engine/lib/ui/geometry.dart

// Copyright 2013 The Flutter Authors. All rights reserved.
// Use of this source code is governed by a BSD-style license that can be
// found in the LICENSE file.

part of dart.ui;

/// Base class for [Size] and [Offset], which are both ways to describe
/// a distance as a two-dimensional axis-aligned vector.
abstract class OffsetBase {
  /// Abstract const constructor. This constructor enables subclasses to provide
  /// const constructors so that they can be used in const expressions.
  ///
  /// The first argument sets the horizontal component, and the second the
  /// vertical component.
  const OffsetBase(this._dx, this._dy);

  final double _dx;
  final double _dy;

  /// Returns true if either component is [double.infinity], and false if both
  /// are finite (or negative infinity, or NaN).
  ///
  /// This is different than comparing for equality with an instance that has
  /// _both_ components set to [double.infinity].
  ///
  /// See also:
  ///
  ///  * [isFinite], which is true if both components are finite (and not NaN).
  bool get isInfinite => _dx >= double.infinity || _dy >= double.infinity;

  /// Whether both components are finite (neither infinite nor NaN).
  ///
  /// See also:
  ///
  ///  * [isInfinite], which returns true if either component is equal to
  ///    positive infinity.
  bool get isFinite => _dx.isFinite && _dy.isFinite;

  /// Less-than operator. Compares an [Offset] or [Size] to another [Offset] or
  /// [Size], and returns true if both the horizontal and vertical values of the
  /// left-hand-side operand are smaller than the horizontal and vertical values
  /// of the right-hand-side operand respectively. Returns false otherwise.
  ///
  /// This is a partial ordering. It is possible for two values to be neither
  /// less, nor greater than, nor equal to, another.
  bool operator <(OffsetBase other) => _dx < other._dx && _dy < other._dy;

  /// Less-than-or-equal-to operator. Compares an [Offset] or [Size] to another
  /// [Offset] or [Size], and returns true if both the horizontal and vertical
  /// values of the left-hand-side operand are smaller than or equal to the
  /// horizontal and vertical values of the right-hand-side operand
  /// respectively. Returns false otherwise.
  ///
  /// This is a partial ordering. It is possible for two values to be neither
  /// less, nor greater than, nor equal to, another.
  bool operator <=(OffsetBase other) => _dx <= other._dx && _dy <= other._dy;

  /// Greater-than operator. Compares an [Offset] or [Size] to another [Offset]
  /// or [Size], and returns true if both the horizontal and vertical values of
  /// the left-hand-side operand are bigger than the horizontal and vertical
  /// values of the right-hand-side operand respectively. Returns false
  /// otherwise.
  ///
  /// This is a partial ordering. It is possible for two values to be neither
  /// less, nor greater than, nor equal to, another.
  bool operator >(OffsetBase other) => _dx > other._dx && _dy > other._dy;

  /// Greater-than-or-equal-to operator. Compares an [Offset] or [Size] to
  /// another [Offset] or [Size], and returns true if both the horizontal and
  /// vertical values of the left-hand-side operand are bigger than or equal to
  /// the horizontal and vertical values of the right-hand-side operand
  /// respectively. Returns false otherwise.
  ///
  /// This is a partial ordering. It is possible for two values to be neither
  /// less, nor greater than, nor equal to, another.
  bool operator >=(OffsetBase other) => _dx >= other._dx && _dy >= other._dy;

  /// Equality operator. Compares an [Offset] or [Size] to another [Offset] or
  /// [Size], and returns true if the horizontal and vertical values of the
  /// left-hand-side operand are equal to the horizontal and vertical values of
  /// the right-hand-side operand respectively. Returns false otherwise.
  @override
  bool operator ==(dynamic other) {
    if (other is! OffsetBase)
      return false;
    final OffsetBase typedOther = other;
    return _dx == typedOther._dx &&
           _dy == typedOther._dy;
  }

  @override
  int get hashCode => hashValues(_dx, _dy);

  @override
  String toString() => 'OffsetBase(${_dx?.toStringAsFixed(1)}, ${_dy?.toStringAsFixed(1)})';
}

