t) { |
| t *= count; |
| return t - t.truncateToDouble(); |
| } |
| |
| @override |
| String toString() { |
| return '${objectRuntimeType(this, 'SawTooth')}($count)'; |
| } |
| } |
| |
| /// A curve that is 0.0 until [begin], then curved (according to [curve]) from |
| /// 0.0 at [begin] to 1.0 at [end], then remains 1.0 past [end]. |
| /// |
| /// An [Interval] can be used to delay an animation. For example, a six second |
| /// animation that uses an [Interval] with its [begin] set to 0.5 and its [end] |
| /// set to 1.0 will essentially become a three-second animation that starts |
| /// three seconds later. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_interval.mp4} |
| class Interval extends Curve { |
| /// Creates an interval curve. |
| /// |
| /// The arguments must not be null. |
| const Interval(this.begin, this.end, { this.curve = Curves.linear }) |
| : assert(begin != null), |
| assert(end != null), |
| assert(curve != null); |
| |
| /// The largest value for which this interval is 0.0. |
| /// |
| /// From t=0.0 to t=`begin`, the interval's value is 0.0. |
| final double begin; |
| |
| /// The smallest value for which this interval is 1.0. |
| /// |
| /// From t=`end` to t=1.0, the interval's value is 1.0. |
| final double end; |
| |
| /// The curve to apply between [begin] and [end]. |
| final Curve curve; |
| |
| @override |
| double transformInternal(double t) { |
| assert(begin >= 0.0); |
| assert(begin <= 1.0); |
| assert(end >= 0.0); |
| assert(end <= 1.0); |
| assert(end >= begin); |
| t = clampDouble((t - begin) / (end - begin), 0.0, 1.0); |
| if (t == 0.0 || t == 1.0) { |
| return t; |
| } |
| return curve.transform(t); |
| } |
| |
| @override |
| String toString() { |
| if (curve is! _Linear) { |
| return '${objectRuntimeType(this, 'Interval')}($begin\u22EF$end)\u27A9$curve'; |
| } |
| return '${objectRuntimeType(this, 'Interval')}($begin\u22EF$end)'; |
| } |
| } |
| |
| /// 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} |
| class Threshold extends Curve { |
| /// Creates a threshold curve. |
| /// |
| /// The [threshold] argument must not be null. |
| const Threshold(this.threshold) : assert(threshold != null); |
| |
| /// The value before which the curve is 0.0 and after which the curve is 1.0. |
| /// |
| /// When t is exactly [threshold], the curve has the value 1.0. |
| final double threshold; |
| |
| @override |
| double transformInternal(double t) { |
| assert(threshold >= 0.0); |
| assert(threshold <= 1.0); |
| return t < threshold ? 0.0 : 1.0; |
| } |
| } |
| |
| /// A cubic polynomial mapping of the unit interval. |
| /// |
| /// The [Curves] class contains some commonly used cubic curves: |
| /// |
| /// * [Curves.fastLinearToSlowEaseIn] |
| /// * [Curves.ease] |
| /// * [Curves.easeIn] |
| /// * [Curves.easeInToLinear] |
| /// * [Curves.easeInSine] |
| /// * [Curves.easeInQuad] |
| /// * [Curves.easeInCubic] |
| /// * [Curves.easeInQuart] |
| /// * [Curves.easeInQuint] |
| /// * [Curves.easeInExpo] |
| /// * [Curves.easeInCirc] |
| /// * [Curves.easeInBack] |
| /// * [Curves.easeOut] |
| /// * [Curves.linearToEaseOut] |
| /// * [Curves.easeOutSine] |
| /// * [Curves.easeOutQuad] |
| /// * [Curves.easeOutCubic] |
| /// * [Curves.easeOutQuart] |
| /// * [Curves.easeOutQuint] |
| /// * [Curves.easeOutExpo] |
| /// * [Curves.easeOutCirc] |
| /// * [Curves.easeOutBack] |
| /// * [Curves.easeInOut] |
| /// * [Curves.easeInOutSine] |
| /// * [Curves.easeInOutQuad] |
| /// * [Curves.easeInOutCubic] |
| /// * [Curves.easeInOutQuart] |
| /// * [Curves.easeInOutQuint] |
| /// * [Curves.easeInOutExpo] |
| /// * [Curves.easeInOutCirc] |
| /// * [Curves.easeInOutBack] |
| /// * [Curves.fastOutSlowIn] |
| /// * [Curves.slowMiddle] |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_fast_linear_to_slow_ease_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_to_linear.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_sine.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quad.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_cubic.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quart.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quint.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_expo.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_circ.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_back.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_linear_to_ease_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_sine.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quad.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_cubic.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quart.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quint.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_expo.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_circ.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_back.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_sine.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quad.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_cubic.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quart.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quint.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_expo.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_circ.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_back.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_fast_out_slow_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_slow_middle.mp4} |
| /// |
| /// The [Cubic] class implements third-order Bézier curves. |
| /// |
| /// See also: |
| /// |
| /// * [Curves], where many more predefined curves are available. |
| /// * [CatmullRomCurve], a curve which passes through specific values. |
| class Cubic extends Curve { |
| /// Creates a cubic curve. |
| /// |
| /// Rather than creating a new instance, consider using one of the common |
| /// cubic curves in [Curves]. |
| /// |
| /// The [a] (x1), [b] (y1), [c] (x2) and [d] (y2) arguments must not be null. |
| const Cubic(this.a, this.b, this.c, this.d) |
| : assert(a != null), |
| assert(b != null), |
| assert(c != null), |
| assert(d != null); |
| |
| /// The x coordinate of the first control point. |
| /// |
| /// The line through the point (0, 0) and the first control point is tangent |
| /// to the curve at the point (0, 0). |
| final double a; |
| |
| /// The y coordinate of the first control point. |
| /// |
| /// The line through the point (0, 0) and the first control point is tangent |
| /// to the curve at the point (0, 0). |
| final double b; |
| |
| /// The x coordinate of the second control point. |
| /// |
| /// The line through the point (1, 1) and the second control point is tangent |
| /// to the curve at the point (1, 1). |
| final double c; |
| |
| /// The y coordinate of the second control point. |
| /// |
| /// The line through the point (1, 1) and the second control point is tangent |
| /// to the curve at the point (1, 1). |
| final double d; |
| |
| static const double _cubicErrorBound = 0.001; |
| |
| double _evaluateCubic(double a, double b, double m) { |
| return 3 * a * (1 - m) * (1 - m) * m + |
| 3 * b * (1 - m) * m * m + |
| m * m * m; |
| } |
| |
| @override |
| double transformInternal(double t) { |
| double start = 0.0; |
| double end = 1.0; |
| while (true) { |
| final double midpoint = (start + end) / 2; |
| final double estimate = _evaluateCubic(a, c, midpoint); |
| if ((t - estimate).abs() < _cubicErrorBound) { |
| return _evaluateCubic(b, d, midpoint); |
| } |
| if (estimate < t) { |
| start = midpoint; |
| } else { |
| end = midpoint; |
| } |
| } |
| } |
| |
| @override |
| String toString() { |
| return '${objectRuntimeType(this, 'Cubic')}(${a.toStringAsFixed(2)}, ${b.toStringAsFixed(2)}, ${c.toStringAsFixed(2)}, ${d.toStringAsFixed(2)})'; |
| } |
| } |