/// An immutable 2D floating-point offset.
///
/// Generally speaking, Offsets can be interpreted in two ways:
///
/// 1. As representing a point in Cartesian space a specified distance from a
///    separately-maintained origin. For example, the top-left position of
///    children in the [RenderBox] protocol is typically represented as an
///    [Offset] from the top left of the parent box.
///
/// 2. As a vector that can be applied to coordinates. For example, when
///    painting a [RenderObject], the parent is passed an [Offset] from the
///    screen's origin which it can add to the offsets of its children to find
///    the [Offset] from the screen's origin to each of the children.
///
/// Because a particular [Offset] can be interpreted as one sense at one time
/// then as the other sense at a later time, the same class is used for both
/// senses.
///
/// See also:
///
///  * [Size], which represents a vector describing the size of a rectangle.
class Offset extends OffsetBase {
  /// Creates an offset. The first argument sets [dx], the horizontal component,
  /// and the second sets [dy], the vertical component.
  const Offset(double dx, double dy) : super(dx, dy);

  /// Creates an offset from its [direction] and [distance].
  ///
  /// The direction is in radians clockwise from the positive x-axis.
  ///
  /// The distance can be omitted, to create a unit vector (distance = 1.0).
  factory Offset.fromDirection(double direction, [ double distance = 1.0 ]) {
    return Offset(distance * math.cos(direction), distance * math.sin(direction));
  }

  /// The x component of the offset.
  ///
  /// The y component is given by [dy].
  double get dx => _dx;

  /// The y component of the offset.
  ///
  /// The x component is given by [dx].
  double get dy => _dy;

  /// The magnitude of the offset.
  ///
  /// If you need this value to compare it to another [Offset]'s distance,
  /// consider using [distanceSquared] instead, since it is cheaper to compute.
  double get distance => math.sqrt(dx * dx + dy * dy);

  /// The square of the magnitude of the offset.
  ///
  /// This is cheaper than computing the [distance] itself.
  double get distanceSquared => dx * dx + dy * dy;

  /// The angle of this offset as radians clockwise from the positive x-axis, in
  /// the range -[pi] to [pi], assuming positive values of the x-axis go to the
  /// left and positive values of the y-axis go down.
  ///
  /// Zero means that [dy] is zero and [dx] is zero or positive.
  ///
  /// Values from zero to [pi]/2 indicate positive values of [dx] and [dy], the
  /// bottom-right quadrant.
  ///
  /// Values from [pi]/2 to [pi] indicate negative values of [dx] and positive
  /// values of [dy], the bottom-left quadrant.
  ///
  /// Values from zero to -[pi]/2 indicate positive values of [dx] and negative
  /// values of [dy], the top-right quadrant.
  ///
  /// Values from -[pi]/2 to -[pi] indicate negative values of [dx] and [dy],
  /// the top-left quadrant.
  ///
  /// When [dy] is zero and [dx] is negative, the [direction] is [pi].
  ///
  /// When [dx] is zero, [direction] is [pi]/2 if [dy] is positive and -[pi]/2
  /// if [dy] is negative.
  ///
  /// See also:
  ///
  ///  * [distance], to compute the magnitude of the vector.
  ///  * [Canvas.rotate], which uses the same convention for its angle.
  double get direction => math.atan2(dy, dx);

  /// An offset with zero magnitude.
  ///
  /// This can be used to represent the origin of a coordinate space.
  static const Offset zero = Offset(0.0, 0.0);

  /// An offset with infinite x and y components.
  ///
  /// See also:
  ///
  ///  * [isInfinite], which checks whether either component is infinite.
  ///  * [isFinite], which checks whether both components are finite.
  // This is included for completeness, because [Size.infinite] exists.
  static const Offset infinite = Offset(double.infinity, double.infinity);

  /// Returns a new offset with the x component scaled by `scaleX` and the y
  /// component scaled by `scaleY`.
  ///
  /// If the two scale arguments are the same, consider using the `*` operator
  /// instead:
  ///
  /// ```dart
  /// Offset a = const Offset(10.0, 10.0);
  /// Offset b = a * 2.0; // same as: a.scale(2.0, 2.0)
  /// ```
  ///
  /// If the two arguments are -1, consider using the unary `-` operator
  /// instead:
  ///
  /// ```dart
  /// Offset a = const Offset(10.0, 10.0);
  /// Offset b = -a; // same as: a.scale(-1.0, -1.0)
  /// ```
  Offset scale(double scaleX, double scaleY) => Offset(dx * scaleX, dy * scaleY);

  /// Returns a new offset with translateX added to the x component and
  /// translateY added to the y component.
  ///
  /// If the arguments come from another [Offset], consider using the `+` or `-`
  /// operators instead:
  ///
  /// ```dart
  /// Offset a = const Offset(10.0, 10.0);
  /// Offset b = const Offset(10.0, 10.0);
  /// Offset c = a + b; // same as: a.translate(b.dx, b.dy)
  /// Offset d = a - b; // same as: a.translate(-b.dx, -b.dy)
  /// ```
  Offset translate(double translateX, double translateY) => Offset(dx + translateX, dy + translateY);

  /// Unary negation operator.
  ///
  /// Returns an offset with the coordinates negated.
  ///
  /// If the [Offset] represents an arrow on a plane, this operator returns the
  /// same arrow but pointing in the reverse direction.
  Offset operator -() => Offset(-dx, -dy);

  /// Binary subtraction operator.
  ///
  /// Returns an offset whose [dx] value is the left-hand-side operand's [dx]
  /// minus the right-hand-side operand's [dx] and whose [dy] value is the
  /// left-hand-side operand's [dy] minus the right-hand-side operand's [dy].
  ///
  /// See also [translate].
  Offset operator -(Offset other) => Offset(dx - other.dx, dy - other.dy);

  /// Binary addition operator.
  ///
  /// Returns an offset whose [dx] value is the sum of the [dx] values of the
  /// two operands, and whose [dy] value is the sum of the [dy] values of the
  /// two operands.
  ///
  /// See also [translate].
  Offset operator +(Offset other) => Offset(dx + other.dx, dy + other.dy);

  /// Multiplication operator.
  ///
  /// Returns an offset whose coordinates are the coordinates of the
  /// left-hand-side operand (an Offset) multiplied by the scalar
  /// right-hand-side operand (a double).
  ///
  /// See also [scale].
  Offset operator *(double operand) => Offset(dx * operand, dy * operand);

  /// Division operator.
  ///
  /// Returns an offset whose coordinates are the coordinates of the
  /// left-hand-side operand (an Offset) divided by the scalar right-hand-side
  /// operand (a double).
  ///
  /// See also [scale].
  Offset operator /(double operand) => Offset(dx / operand, dy / operand);

  /// Integer (truncating) division operator.
  ///
  /// Returns an offset whose coordinates are the coordinates of the
  /// left-hand-side operand (an Offset) divided by the scalar right-hand-side
  /// operand (a double), rounded towards zero.
  Offset operator ~/(double operand) => Offset((dx ~/ operand).toDouble(), (dy ~/ operand).toDouble());

  /// Modulo (remainder) operator.
  ///
  /// Returns an offset whose coordinates are the remainder of dividing the
  /// coordinates of the left-hand-side operand (an Offset) by the scalar
  /// right-hand-side operand (a double).
  Offset operator %(double operand) => Offset(dx % operand, dy % operand);

  /// Rectangle constructor operator.
  ///
  /// Combines an [Offset] and a [Size] to form a [Rect] whose top-left
  /// coordinate is the point given by adding this offset, the left-hand-side
  /// operand, to the origin, and whose size is the right-hand-side operand.
  ///
  /// ```dart
  /// Rect myRect = Offset.zero & const Size(100.0, 100.0);
  /// // same as: Rect.fromLTWH(0.0, 0.0, 100.0, 100.0)
  /// ```
  Rect operator &(Size other) => Rect.fromLTWH(dx, dy, other.width, other.height);

  /// Linearly interpolate between two offsets.
  ///
  /// If either offset is null, this function interpolates from [Offset.zero].
  ///
  /// The `t` argument represents position on the timeline, with 0.0 meaning
  /// that the interpolation has not started, returning `a` (or something
  /// equivalent to `a`), 1.0 meaning that the interpolation has finished,
  /// returning `b` (or something equivalent to `b`), and values in between
  /// meaning that the interpolation is at the relevant point on the timeline
  /// between `a` and `b`. The interpolation can be extrapolated beyond 0.0 and
  /// 1.0, so negative values and values greater than 1.0 are valid (and can
  /// easily be generated by curves such as [Curves.elasticInOut]).
  ///
  /// Values for `t` are usually obtained from an [Animation<double>], such as
  /// an [AnimationController].
  static Offset lerp(Offset a, Offset b, double t) {
    assert(t != null);
    if (a == null && b == null)
      return null;
    if (a == null)
      return b * t;
    if (b == null)
      return a * (1.0 - t);
    return Offset(lerpDouble(a.dx, b.dx, t), lerpDouble(a.dy, b.dy, t));
  }

  /// Compares two Offsets for equality.
  @override
  bool operator ==(dynamic other) {
    if (other is! Offset)
      return false;
    final Offset typedOther = other;
    return dx == typedOther.dx &&
           dy == typedOther.dy;
  }

  @override
  int get hashCode => hashValues(dx, dy);

  @override
  String toString() => 'Offset(${dx?.toStringAsFixed(1)}, ${dy?.toStringAsFixed(1)})';
}