| |
| /// A cubic polynomial composed of two curves that share a common center point. |
| /// |
| /// The curve runs through three points: (0,0), the [midpoint], and (1,1). |
| /// |
| /// The [Curves] class contains a curve defined with this class: |
| /// [Curves.easeInOutCubicEmphasized]. |
| /// |
| /// The [ThreePointCubic] class implements third-order Bézier curves, where two |
| /// curves share an interior [midpoint] that the curve passes through. If the |
| /// control points surrounding the middle point ([b1], and [a2]) are not |
| /// colinear with the middle point, then the curve's derivative will have a |
| /// discontinuity (a cusp) at the shared middle point. |
| /// |
| /// See also: |
| /// |
| /// * [Curves], where many more predefined curves are available. |
| /// * [Cubic], which defines a single cubic polynomial. |
| /// * [CatmullRomCurve], a curve which passes through specific values. |
| class ThreePointCubic extends Curve { |
| /// Creates two cubic curves that share a common control point. |
| /// |
| /// Rather than creating a new instance, consider using one of the common |
| /// three-point cubic curves in [Curves]. |
| /// |
| /// The arguments correspond to the control points for the two curves, |
| /// including the [midpoint], but do not include the two implied end points at |
| /// (0,0) and (1,1), which are fixed. |
| const ThreePointCubic(this.a1, this.b1, this.midpoint, this.a2, this.b2); |
| |
| /// The coordinates of the first control point of the first curve. |
| /// |
| /// The line through the point (0, 0) and this control point is tangent to the |
| /// curve at the point (0, 0). |
| final Offset a1; |
| |
| /// The coordinates of the second control point of the first curve. |
| /// |
| /// The line through the [midpoint] and this control point is tangent to the |
| /// curve approaching the [midpoint]. |
| final Offset b1; |
| |
| /// The coordinates of the middle shared point. |
| /// |
| /// The curve will go through this point. If the control points surrounding |
| /// this middle point ([b1], and [a2]) are not colinear with this point, then |
| /// the curve's derivative will have a discontinuity (a cusp) at this point. |
| final Offset midpoint; |
| |
| /// The coordinates of the first control point of the second curve. |
| /// |
| /// The line through the [midpoint] and this control point is tangent to the |
| /// curve approaching the [midpoint]. |
| final Offset a2; |
| |
| /// The coordinates of the second control point of the second curve. |
| /// |
| /// The line through the point (1, 1) and this control point is tangent to the |
| /// curve at (1, 1). |
| final Offset b2; |
| |
| @override |
| double transformInternal(double t) { |
| final bool firstCurve = t < midpoint.dx; |
| final double scaleX = firstCurve ? midpoint.dx : 1.0 - midpoint.dx; |
| final double scaleY = firstCurve ? midpoint.dy : 1.0 - midpoint.dy; |
| final double scaledT = (t - (firstCurve ? 0.0 : midpoint.dx)) / scaleX; |
| if (firstCurve) { |
| return Cubic( |
| a1.dx / scaleX, |
| a1.dy / scaleY, |
| b1.dx / scaleX, |
| b1.dy / scaleY, |
| ).transform(scaledT) * scaleY; |
| } else { |
| return Cubic( |
| (a2.dx - midpoint.dx) / scaleX, |
| (a2.dy - midpoint.dy) / scaleY, |
| (b2.dx - midpoint.dx) / scaleX, |
| (b2.dy - midpoint.dy) / scaleY, |
| ).transform(scaledT) * scaleY + midpoint.dy; |
| } |
| } |
| |
| @override |
| String toString() { |
| return '${objectRuntimeType(this, 'ThreePointCubic($a1, $b1, $midpoint, $a2, $b2)')} '; |
| } |
| } |
| |
| /// Abstract class that defines an API for evaluating 2D parametric curves. |
| /// |
| /// [Curve2D] differs from [Curve] in that the values interpolated are [Offset] |
| /// values instead of [double] values, hence the "2D" in the name. They both |
| /// take a single double `t` that has a range of 0.0 to 1.0, inclusive, as input |
| /// to the [transform] function . Unlike [Curve], [Curve2D] is not required to |
| /// map `t=0.0` and `t=1.0` to specific output values. |
| /// |
| /// The interpolated `t` value given to [transform] represents the progression |
| /// along the curve, but it doesn't necessarily progress at a constant velocity, so |
| /// incrementing `t` by, say, 0.1 might move along the curve by quite a lot at one |
| /// part of the curve, or hardly at all in another part of the curve, depending |
| /// on the definition of the curve. |
| /// |
| /// {@tool dartpad} |
| /// This example shows how to use a [Curve2D] to modify the position of a widget |
| /// so that it can follow an arbitrary path. |
| /// |
| /// ** See code in examples/api/lib/animation/curves/curve2_d.0.dart ** |
| /// {@end-tool} |
| /// |
| abstract class Curve2D extends ParametricCurve<Offset> { |
| /// Abstract const constructor to enable subclasses to provide const |
| /// constructors so that they can be used in const expressions. |
| const Curve2D(); |
| |
| /// Generates a list of samples with a recursive subdivision until a tolerance |
| /// of `tolerance` is reached. |
| /// |
| /// Samples are generated in order. |
| /// |
| /// Samples can be used to render a curve efficiently, since the samples |
| /// constitute line segments which vary in size with the curvature of the |
| /// curve. They can also be used to quickly approximate the value of the curve |
| /// by searching for the desired range in X and linearly interpolating between |
| /// samples to obtain an approximation of Y at the desired X value. The |
| /// implementation of [CatmullRomCurve] uses samples for this purpose |
| /// internally. |
| /// |
| /// The tolerance is computed as the area of a triangle formed by a new point |
| /// and the preceding and following point. |
| /// |
| /// See also: |
| /// |
| /// * Luiz Henrique de Figueire's Graphics Gem on [the algorithm](http://ariel.chronotext.org/dd/defigueiredo93adaptive.pdf). |
| Iterable<Curve2DSample> generateSamples({ |
| double start = 0.0, |
| double end = 1.0, |
| double tolerance = 1e-10, |
| }) { |
| // The sampling algorithm is: |
| // 1. Evaluate the area of the triangle (a proxy for the "flatness" of the |
| // curve) formed by two points and a test point. |
| // 2. If the area of the triangle is small enough (below tolerance), then |
| // the two points form the final segment. |
| // 3. If the area is still too large, divide the interval into two parts |
| // using a random subdivision point to avoid aliasing. |
| // 4. Recursively sample the two parts. |
| // |
| // This algorithm concentrates samples in areas of high curvature. |
| assert(tolerance != null); |
| assert(start != null); |
| assert(end != null); |
| assert(end > start); |
| // We want to pick a random seed that will keep the result stable if |
| // evaluated again, so we use the first non-generated control point. |
| final math.Random rand = math.Random(samplingSeed); |
| bool isFlat(Offset p, Offset q, Offset r) { |
| // Calculates the area of the triangle given by the three points. |
| final Offset pr = p - r; |
| final Offset qr = q - r; |
| final double z = pr.dx * qr.dy - qr.dx * pr.dy; |
| return (z * z) < tolerance; |
| } |
| |
| final Curve2DSample first = Curve2DSample(start, transform(start)); |
| final Curve2DSample last = Curve2DSample(end, transform(end)); |
| final List<Curve2DSample> samples = <Curve2DSample>[first]; |
| void sample(Curve2DSample p, Curve2DSample q, {bool forceSubdivide = false}) { |
| // Pick a random point somewhat near the center, which avoids aliasing |
| // problems with periodic curves. |
| final double t = p.t + (0.45 + 0.1 * rand.nextDouble()) * (q.t - p.t); |
| final Curve2DSample r = Curve2DSample(t, transform(t)); |
| |
| if (!forceSubdivide && isFlat(p.value, q.value, r.value)) { |
| samples.add(q); |
| } else { |
| sample(p, r); |
| sample(r, q); |
| } |
| } |
| // If the curve starts and ends on the same point, then we force it to |
| // subdivide at least once, because otherwise it will terminate immediately. |
| sample( |
| first, |
| last, |
| forceSubdivide: (first.value.dx - last.value.dx).abs() < tolerance && (first.value.dy - last.value.dy).abs() < tolerance, |
| ); |
| return samples; |
| } |
| |
| /// Returns a seed value used by [generateSamples] to seed a random number |
| /// generator to avoid sample aliasing. |
| /// |
| /// Subclasses should override this and provide a custom seed. |
| /// |
| /// The value returned should be the same each time it is called, unless the |
| /// curve definition changes. |
| @protected |
| int get samplingSeed => 0; |
| |
| /// Returns the parameter `t` that corresponds to the given x value of the spline. |
| /// |
| /// This will only work properly for curves which are single-valued in x |
| /// (where every value of `x` maps to only one value in 'y', i.e. the curve |
| /// does not loop or curve back over itself). For curves that are not |
| /// single-valued, it will return the parameter for only one of the values at |
| /// the given `x` location. |
| double findInverse(double x) { |
| assert(x != null); |
| double start = 0.0; |
| double end = 1.0; |
| late double mid; |
| double offsetToOrigin(double pos) => x - transform(pos).dx; |
| // Use a binary search to find the inverse point within 1e-6, or 100 |
| // subdivisions, whichever comes first. |
| const double errorLimit = 1e-6; |
| int count = 100; |
| final double startValue = offsetToOrigin(start); |
| while ((end - start) / 2.0 > errorLimit && count > 0) { |
| mid = (end + start) / 2.0; |
| final double value = offsetToOrigin(mid); |
| if (value.sign == startValue.sign) { |
| start = mid; |
| } else { |
| end = mid; |
| } |
| count--; |
| } |
| return mid; |
| } |
| } |
| |
| /// A class that holds a sample of a 2D parametric curve, containing the [value] |
| /// (the X, Y coordinates) of the curve at the parametric value [t]. |
| /// |
| /// See also: |
| /// |
| /// * [Curve2D.generateSamples], which generates samples of this type. |
| /// * [Curve2D], a parametric curve that maps a double parameter to a 2D location. |
| class Curve2DSample { |
| /// Creates an object that holds a sample; used with [Curve2D] subclasses. |
| /// |
| /// All arguments must not be null. |
| const Curve2DSample(this.t, this.value) : assert(t != null), assert(value != null); |
| |
| /// The parametric location of this sample point along the curve. |
| final double t; |
| |
| /// The value (the X, Y coordinates) of the curve at parametric value [t]. |
| final Offset value; |
| |
| @override |
| String toString() { |
| return '[(${value.dx.toStringAsFixed(2)}, ${value.dy.toStringAsFixed(2)}), ${t.toStringAsFixed(2)}]'; |
| } |
| } |
| |
| /// A 2D spline that passes smoothly through the given control points using a |
| /// centripetal Catmull-Rom spline. |
| /// |
| /// When the curve is evaluated with [transform], the output values will move |
| /// smoothly from one control point to the next, passing through the control |
| /// points. |
| /// |
| /// {@template flutter.animation.CatmullRomSpline} |
| /// Unlike most cubic splines, Catmull-Rom splines have the advantage that their |
| /// curves pass through the control points given to them. They are cubic |
| /// polynomial representations, and, in fact, Catmull-Rom splines can be |
| /// converted mathematically into cubic splines. This class implements a |
| /// "centripetal" Catmull-Rom spline. The term centripetal implies that it won't |
| /// form loops or self-intersections within a single segment. |
| /// {@endtemplate} |
| /// |
| /// See also: |
| /// * [Centripetal Catmull–Rom splines](https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline) |
| /// on Wikipedia. |
| /// * [Parameterization and Applications of Catmull-Rom Curves](http://faculty.cs.tamu.edu/schaefer/research/cr_cad.pdf), |
| /// a paper on using Catmull-Rom splines. |
| /// * [CatmullRomCurve], an animation curve that uses a [CatmullRomSpline] as its |
| /// internal representation. |
| class CatmullRomSpline extends Curve2D { |
| /// Constructs a centripetal Catmull-Rom spline curve. |
| /// |
| /// The `controlPoints` argument is a list of four or more points that |
| /// describe the points that the curve must pass through. |
| /// |
| /// The optional `tension` argument controls how tightly the curve approaches |
| /// the given `controlPoints`. It must be in the range 0.0 to 1.0, inclusive. It |
| /// defaults to 0.0, which provides the smoothest curve. A value of 1.0 |
| /// produces a linear interpolation between points. |
| /// |
| /// The optional `endHandle` and `startHandle` points are the beginning and |
| /// ending handle positions. If not specified, they are created automatically |
| /// by extending the line formed by the first and/or last line segment in the |
| /// `controlPoints`, respectively. The spline will not go through these handle |
| /// points, but they will affect the slope of the line at the beginning and |
| /// end of the spline. The spline will attempt to match the slope of the line |
| /// formed by the start or end handle and the neighboring first or last |
| /// control point. The default is chosen so that the slope of the line at the |
| /// ends matches that of the first or last line segment in the control points. |
| /// |
| /// The `tension` and `controlPoints` arguments must not be null, and the |
| /// `controlPoints` list must contain at least four control points to |
| /// interpolate. |
| /// |
| /// The internal curve data structures are lazily computed the first time |
| /// [transform] is called. If you would rather pre-compute the structures, |
| /// use [CatmullRomSpline.precompute] instead. |
| CatmullRomSpline( |
| List<Offset> controlPoints, { |
| double tension = 0.0, |
| Offset? startHandle, |
| Offset? endHandle, |
| }) : assert(controlPoints != null), |
| assert(tension != null), |
| assert(tension <= 1.0, 'tension $tension must not be greater than 1.0.'), |
| assert(tension >= 0.0, 'tension $tension must not be negative.'), |
| assert(controlPoints.length > 3, 'There must be at least four control points to create a CatmullRomSpline.'), |
| _controlPoints = controlPoints, |
| _startHandle = startHandle, |
| _endHandle = endHandle, |
| _tension = tension, |
| _cubicSegments = <List<Offset>>[]; |
| |
| /// Constructs a centripetal Catmull-Rom spline curve. |
| /// |
| /// The same as [CatmullRomSpline.new], except that the internal data |
| /// structures are precomputed instead of being computed lazily. |
| CatmullRomSpline.precompute( |
| List<Offset> controlPoints, { |
| double tension = 0.0, |
| Offset? startHandle, |
| Offset? endHandle, |
| }) : assert(controlPoints != null), |
| assert(tension != null), |
| assert(tension <= 1.0, 'tension $tension must not be greater than 1.0.'), |
| assert(tension >= 0.0, 'tension $tension must not be negative.'), |
| assert(controlPoints.length > 3, 'There must be at least four control points to create a CatmullRomSpline.'), |
| _controlPoints = null, |
| _startHandle = null, |
| _endHandle = null, |
| _tension = null, |
| _cubicSegments = _computeSegments(controlPoints, tension, startHandle: startHandle, endHandle: endHandle); |
| |
| |
| static List<List<Offset>> _computeSegments( |
| List<Offset> controlPoints, |
| double tension, { |
| Offset? startHandle, |
| Offset? endHandle, |
| }) { |
| // If not specified, select the first and last control points (which are |
| // handles: they are not intersected by the resulting curve) so that they |
| // extend the first and last segments, respectively. |
| startHandle ??= controlPoints[0] * 2.0 - controlPoints[1]; |
| endHandle ??= controlPoints.last * 2.0 - controlPoints[controlPoints.length - 2]; |