/// Holds a 2D floating-point size.
///
/// You can think of this as an [Offset] from the origin.
class Size extends OffsetBase {
  /// Creates a [Size] with the given [width] and [height].
  const Size(double width, double height) : super(width, height);

  /// Creates an instance of [Size] that has the same values as another.
  // Used by the rendering library's _DebugSize hack.
  Size.copy(Size source) : super(source.width, source.height);

  /// Creates a square [Size] whose [width] and [height] are the given dimension.
  ///
  /// See also:
  ///
  ///  * [Size.fromRadius], which is more convenient when the available size
  ///    is the radius of a circle.
  const Size.square(double dimension) : super(dimension, dimension);

  /// Creates a [Size] with the given [width] and an infinite [height].
  const Size.fromWidth(double width) : super(width, double.infinity);

  /// Creates a [Size] with the given [height] and an infinite [width].
  const Size.fromHeight(double height) : super(double.infinity, height);

  /// Creates a square [Size] whose [width] and [height] are twice the given
  /// dimension.
  ///
  /// This is a square that contains a circle with the given radius.
  ///
  /// See also:
  ///
  ///  * [Size.square], which creates a square with the given dimension.
  const Size.fromRadius(double radius) : super(radius * 2.0, radius * 2.0);

  /// The horizontal extent of this size.
  double get width => _dx;

  /// The vertical extent of this size.
  double get height => _dy;

  /// The aspect ratio of this size.
  ///
  /// This returns the [width] divided by the [height].
  ///
  /// If the [width] is zero, the result will be zero. If the [height] is zero
  /// (and the [width] is not), the result will be [double.infinity] or
  /// [double.negativeInfinity] as determined by the sign of [width].
  ///
  /// See also:
  ///
  ///  * [AspectRatio], a widget for giving a child widget a specific aspect
  ///    ratio.
  ///  * [FittedBox], a widget that (in most modes) attempts to maintain a
  ///    child widget's aspect ratio while changing its size.
  double get aspectRatio {
    if (height != 0.0)
      return width / height;
    if (width > 0.0)
      return double.infinity;
    if (width < 0.0)
      return double.negativeInfinity;
    return 0.0;
  }

  /// An empty size, one with a zero width and a zero height.
  static const Size zero = Size(0.0, 0.0);

  /// A size whose [width] and [height] are infinite.
  ///
  /// See also:
  ///
  ///  * [isInfinite], which checks whether either dimension is infinite.
  ///  * [isFinite], which checks whether both dimensions are finite.
  static const Size infinite = Size(double.infinity, double.infinity);

  /// Whether this size encloses a non-zero area.
  ///
  /// Negative areas are considered empty.
  bool get isEmpty => width <= 0.0 || height <= 0.0;

  /// Binary subtraction operator for [Size].
  ///
  /// Subtracting a [Size] from a [Size] returns the [Offset] that describes how
  /// much bigger the left-hand-side operand is than the right-hand-side
  /// operand. Adding that resulting [Offset] to the [Size] that was the
  /// right-hand-side operand would return a [Size] equal to the [Size] that was
  /// the left-hand-side operand. (i.e. if `sizeA - sizeB -> offsetA`, then
  /// `offsetA + sizeB -> sizeA`)
  ///
  /// Subtracting an [Offset] from a [Size] returns the [Size] that is smaller than
  /// the [Size] operand by the difference given by the [Offset] operand. In other
  /// words, the returned [Size] has a [width] consisting of the [width] of the
  /// left-hand-side operand minus the [Offset.dx] dimension of the
  /// right-hand-side operand, and a [height] consisting of the [height] of the
  /// left-hand-side operand minus the [Offset.dy] dimension of the
  /// right-hand-side operand.
  OffsetBase operator -(OffsetBase other) {
    if (other is Size)
      return Offset(width - other.width, height - other.height);
    if (other is Offset)
      return Size(width - other.dx, height - other.dy);
    throw ArgumentError(other);
  }

  /// Binary addition operator for adding an [Offset] to a [Size].
  ///
  /// Returns a [Size] whose [width] is the sum of the [width] of the
  /// left-hand-side operand, a [Size], and the [Offset.dx] dimension of the
  /// right-hand-side operand, an [Offset], and whose [height] is the sum of the
  /// [height] of the left-hand-side operand and the [Offset.dy] dimension of
  /// the right-hand-side operand.
  Size operator +(Offset other) => Size(width + other.dx, height + other.dy);

  /// Multiplication operator.
  ///
  /// Returns a [Size] whose dimensions are the dimensions of the left-hand-side
  /// operand (a [Size]) multiplied by the scalar right-hand-side operand (a
  /// [double]).
  Size operator *(double operand) => Size(width * operand, height * operand);