| final List<Offset> allPoints = <Offset>[ |
| startHandle, |
| ...controlPoints, |
| endHandle, |
| ]; |
| |
| // An alpha of 0.5 is what makes it a centripetal Catmull-Rom spline. A |
| // value of 0.0 would make it a uniform Catmull-Rom spline, and a value of |
| // 1.0 would make it a chordal Catmull-Rom spline. Non-centripetal values |
| // for alpha can give self-intersecting behavior or looping within a |
| // segment. |
| const double alpha = 0.5; |
| final double reverseTension = 1.0 - tension; |
| final List<List<Offset>> result = <List<Offset>>[]; |
| for (int i = 0; i < allPoints.length - 3; ++i) { |
| final List<Offset> curve = <Offset>[allPoints[i], allPoints[i + 1], allPoints[i + 2], allPoints[i + 3]]; |
| final Offset diffCurve10 = curve[1] - curve[0]; |
| final Offset diffCurve21 = curve[2] - curve[1]; |
| final Offset diffCurve32 = curve[3] - curve[2]; |
| final double t01 = math.pow(diffCurve10.distance, alpha).toDouble(); |
| final double t12 = math.pow(diffCurve21.distance, alpha).toDouble(); |
| final double t23 = math.pow(diffCurve32.distance, alpha).toDouble(); |
| |
| final Offset m1 = (diffCurve21 + (diffCurve10 / t01 - (curve[2] - curve[0]) / (t01 + t12)) * t12) * reverseTension; |
| final Offset m2 = (diffCurve21 + (diffCurve32 / t23 - (curve[3] - curve[1]) / (t12 + t23)) * t12) * reverseTension; |
| final Offset sumM12 = m1 + m2; |
| |
| final List<Offset> segment = <Offset>[ |
| diffCurve21 * -2.0 + sumM12, |
| diffCurve21 * 3.0 - m1 - sumM12, |
| m1, |
| curve[1], |
| ]; |
| result.add(segment); |
| } |
| return result; |
| } |
| |
| // The list of control point lists for each cubic segment of the spline. |
| final List<List<Offset>> _cubicSegments; |
| |
| // This is non-empty only if the _cubicSegments are being computed lazily. |
| final List<Offset>? _controlPoints; |
| final Offset? _startHandle; |
| final Offset? _endHandle; |
| final double? _tension; |
| |
| void _initializeIfNeeded() { |
| if (_cubicSegments.isNotEmpty) { |
| return; |
| } |
| _cubicSegments.addAll( |
| _computeSegments(_controlPoints!, _tension!, startHandle: _startHandle, endHandle: _endHandle), |
| ); |
| } |
| |
| @override |
| @protected |
| int get samplingSeed { |
| _initializeIfNeeded(); |
| final Offset seedPoint = _cubicSegments[0][1]; |
| return ((seedPoint.dx + seedPoint.dy) * 10000).round(); |
| } |
| |
| @override |
| Offset transformInternal(double t) { |
| _initializeIfNeeded(); |
| final double length = _cubicSegments.length.toDouble(); |
| final double position; |
| final double localT; |
| final int index; |
| if (t < 1.0) { |
| position = t * length; |
| localT = position % 1.0; |
| index = position.floor(); |
| } else { |
| position = length; |
| localT = 1.0; |
| index = _cubicSegments.length - 1; |
| } |
| final List<Offset> cubicControlPoints = _cubicSegments[index]; |
| final double localT2 = localT * localT; |
| return cubicControlPoints[0] * localT2 * localT |
| + cubicControlPoints[1] * localT2 |
| + cubicControlPoints[2] * localT |
| + cubicControlPoints[3]; |
| } |
| } |
| |
| /// An animation easing curve that passes smoothly through the given control |
| /// points using a centripetal Catmull-Rom spline. |
| /// |
| /// When this curve is evaluated with [transform], the values will interpolate |
| /// smoothly from one control point to the next, passing through (0.0, 0.0), the |
| /// given points, and then (1.0, 1.0). |
| /// |
| /// {@macro flutter.animation.CatmullRomSpline} |
| /// |
| /// This class uses a centripetal Catmull-Rom curve (a [CatmullRomSpline]) as |
| /// its internal representation. The term centripetal implies that it won't form |
| /// loops or self-intersections within a single segment, and corresponds to a |
| /// Catmull-Rom α (alpha) value of 0.5. |
| /// |
| /// See also: |
| /// |
| /// * [CatmullRomSpline], the 2D spline that this curve uses to generate its values. |
| /// * A Wikipedia article on [centripetal Catmull-Rom splines](https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline). |
| /// * [CatmullRomCurve.new] for a description of the constraints put on the |
| /// input control points. |
| /// * This [paper on using Catmull-Rom splines](http://faculty.cs.tamu.edu/schaefer/research/cr_cad.pdf). |
| class CatmullRomCurve extends Curve { |
| /// Constructs a centripetal [CatmullRomCurve]. |
| /// |
| /// It takes a list of two or more points that describe the points that the |
| /// curve must pass through. See [controlPoints] for a description of the |
| /// restrictions placed on control points. In addition to the given |
| /// [controlPoints], the curve will begin with an implicit control point at |
| /// (0.0, 0.0) and end with an implicit control point at (1.0, 1.0), so that |
| /// the curve begins and ends at those points. |
| /// |
| /// The optional [tension] argument controls how tightly the curve approaches |
| /// the given `controlPoints`. It must be in the range 0.0 to 1.0, inclusive. It |
| /// defaults to 0.0, which provides the smoothest curve. A value of 1.0 |
| /// is equivalent to a linear interpolation between points. |
| /// |
| /// The internal curve data structures are lazily computed the first time |
| /// [transform] is called. If you would rather pre-compute the curve, use |
| /// [CatmullRomCurve.precompute] instead. |
| /// |
| /// All of the arguments must not be null. |
| /// |
| /// See also: |
| /// |
| /// * This [paper on using Catmull-Rom splines](http://faculty.cs.tamu.edu/schaefer/research/cr_cad.pdf). |
| CatmullRomCurve(this.controlPoints, {this.tension = 0.0}) |
| : assert(tension != null), |
| assert(() { |
| return validateControlPoints( |
| controlPoints, |
| tension: tension, |
| reasons: _debugAssertReasons..clear(), |
| ); |
| }(), 'control points $controlPoints could not be validated:\n ${_debugAssertReasons.join('\n ')}'), |
| // Pre-compute samples so that we don't have to evaluate the spline's inverse |
| // all the time in transformInternal. |
| _precomputedSamples = <Curve2DSample>[]; |
| |
| /// Constructs a centripetal [CatmullRomCurve]. |
| /// |
| /// Same as [CatmullRomCurve.new], but it precomputes the internal curve data |
| /// structures for a more predictable computation load. |
| CatmullRomCurve.precompute(this.controlPoints, {this.tension = 0.0}) |
| : assert(tension != null), |
| assert(() { |
| return validateControlPoints( |
| controlPoints, |
| tension: tension, |
| reasons: _debugAssertReasons..clear(), |
| ); |
| }(), 'control points $controlPoints could not be validated:\n ${_debugAssertReasons.join('\n ')}'), |
| // Pre-compute samples so that we don't have to evaluate the spline's inverse |
| // all the time in transformInternal. |
| _precomputedSamples = _computeSamples(controlPoints, tension); |
| |
| static List<Curve2DSample> _computeSamples(List<Offset> controlPoints, double tension) { |
| return CatmullRomSpline.precompute( |
| // Force the first and last control points for the spline to be (0, 0) |
| // and (1, 1), respectively. |
| <Offset>[Offset.zero, ...controlPoints, const Offset(1.0, 1.0)], |
| tension: tension, |
| ).generateSamples(tolerance: 1e-12).toList(); |
| } |
| |
| /// A static accumulator for assertion failures. Not used in release mode. |
| static final List<String> _debugAssertReasons = <String>[]; |
| |
| // The precomputed approximation curve, so that evaluation of the curve is |
| // efficient. |
| // |
| // If the curve is constructed lazily, then this will be empty, and will be filled |
| // the first time transform is called. |
| final List<Curve2DSample> _precomputedSamples; |
| |
| /// The control points used to create this curve. |
| /// |
| /// The `dx` value of each [Offset] in [controlPoints] represents the |
| /// animation value at which the curve should pass through the `dy` value of |
| /// the same control point. |