  /// Division operator.
  ///
  /// Returns a [Size] whose dimensions are the dimensions of the left-hand-side
  /// operand (a [Size]) divided by the scalar right-hand-side operand (a
  /// [double]).
  Size operator /(double operand) => Size(width / operand, height / operand);

  /// Integer (truncating) division operator.
  ///
  /// Returns a [Size] whose dimensions are the dimensions of the left-hand-side
  /// operand (a [Size]) divided by the scalar right-hand-side operand (a
  /// [double]), rounded towards zero.
  Size operator ~/(double operand) => Size((width ~/ operand).toDouble(), (height ~/ operand).toDouble());

  /// Modulo (remainder) operator.
  ///
  /// Returns a [Size] whose dimensions are the remainder of dividing the
  /// left-hand-side operand (a [Size]) by the scalar right-hand-side operand (a
  /// [double]).
  Size operator %(double operand) => Size(width % operand, height % operand);

  /// The lesser of the magnitudes of the [width] and the [height].
  double get shortestSide => math.min(width.abs(), height.abs());

  /// The greater of the magnitudes of the [width] and the [height].
  double get longestSide => math.max(width.abs(), height.abs());

  // Convenience methods that do the equivalent of calling the similarly named
  // methods on a Rect constructed from the given origin and this size.

  /// The offset to the intersection of the top and left edges of the rectangle
  /// described by the given [Offset] (which is interpreted as the top-left corner)
  /// and this [Size].
  ///
  /// See also [Rect.topLeft].
  Offset topLeft(Offset origin) => origin;

  /// The offset to the center of the top edge of the rectangle described by the
  /// given offset (which is interpreted as the top-left corner) and this size.
  ///
  /// See also [Rect.topCenter].
  Offset topCenter(Offset origin) => Offset(origin.dx + width / 2.0, origin.dy);

  /// The offset to the intersection of the top and right edges of the rectangle
  /// described by the given offset (which is interpreted as the top-left corner)
  /// and this size.
  ///
  /// See also [Rect.topRight].
  Offset topRight(Offset origin) => Offset(origin.dx + width, origin.dy);

  /// The offset to the center of the left edge of the rectangle described by the
  /// given offset (which is interpreted as the top-left corner) and this size.
  ///
  /// See also [Rect.centerLeft].
  Offset centerLeft(Offset origin) => Offset(origin.dx, origin.dy + height / 2.0);

  /// The offset to the point halfway between the left and right and the top and
  /// bottom edges of the rectangle described by the given offset (which is
  /// interpreted as the top-left corner) and this size.
  ///
  /// See also [Rect.center].
  Offset center(Offset origin) => Offset(origin.dx + width / 2.0, origin.dy + height / 2.0);

  /// The offset to the center of the right edge of the rectangle described by the
  /// given offset (which is interpreted as the top-left corner) and this size.
  ///
  /// See also [Rect.centerLeft].
  Offset centerRight(Offset origin) => Offset(origin.dx + width, origin.dy + height / 2.0);

  /// The offset to the intersection of the bottom and left edges of the
  /// rectangle described by the given offset (which is interpreted as the
  /// top-left corner) and this size.
  ///
  /// See also [Rect.bottomLeft].
  Offset bottomLeft(Offset origin) => Offset(origin.dx, origin.dy + height);

  /// The offset to the center of the bottom edge of the rectangle described by
  /// the given offset (which is interpreted as the top-left corner) and this
  /// size.
  ///
  /// See also [Rect.bottomLeft].
  Offset bottomCenter(Offset origin) => Offset(origin.dx + width / 2.0, origin.dy + height);

  /// The offset to the intersection of the bottom and right edges of the
  /// rectangle described by the given offset (which is interpreted as the
  /// top-left corner) and this size.
  ///
  /// See also [Rect.bottomRight].
  Offset bottomRight(Offset origin) => Offset(origin.dx + width, origin.dy + height);

  /// Whether the point specified by the given offset (which is assumed to be
  /// relative to the top left of the size) lies between the left and right and
  /// the top and bottom edges of a rectangle of this size.
  ///
  /// Rectangles include their top and left edges but exclude their bottom and
  /// right edges.
  bool contains(Offset offset) {
    return offset.dx >= 0.0 && offset.dx < width && offset.dy >= 0.0 && offset.dy < height;
  }

  /// A [Size] with the [width] and [height] swapped.
  Size get flipped => Size(height, width);

  /// Linearly interpolate between two sizes
  ///
  /// If either size is null, this function interpolates from [Size.zero].
  ///
  /// The `t` argument represents position on the timeline, with 0.0 meaning
  /// that the interpolation has not started, returning `a` (or something
  /// equivalent to `a`), 1.0 meaning that the interpolation has finished,
  /// returning `b` (or something equivalent to `b`), and values in between
  /// meaning that the interpolation is at the relevant point on the timeline
  /// between `a` and `b`. The interpolation can be extrapolated beyond 0.0 and
  /// 1.0, so negative values and values greater than 1.0 are valid (and can
  /// easily be generated by curves such as [Curves.elasticInOut]).
  ///
  /// Values for `t` are usually obtained from an [Animation<double>], such as
  /// an [AnimationController].
  static Size lerp(Size a, Size b, double t) {
    assert(t != null);
    if (a == null && b == null)
      return null;
    if (a == null)
      return b * t;
    if (b == null)
      return a * (1.0 - t);
    return Size(lerpDouble(a.width, b.width, t), lerpDouble(a.height, b.height, t));
  }

  /// Compares two Sizes for equality.
  // We don't compare the runtimeType because of _DebugSize in the framework.
  @override
  bool operator ==(dynamic other) {
    if (other is! Size)
      return false;
    final Size typedOther = other;
    return _dx == typedOther._dx &&
           _dy == typedOther._dy;
  }

  @override
  int get hashCode => hashValues(_dx, _dy);

  @override
  String toString() => 'Size(${width?.toStringAsFixed(1)}, ${height?.toStringAsFixed(1)})';
}

/// An immutable, 2D, axis-aligned, floating-point rectangle whose coordinates
/// are relative to a given origin.
///
/// A Rect can be created with one its constructors or from an [Offset] and a
/// [Size] using the `&` operator:
///
/// ```dart
/// Rect myRect = const Offset(1.0, 2.0) & const Size(3.0, 4.0);
/// ```
class Rect {
  /// Construct a rectangle from its left, top, right, and bottom edges.
  @pragma('vm:entry-point')
  const Rect.fromLTRB(this.left, this.top, this.right, this.bottom)
    : assert(left != null),
      assert(top != null),
      assert(right != null),
      assert(bottom != null);

  /// Construct a rectangle from its left and top edges, its width, and its
  /// height.
  ///
  /// To construct a [Rect] from an [Offset] and a [Size], you can use the
  /// rectangle constructor operator `&`. See [Offset.&].
  const Rect.fromLTWH(double left, double top, double width, double height) : this.fromLTRB(left, top, left + width, top + height);

  /// Construct a rectangle that bounds the given circle.
  ///
  /// The `center` argument is assumed to be an offset from the origin.
  Rect.fromCircle({ Offset center, double radius }) : this.fromCenter(
    center: center,
    width: radius * 2,
    height: radius * 2,
  );

  /// Constructs a rectangle from its center point, width, and height.
  ///
  /// The `center` argument is assumed to be an offset from the origin.
  Rect.fromCenter({ Offset center, double width, double height }) : this.fromLTRB(
    center.dx - width / 2,
    center.dy - height / 2,
    center.dx + width / 2,
    center.dy + height / 2,
  );

  /// Construct the smallest rectangle that encloses the given offsets, treating
  /// them as vectors from the origin.
  Rect.fromPoints(Offset a, Offset b) : this.fromLTRB(
    math.min(a.dx, b.dx),
    math.min(a.dy, b.dy),
    math.max(a.dx, b.dx),
    math.max(a.dy, b.dy),
  );

  Float32List get _value32 => Float32List.fromList(<double>[left, top, right, bottom]);

  /// The offset of the left edge of this rectangle from the x axis.
  final double left;

  /// The offset of the top edge of this rectangle from the y axis.
  final double top;

  /// The offset of the right edge of this rectangle from the x axis.
  final double right;

  /// The offset of the bottom edge of this rectangle from the y axis.
  final double bottom;

  /// The distance between the left and right edges of this rectangle.
  double get width => right - left;

  /// The distance between the top and bottom edges of this rectangle.
  double get height => bottom - top;

  /// The distance between the upper-left corner and the lower-right corner of
  /// this rectangle.
  Size get size => Size(width, height);

  /// Whether any of the dimensions are `NaN`.
  bool get hasNaN => left.isNaN || top.isNaN || right.isNaN || bottom.isNaN;