| /// |
| /// The [controlPoints] list must meet the following criteria: |
| /// |
| /// * The list must contain at least two points. |
| /// * The X value of each point must be greater than 0.0 and less then 1.0. |
| /// * The X values of each point must be greater than the |
| /// previous point's X value (i.e. monotonically increasing). The Y values |
| /// are not constrained. |
| /// * The resulting spline must be single-valued in X. That is, for each X |
| /// value, there must be exactly one Y value. This means that the control |
| /// points must not generated a spline that loops or overlaps itself. |
| /// |
| /// The static function [validateControlPoints] can be used to check that |
| /// these conditions are met, and will return true if they are. In debug mode, |
| /// it will also optionally return a list of reasons in text form. In debug |
| /// mode, the constructor will assert that these conditions are met and print |
| /// the reasons if the assert fires. |
| /// |
| /// When the curve is evaluated with [transform], the values will interpolate |
| /// smoothly from one control point to the next, passing through (0.0, 0.0), the |
| /// given control points, and (1.0, 1.0). |
| final List<Offset> controlPoints; |
| |
| /// The "tension" of the curve. |
| /// |
| /// The `tension` attribute controls how tightly the curve approaches the |
| /// given [controlPoints]. It must be in the range 0.0 to 1.0, inclusive. It |
| /// is optional, and defaults to 0.0, which provides the smoothest curve. A |
| /// value of 1.0 is equivalent to a linear interpolation between control |
| /// points. |
| final double tension; |
| |
| /// Validates that a given set of control points for a [CatmullRomCurve] is |
| /// well-formed and will not produce a spline that self-intersects. |
| /// |
| /// This method is also used in debug mode to validate a curve to make sure |
| /// that it won't violate the contract for the [CatmullRomCurve.new] |
| /// constructor. |
| /// |
| /// If in debug mode, and `reasons` is non-null, this function will fill in |
| /// `reasons` with descriptions of the problems encountered. The `reasons` |
| /// argument is ignored in release mode. |
| /// |
| /// In release mode, this function can be used to decide if a proposed |
| /// modification to the curve will result in a valid curve. |
| static bool validateControlPoints( |
| List<Offset>? controlPoints, { |
| double tension = 0.0, |
| List<String>? reasons, |
| }) { |
| assert(tension != null); |
| if (controlPoints == null) { |
| assert(() { |
| reasons?.add('Supplied control points cannot be null'); |
| return true; |
| }()); |
| return false; |
| } |
| |
| if (controlPoints.length < 2) { |
| assert(() { |
| reasons?.add('There must be at least two points supplied to create a valid curve.'); |
| return true; |
| }()); |
| return false; |
| } |
| |
| controlPoints = <Offset>[Offset.zero, ...controlPoints, const Offset(1.0, 1.0)]; |
| final Offset startHandle = controlPoints[0] * 2.0 - controlPoints[1]; |
| final Offset endHandle = controlPoints.last * 2.0 - controlPoints[controlPoints.length - 2]; |
| controlPoints = <Offset>[startHandle, ...controlPoints, endHandle]; |
| double lastX = -double.infinity; |
| for (int i = 0; i < controlPoints.length; ++i) { |
| if (i > 1 && |
| i < controlPoints.length - 2 && |
| (controlPoints[i].dx <= 0.0 || controlPoints[i].dx >= 1.0)) { |
| assert(() { |
| reasons?.add( |
| 'Control points must have X values between 0.0 and 1.0, exclusive. ' |
| 'Point $i has an x value (${controlPoints![i].dx}) which is outside the range.', |
| ); |
| return true; |
| }()); |
| return false; |
| } |
| if (controlPoints[i].dx <= lastX) { |
| assert(() { |
| reasons?.add( |
| 'Each X coordinate must be greater than the preceding X coordinate ' |
| '(i.e. must be monotonically increasing in X). Point $i has an x value of ' |
| '${controlPoints![i].dx}, which is not greater than $lastX', |
| ); |
| return true; |
| }()); |
| return false; |
| } |
| lastX = controlPoints[i].dx; |
| } |
| |
| bool success = true; |
| |
| // An empirical test to make sure things are single-valued in X. |
| lastX = -double.infinity; |
| const double tolerance = 1e-3; |
| final CatmullRomSpline testSpline = CatmullRomSpline(controlPoints, tension: tension); |
| final double start = testSpline.findInverse(0.0); |
| final double end = testSpline.findInverse(1.0); |
| final Iterable<Curve2DSample> samplePoints = testSpline.generateSamples(start: start, end: end); |
| /// If the first and last points in the samples aren't at (0,0) or (1,1) |
| /// respectively, then the curve is multi-valued at the ends. |
| if (samplePoints.first.value.dy.abs() > tolerance || (1.0 - samplePoints.last.value.dy).abs() > tolerance) { |
| bool bail = true; |
| success = false; |
| assert(() { |
| reasons?.add( |
| 'The curve has more than one Y value at X = ${samplePoints.first.value.dx}. ' |
| 'Try moving some control points further away from this value of X, or increasing ' |
| 'the tension.', |
| ); |
| // No need to keep going if we're not giving reasons. |
| bail = reasons == null; |
| return true; |
| }()); |
| if (bail) { |
| // If we're not in debug mode, then we want to bail immediately |
| // instead of checking everything else. |
| return false; |
| } |
| } |
| for (final Curve2DSample sample in samplePoints) { |
| final Offset point = sample.value; |
| final double t = sample.t; |
| final double x = point.dx; |
| if (t >= start && t <= end && (x < -1e-3 || x > 1.0 + 1e-3)) { |
| bool bail = true; |
| success = false; |
| assert(() { |
| reasons?.add( |
| 'The resulting curve has an X value ($x) which is outside ' |
| 'the range [0.0, 1.0], inclusive.', |
| ); |
| // No need to keep going if we're not giving reasons. |
| bail = reasons == null; |
| return true; |
| }()); |
| if (bail) { |
| // If we're not in debug mode, then we want to bail immediately |
| // instead of checking all the segments. |
| return false; |
| } |
| } |
| if (x < lastX) { |
| bool bail = true; |
| success = false; |
| assert(() { |
| reasons?.add( |
| 'The curve has more than one Y value at x = $x. Try moving ' |
| 'some control points further apart in X, or increasing the tension.', |
| ); |
| // No need to keep going if we're not giving reasons. |
| bail = reasons == null; |
| return true; |
| }()); |
| if (bail) { |
| // If we're not in debug mode, then we want to bail immediately |
| // instead of checking all the segments. |
| return false; |
| } |
| } |
| lastX = x; |
| } |
| return success; |
| } |
| |
| @override |
| double transformInternal(double t) { |
| // Linearly interpolate between the two closest samples generated when the |
| // curve was created. |
| if (_precomputedSamples.isEmpty) { |
| // Compute the samples now if we were constructed lazily. |
| _precomputedSamples.addAll(_computeSamples(controlPoints, tension)); |
| } |
| int start = 0; |
| int end = _precomputedSamples.length - 1; |
| int mid; |
| Offset value; |
| Offset startValue = _precomputedSamples[start].value; |
| Offset endValue = _precomputedSamples[end].value; |
| // Use a binary search to find the index of the sample point that is just |
| // before t. |
| while (end - start > 1) { |
| mid = (end + start) ~/ 2; |
| value = _precomputedSamples[mid].value; |
| if (t >= value.dx) { |
| start = mid; |
| startValue = value; |
| } else { |
| end = mid; |
| endValue = value; |
| } |
| } |
| |
| // Now interpolate between the found sample and the next one. |
| final double t2 = (t - startValue.dx) / (endValue.dx - startValue.dx); |
| return lerpDouble(startValue.dy, endValue.dy, t2)!; |
| } |
| } |
| |
| /// A curve that is the reversed inversion of its given curve. |
| /// |
| /// This curve evaluates the given curve in reverse (i.e., from 1.0 to 0.0 as t |