  /// A rectangle with left, top, right, and bottom edges all at zero.
  static const Rect zero = Rect.fromLTRB(0.0, 0.0, 0.0, 0.0);

  static const double _giantScalar = 1.0E+9; // matches kGiantRect from layer.h

  /// A rectangle that covers the entire coordinate space.
  ///
  /// This covers the space from -1e9,-1e9 to 1e9,1e9.
  /// This is the space over which graphics operations are valid.
  static const Rect largest = Rect.fromLTRB(-_giantScalar, -_giantScalar, _giantScalar, _giantScalar);

  /// Whether any of the coordinates of this rectangle are equal to positive infinity.
  // included for consistency with Offset and Size
  bool get isInfinite {
    return left >= double.infinity
        || top >= double.infinity
        || right >= double.infinity
        || bottom >= double.infinity;
  }

  /// Whether all coordinates of this rectangle are finite.
  bool get isFinite => left.isFinite && top.isFinite && right.isFinite && bottom.isFinite;

  /// Whether this rectangle encloses a non-zero area. Negative areas are
  /// considered empty.
  bool get isEmpty => left >= right || top >= bottom;

  /// Returns a new rectangle translated by the given offset.
  ///
  /// To translate a rectangle by separate x and y components rather than by an
  /// [Offset], consider [translate].
  Rect shift(Offset offset) {
    return Rect.fromLTRB(left + offset.dx, top + offset.dy, right + offset.dx, bottom + offset.dy);
  }

  /// Returns a new rectangle with translateX added to the x components and
  /// translateY added to the y components.
  ///
  /// To translate a rectangle by an [Offset] rather than by separate x and y
  /// components, consider [shift].
  Rect translate(double translateX, double translateY) {
    return Rect.fromLTRB(left + translateX, top + translateY, right + translateX, bottom + translateY);
  }

  /// Returns a new rectangle with edges moved outwards by the given delta.
  Rect inflate(double delta) {
    return Rect.fromLTRB(left - delta, top - delta, right + delta, bottom + delta);
  }

  /// Returns a new rectangle with edges moved inwards by the given delta.
  Rect deflate(double delta) => inflate(-delta);

  /// Returns a new rectangle that is the intersection of the given
  /// rectangle and this rectangle. The two rectangles must overlap
  /// for this to be meaningful. If the two rectangles do not overlap,
  /// then the resulting Rect will have a negative width or height.
  Rect intersect(Rect other) {
    return Rect.fromLTRB(
      math.max(left, other.left),
      math.max(top, other.top),
      math.min(right, other.right),
      math.min(bottom, other.bottom)
    );
  }

  /// Returns a new rectangle which is the bounding box containing this
  /// rectangle and the given rectangle.
  Rect expandToInclude(Rect other) {
    return Rect.fromLTRB(
        math.min(left, other.left),
        math.min(top, other.top),
        math.max(right, other.right),
        math.max(bottom, other.bottom),
    );
  }

  /// Whether `other` has a nonzero area of overlap with this rectangle.
  bool overlaps(Rect other) {
    if (right <= other.left || other.right <= left)
      return false;
    if (bottom <= other.top || other.bottom <= top)
      return false;
    return true;
  }

  /// The lesser of the magnitudes of the [width] and the [height] of this
  /// rectangle.
  double get shortestSide => math.min(width.abs(), height.abs());

  /// The greater of the magnitudes of the [width] and the [height] of this
  /// rectangle.
  double get longestSide => math.max(width.abs(), height.abs());

  /// The offset to the intersection of the top and left edges of this rectangle.
  ///
  /// See also [Size.topLeft].
  Offset get topLeft => Offset(left, top);

  /// The offset to the center of the top edge of this rectangle.
  ///
  /// See also [Size.topCenter].
  Offset get topCenter => Offset(left + width / 2.0, top);

  /// The offset to the intersection of the top and right edges of this rectangle.
  ///
  /// See also [Size.topRight].
  Offset get topRight => Offset(right, top);

  /// The offset to the center of the left edge of this rectangle.
  ///
  /// See also [Size.centerLeft].
  Offset get centerLeft => Offset(left, top + height / 2.0);

  /// The offset to the point halfway between the left and right and the top and
  /// bottom edges of this rectangle.
  ///
  /// See also [Size.center].
  Offset get center => Offset(left + width / 2.0, top + height / 2.0);

  /// The offset to the center of the right edge of this rectangle.
  ///
  /// See also [Size.centerLeft].
  Offset get centerRight => Offset(right, top + height / 2.0);

  /// The offset to the intersection of the bottom and left edges of this rectangle.
  ///
  /// See also [Size.bottomLeft].
  Offset get bottomLeft => Offset(left, bottom);