| /// increases from 0.0 to 1.0) and returns the inverse of the given curve's |
| /// value (i.e., 1.0 minus the given curve's value). |
| /// |
| /// This is the class used to implement the [flipped] getter on curves. |
| /// |
| /// This is often useful with [CurvedAnimation.reverseCurve]. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_flipped.mp4} |
| /// |
| /// See also: |
| /// |
| /// * [Curve.flipped], which provides the [FlippedCurve] of a [Curve]. |
| /// * [ReverseAnimation], which reverses an [Animation] rather than a [Curve]. |
| /// * [CurvedAnimation], which can take a separate curve and reverse curve. |
| class FlippedCurve extends Curve { |
| /// Creates a flipped curve. |
| /// |
| /// The [curve] argument must not be null. |
| const FlippedCurve(this.curve) : assert(curve != null); |
| |
| /// The curve that is being flipped. |
| final Curve curve; |
| |
| @override |
| double transformInternal(double t) => 1.0 - curve.transform(1.0 - t); |
| |
| @override |
| String toString() { |
| return '${objectRuntimeType(this, 'FlippedCurve')}($curve)'; |
| } |
| } |
| |
| /// A curve where the rate of change starts out quickly and then decelerates; an |
| /// upside-down `f(t) = t²` parabola. |
| /// |
| /// This is equivalent to the Android `DecelerateInterpolator` class with a unit |
| /// factor (the default factor). |
| /// |
| /// See [Curves.decelerate] for an instance of this class. |
| class _DecelerateCurve extends Curve { |
| const _DecelerateCurve._(); |
| |
| @override |
| double transformInternal(double t) { |
| // Intended to match the behavior of: |
| // https://android.googlesource.com/platform/frameworks/base/+/master/core/java/android/view/animation/DecelerateInterpolator.java |
| // ...as of December 2016. |
| t = 1.0 - t; |
| return 1.0 - t * t; |
| } |
| } |
| |
| // BOUNCE CURVES |
| |
| double _bounce(double t) { |
| if (t < 1.0 / 2.75) { |
| return 7.5625 * t * t; |
| } else if (t < 2 / 2.75) { |
| t -= 1.5 / 2.75; |
| return 7.5625 * t * t + 0.75; |
| } else if (t < 2.5 / 2.75) { |
| t -= 2.25 / 2.75; |
| return 7.5625 * t * t + 0.9375; |
| } |
| t -= 2.625 / 2.75; |
| return 7.5625 * t * t + 0.984375; |
| } |
| |
| /// An oscillating curve that grows in magnitude. |
| /// |
| /// See [Curves.bounceIn] for an instance of this class. |
| class _BounceInCurve extends Curve { |
| const _BounceInCurve._(); |
| |
| @override |
| double transformInternal(double t) { |
| return 1.0 - _bounce(1.0 - t); |
| } |
| } |
| |
| /// An oscillating curve that shrink in magnitude. |
| /// |
| /// See [Curves.bounceOut] for an instance of this class. |
| class _BounceOutCurve extends Curve { |
| const _BounceOutCurve._(); |
| |
| @override |
| double transformInternal(double t) { |
| return _bounce(t); |
| } |
| } |
| |
| /// An oscillating curve that first grows and then shrink in magnitude. |
| /// |
| /// See [Curves.bounceInOut] for an instance of this class. |
| class _BounceInOutCurve extends Curve { |
| const _BounceInOutCurve._(); |
| |
| @override |
| double transformInternal(double t) { |
| if (t < 0.5) { |
| return (1.0 - _bounce(1.0 - t * 2.0)) * 0.5; |
| } else { |
| return _bounce(t * 2.0 - 1.0) * 0.5 + 0.5; |
| } |
| } |
| } |
| |
| |
| // ELASTIC CURVES |
| |
| /// An oscillating curve that grows in magnitude while overshooting its bounds. |
| /// |
| /// An instance of this class using the default period of 0.4 is available as |
| /// [Curves.elasticIn]. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_in.mp4} |
| class ElasticInCurve extends Curve { |
| /// Creates an elastic-in curve. |
| /// |
| /// Rather than creating a new instance, consider using [Curves.elasticIn]. |
| const ElasticInCurve([this.period = 0.4]); |
| |
| /// The duration of the oscillation. |
| final double period; |
| |
| @override |
| double transformInternal(double t) { |
| final double s = period / 4.0; |
| t = t - 1.0; |
| return -math.pow(2.0, 10.0 * t) * math.sin((t - s) * (math.pi * 2.0) / period); |
| } |
| |
| @override |
| String toString() { |
| return '${objectRuntimeType(this, 'ElasticInCurve')}($period)'; |
| } |
| } |
| |
| /// An oscillating curve that shrinks in magnitude while overshooting its bounds. |
| /// |
| /// An instance of this class using the default period of 0.4 is available as |
| /// [Curves.elasticOut]. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_out.mp4} |
| class ElasticOutCurve extends Curve { |
| /// Creates an elastic-out curve. |
| /// |
| /// Rather than creating a new instance, consider using [Curves.elasticOut]. |
| const ElasticOutCurve([this.period = 0.4]); |
| |
| /// The duration of the oscillation. |
| final double period; |
| |
| @override |
| double transformInternal(double t) { |
| final double s = period / 4.0; |
| return math.pow(2.0, -10 * t) * math.sin((t - s) * (math.pi * 2.0) / period) + 1.0; |
| } |
| |
| @override |
| String toString() { |
| return '${objectRuntimeType(this, 'ElasticOutCurve')}($period)'; |
| } |
| } |
| |
| /// An oscillating curve that grows and then shrinks in magnitude while |
| /// overshooting its bounds. |
| /// |
| /// An instance of this class using the default period of 0.4 is available as |
| /// [Curves.elasticInOut]. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_in_out.mp4} |
| class ElasticInOutCurve extends Curve { |
| /// Creates an elastic-in-out curve. |
| /// |
| /// Rather than creating a new instance, consider using [Curves.elasticInOut]. |
| const ElasticInOutCurve([this.period = 0.4]); |
| |
| /// The duration of the oscillation. |
| final double period; |
| |
| @override |
| double transformInternal(double t) { |
| final double s = period / 4.0; |
| t = 2.0 * t - 1.0; |
| if (t < 0.0) { |
| return -0.5 * math.pow(2.0, 10.0 * t) * math.sin((t - s) * (math.pi * 2.0) / period); |
| } else { |
| return math.pow(2.0, -10.0 * t) * math.sin((t - s) * (math.pi * 2.0) / period) * 0.5 + 1.0; |
| } |
| } |
| |
| @override |
| String toString() { |
| return '${objectRuntimeType(this, 'ElasticInOutCurve')}($period)'; |
| } |
| } |
| |
| |
| // PREDEFINED CURVES |
| |
| /// A collection of common animation curves. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_in_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_decelerate.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_sine.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quad.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_cubic.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quart.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quint.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_expo.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_circ.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_back.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_sine.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quad.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_cubic.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quart.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quint.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_expo.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_circ.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_back.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_sine.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quad.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_cubic.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quart.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quint.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_expo.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_circ.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_back.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_in_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_out.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_fast_out_slow_in.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_slow_middle.mp4} |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_linear.mp4} |
| /// |
| /// See also: |
| /// |
| /// * [Curve], the interface implemented by the constants available from the |
| /// [Curves] class. |
| class Curves { |
| // This class is not meant to be instantiated or extended; this constructor |
| // prevents instantiation and extension. |
| Curves._(); |
| |
| /// A linear animation curve. |
| /// |
| /// This is the identity map over the unit interval: its [Curve.transform] |
| /// method returns its input unmodified. This is useful as a default curve for |
| /// cases where a [Curve] is required but no actual curve is desired. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_linear.mp4} |
| static const Curve linear = _Linear._(); |
| |
| /// A curve where the rate of change starts out quickly and then decelerates; an |
| /// upside-down `f(t) = t²` parabola. |
| /// |
| /// This is equivalent to the Android `DecelerateInterpolator` class with a unit |
| /// factor (the default factor). |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_decelerate.mp4} |
| static const Curve decelerate = _DecelerateCurve._(); |
| |
| /// A curve that is very steep and linear at the beginning, but quickly flattens out |
| /// and very slowly eases in. |
| /// |
| /// By default is the curve used to animate pages on iOS back to their original |
| /// position if a swipe gesture is ended midway through a swipe. |
| /// |
| /// {@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 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} |
| static const Cubic ease = Cubic(0.25, 0.1, 0.25, 1.0); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in.mp4} |
| static const Cubic easeIn = Cubic(0.42, 0.0, 1.0, 1.0); |
| |
| /// A cubic animation curve that starts slowly and ends linearly. |
| /// |
| /// The symmetric animation to [linearToEaseOut]. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_to_linear.mp4} |
| static const Cubic easeInToLinear = Cubic(0.67, 0.03, 0.65, 0.09); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. This is |
| /// similar to [Curves.easeIn], but with sinusoidal easing for a slightly less |
| /// abrupt beginning and end. Nonetheless, the result is quite gentle and is |
| /// hard to distinguish from [Curves.linear] at a glance. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_sine.mp4} |
| static const Cubic easeInSine = Cubic(0.47, 0.0, 0.745, 0.715); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. Based on a |
| /// quadratic equation where `f(t) = t²`, this is effectively the inverse of |
| /// [Curves.decelerate]. |
| /// |
| /// Compared to [Curves.easeInSine], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quad.mp4} |
| static const Cubic easeInQuad = Cubic(0.55, 0.085, 0.68, 0.53); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. This curve is |
| /// based on a cubic equation where `f(t) = t³`. The result is a safe sweet |
| /// spot when choosing a curve for widgets animating off the viewport. |
| /// |
| /// Compared to [Curves.easeInQuad], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_cubic.mp4} |
| static const Cubic easeInCubic = Cubic(0.55, 0.055, 0.675, 0.19); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. This curve is |
| /// based on a quartic equation where `f(t) = t⁴`. |
| /// |
| /// Animations using this curve or steeper curves will benefit from a longer |
| /// duration to avoid motion feeling unnatural. |
| /// |
| /// Compared to [Curves.easeInCubic], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quart.mp4} |
| static const Cubic easeInQuart = Cubic(0.895, 0.03, 0.685, 0.22); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. This curve is |
| /// based on a quintic equation where `f(t) = t⁵`. |
| /// |
| /// Compared to [Curves.easeInQuart], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_quint.mp4} |
| static const Cubic easeInQuint = Cubic(0.755, 0.05, 0.855, 0.06); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. This curve is |
| /// based on an exponential equation where `f(t) = 2¹⁰⁽ᵗ⁻¹⁾`. |
| /// |
| /// Using this curve can give your animations extra flare, but a longer |
| /// duration may need to be used to compensate for the steepness of the curve. |
| /// |
| /// Compared to [Curves.easeInQuint], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_expo.mp4} |
| static const Cubic easeInExpo = Cubic(0.95, 0.05, 0.795, 0.035); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. This curve is |
| /// effectively the bottom-right quarter of a circle. |
| /// |
| /// Like [Curves.easeInExpo], this curve is fairly dramatic and will reduce |
| /// the clarity of an animation if not given a longer duration. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_circ.mp4} |
| static const Cubic easeInCirc = Cubic(0.6, 0.04, 0.98, 0.335); |
| |
| /// A cubic animation curve that starts slowly and ends quickly. This curve |
| /// is similar to [Curves.elasticIn] in that it overshoots its bounds before |
| /// reaching its end. Instead of repeated swinging motions before ascending, |
| /// though, this curve overshoots once, then continues to ascend. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_back.mp4} |
| static const Cubic easeInBack = Cubic(0.6, -0.28, 0.735, 0.045); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out.mp4} |
| static const Cubic easeOut = Cubic(0.0, 0.0, 0.58, 1.0); |
| |
| /// A cubic animation curve that starts linearly and ends slowly. |
| /// |
| /// A symmetric animation to [easeInToLinear]. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_linear_to_ease_out.mp4} |
| static const Cubic linearToEaseOut = Cubic(0.35, 0.91, 0.33, 0.97); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This is |
| /// similar to [Curves.easeOut], but with sinusoidal easing for a slightly |
| /// less abrupt beginning and end. Nonetheless, the result is quite gentle and |
| /// is hard to distinguish from [Curves.linear] at a glance. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_sine.mp4} |
| static const Cubic easeOutSine = Cubic(0.39, 0.575, 0.565, 1.0); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This is |
| /// effectively the same as [Curves.decelerate], only simulated using a cubic |
| /// bezier function. |
| /// |
| /// Compared to [Curves.easeOutSine], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quad.mp4} |
| static const Cubic easeOutQuad = Cubic(0.25, 0.46, 0.45, 0.94); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This curve is |
| /// a flipped version of [Curves.easeInCubic]. |
| /// |
| /// The result is a safe sweet spot when choosing a curve for animating a |
| /// widget's position entering or already inside the viewport. |
| /// |
| /// Compared to [Curves.easeOutQuad], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_cubic.mp4} |
| static const Cubic easeOutCubic = Cubic(0.215, 0.61, 0.355, 1.0); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This curve is |
| /// a flipped version of [Curves.easeInQuart]. |
| /// |
| /// Animations using this curve or steeper curves will benefit from a longer |
| /// duration to avoid motion feeling unnatural. |
| /// |
| /// Compared to [Curves.easeOutCubic], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quart.mp4} |
| static const Cubic easeOutQuart = Cubic(0.165, 0.84, 0.44, 1.0); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This curve is |
| /// a flipped version of [Curves.easeInQuint]. |
| /// |
| /// Compared to [Curves.easeOutQuart], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_quint.mp4} |
| static const Cubic easeOutQuint = Cubic(0.23, 1.0, 0.32, 1.0); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This curve is |
| /// a flipped version of [Curves.easeInExpo]. Using this curve can give your |
| /// animations extra flare, but a longer duration may need to be used to |
| /// compensate for the steepness of the curve. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_expo.mp4} |
| static const Cubic easeOutExpo = Cubic(0.19, 1.0, 0.22, 1.0); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This curve is |
| /// effectively the top-left quarter of a circle. |
| /// |
| /// Like [Curves.easeOutExpo], this curve is fairly dramatic and will reduce |
| /// the clarity of an animation if not given a longer duration. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_circ.mp4} |
| static const Cubic easeOutCirc = Cubic(0.075, 0.82, 0.165, 1.0); |
| |
| /// A cubic animation curve that starts quickly and ends slowly. This curve is |
| /// similar to [Curves.elasticOut] in that it overshoots its bounds before |
| /// reaching its end. Instead of repeated swinging motions after ascending, |
| /// though, this curve only overshoots once. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_out_back.mp4} |
| static const Cubic easeOutBack = Cubic(0.175, 0.885, 0.32, 1.275); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out.mp4} |
| static const Cubic easeInOut = Cubic(0.42, 0.0, 0.58, 1.0); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. This is similar to [Curves.easeInOut], but with sinusoidal easing |
| /// for a slightly less abrupt beginning and end. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_sine.mp4} |
| static const Cubic easeInOutSine = Cubic(0.445, 0.05, 0.55, 0.95); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. This curve can be imagined as [Curves.easeInQuad] as the first |
| /// half, and [Curves.easeOutQuad] as the second. |
| /// |
| /// Compared to [Curves.easeInOutSine], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quad.mp4} |
| static const Cubic easeInOutQuad = Cubic(0.455, 0.03, 0.515, 0.955); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. This curve can be imagined as [Curves.easeInCubic] as the first |
| /// half, and [Curves.easeOutCubic] as the second. |
| /// |
| /// The result is a safe sweet spot when choosing a curve for a widget whose |
| /// initial and final positions are both within the viewport. |
| /// |
| /// Compared to [Curves.easeInOutQuad], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_cubic.mp4} |
| static const Cubic easeInOutCubic = Cubic(0.645, 0.045, 0.355, 1.0); |
| |
| /// A cubic animation curve that starts slowly, speeds up shortly thereafter, |
| /// and then ends slowly. This curve can be imagined as a steeper version of |
| /// [easeInOutCubic]. |
| /// |
| /// The result is a more emphasized eased curve when choosing a curve for a |
| /// widget whose initial and final positions are both within the viewport. |
| /// |
| /// Compared to [Curves.easeInOutCubic], this curve is slightly steeper. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_cubic_emphasized.mp4} |
| static const ThreePointCubic easeInOutCubicEmphasized = ThreePointCubic( |
| Offset(0.05, 0), Offset(0.133333, 0.06), |
| Offset(0.166666, 0.4), |
| Offset(0.208333, 0.82), Offset(0.25, 1), |
| ); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. This curve can be imagined as [Curves.easeInQuart] as the first |
| /// half, and [Curves.easeOutQuart] as the second. |
| /// |
| /// Animations using this curve or steeper curves will benefit from a longer |
| /// duration to avoid motion feeling unnatural. |
| /// |
| /// Compared to [Curves.easeInOutCubic], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quart.mp4} |
| static const Cubic easeInOutQuart = Cubic(0.77, 0.0, 0.175, 1.0); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. This curve can be imagined as [Curves.easeInQuint] as the first |
| /// half, and [Curves.easeOutQuint] as the second. |
| /// |
| /// Compared to [Curves.easeInOutQuart], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_quint.mp4} |
| static const Cubic easeInOutQuint = Cubic(0.86, 0.0, 0.07, 1.0); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. |
| /// |
| /// Since this curve is arrived at with an exponential function, the midpoint |
| /// is exceptionally steep. Extra consideration should be taken when designing |
| /// an animation using this. |
| /// |
| /// Compared to [Curves.easeInOutQuint], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_expo.mp4} |
| static const Cubic easeInOutExpo = Cubic(1.0, 0.0, 0.0, 1.0); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. This curve can be imagined as [Curves.easeInCirc] as the first |
| /// half, and [Curves.easeOutCirc] as the second. |
| /// |
| /// Like [Curves.easeInOutExpo], this curve is fairly dramatic and will reduce |
| /// the clarity of an animation if not given a longer duration. |
| /// |
| /// Compared to [Curves.easeInOutExpo], this curve is slightly steeper. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_circ.mp4} |
| static const Cubic easeInOutCirc = Cubic(0.785, 0.135, 0.15, 0.86); |
| |
| /// A cubic animation curve that starts slowly, speeds up, and then ends |
| /// slowly. This curve can be imagined as [Curves.easeInBack] as the first |
| /// half, and [Curves.easeOutBack] as the second. |
| /// |
| /// Since two curves are used as a basis for this curve, the resulting |
| /// animation will overshoot its bounds twice before reaching its end - first |
| /// by exceeding its lower bound, then exceeding its upper bound and finally |
| /// descending to its final position. |
| /// |
| /// Derived from Robert Penner’s easing functions. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_ease_in_out_back.mp4} |
| static const Cubic easeInOutBack = Cubic(0.68, -0.55, 0.265, 1.55); |
| |
| /// A curve that starts quickly and eases into its final position. |
| /// |
| /// Over the course of the animation, the object spends more time near its |
| /// final destination. As a result, the user isn’t left waiting for the |
| /// animation to finish, and the negative effects of motion are minimized. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_fast_out_slow_in.mp4} |
| /// |
| /// See also: |
| /// |
| /// * [standardEasing], the name for this curve in the Material specification. |
| static const Cubic fastOutSlowIn = Cubic(0.4, 0.0, 0.2, 1.0); |
| |
| /// A cubic animation curve that starts quickly, slows down, and then ends |
| /// quickly. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_slow_middle.mp4} |
| static const Cubic slowMiddle = Cubic(0.15, 0.85, 0.85, 0.15); |
| |
| /// An oscillating curve that grows in magnitude. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_in.mp4} |
| static const Curve bounceIn = _BounceInCurve._(); |
| |
| /// An oscillating curve that first grows and then shrink in magnitude. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_out.mp4} |
| static const Curve bounceOut = _BounceOutCurve._(); |
| |
| /// An oscillating curve that first grows and then shrink in magnitude. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_bounce_in_out.mp4} |
| static const Curve bounceInOut = _BounceInOutCurve._(); |
| |
| /// An oscillating curve that grows in magnitude while overshooting its bounds. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_in.mp4} |
| static const ElasticInCurve elasticIn = ElasticInCurve(); |
| |
| /// An oscillating curve that shrinks in magnitude while overshooting its bounds. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_out.mp4} |
| static const ElasticOutCurve elasticOut = ElasticOutCurve(); |
| |
| /// An oscillating curve that grows and then shrinks in magnitude while overshooting its bounds. |
| /// |
| /// {@animation 464 192 https://flutter.github.io/assets-for-api-docs/assets/animation/curve_elastic_in_out.mp4} |
| static const ElasticInOutCurve elasticInOut = ElasticInOutCurve(); |
| } |