  /// The offset to the center of the bottom edge of this rectangle.
  ///
  /// See also [Size.bottomLeft].
  Offset get bottomCenter => Offset(left + width / 2.0, bottom);

  /// The offset to the intersection of the bottom and right edges of this rectangle.
  ///
  /// See also [Size.bottomRight].
  Offset get bottomRight => Offset(right, bottom);

  /// Whether the point specified by the given offset (which is assumed to be
  /// relative to the origin) lies between the left and right and the top and
  /// bottom edges of this rectangle.
  ///
  /// Rectangles include their top and left edges but exclude their bottom and
  /// right edges.
  bool contains(Offset offset) {
    return offset.dx >= left && offset.dx < right && offset.dy >= top && offset.dy < bottom;
  }

  /// Linearly interpolate between two rectangles.
  ///
  /// If either rect is null, [Rect.zero] is used as a substitute.
  ///
  /// The `t` argument represents position on the timeline, with 0.0 meaning
  /// that the interpolation has not started, returning `a` (or something
  /// equivalent to `a`), 1.0 meaning that the interpolation has finished,
  /// returning `b` (or something equivalent to `b`), and values in between
  /// meaning that the interpolation is at the relevant point on the timeline
  /// between `a` and `b`. The interpolation can be extrapolated beyond 0.0 and
  /// 1.0, so negative values and values greater than 1.0 are valid (and can
  /// easily be generated by curves such as [Curves.elasticInOut]).
  ///
  /// Values for `t` are usually obtained from an [Animation<double>], such as
  /// an [AnimationController].
  static Rect lerp(Rect a, Rect b, double t) {
    assert(t != null);
    if (a == null && b == null)
      return null;
    if (a == null)
      return Rect.fromLTRB(b.left * t, b.top * t, b.right * t, b.bottom * t);
    if (b == null) {
      final double k = 1.0 - t;
      return Rect.fromLTRB(a.left * k, a.top * k, a.right * k, a.bottom * k);
    }
    return Rect.fromLTRB(
      lerpDouble(a.left, b.left, t),
      lerpDouble(a.top, b.top, t),
      lerpDouble(a.right, b.right, t),
      lerpDouble(a.bottom, b.bottom, t),
    );
  }

  @override
  bool operator ==(dynamic other) {
    if (identical(this, other))
      return true;
    if (runtimeType != other.runtimeType)
      return false;
    final Rect typedOther = other;
    return left   == typedOther.left   &&
           top    == typedOther.top    &&
           right  == typedOther.right  &&
           bottom == typedOther.bottom;
  }

  @override
  int get hashCode => hashValues(left, top, right, bottom);

  @override
  String toString() => 'Rect.fromLTRB(${left.toStringAsFixed(1)}, ${top.toStringAsFixed(1)}, ${right.toStringAsFixed(1)}, ${bottom.toStringAsFixed(1)})';
}

/// A radius for either circular or elliptical shapes.
class Radius {
  /// Constructs a circular radius. [x] and [y] will have the same radius value.
  const Radius.circular(double radius) : this.elliptical(radius, radius);

  /// Constructs an elliptical radius with the given radii.
  const Radius.elliptical(this.x, this.y);

  /// The radius value on the horizontal axis.
  final double x;

  /// The radius value on the vertical axis.
  final double y;

  /// A radius with [x] and [y] values set to zero.
  ///
  /// You can use [Radius.zero] with [RRect] to have right-angle corners.
  static const Radius zero = Radius.circular(0.0);

  /// Unary negation operator.
  ///
  /// Returns a Radius with the distances negated.
  ///
  /// Radiuses with negative values aren't geometrically meaningful, but could
  /// occur as part of expressions. For example, negating a radius of one pixel
  /// and then adding the result to another radius is equivalent to subtracting
  /// a radius of one pixel from the other.
  Radius operator -() => Radius.elliptical(-x, -y);

  /// Binary subtraction operator.
  ///
  /// Returns a radius whose [x] value is the left-hand-side operand's [x]
  /// minus the right-hand-side operand's [x] and whose [y] value is the
  /// left-hand-side operand's [y] minus the right-hand-side operand's [y].
  Radius operator -(Radius other) => Radius.elliptical(x - other.x, y - other.y);

  /// Binary addition operator.
  ///
  /// Returns a radius whose [x] value is the sum of the [x] values of the
  /// two operands, and whose [y] value is the sum of the [y] values of the
  /// two operands.
  Radius operator +(Radius other) => Radius.elliptical(x + other.x, y + other.y);

  /// Multiplication operator.
  ///
  /// Returns a radius whose coordinates are the coordinates of the
  /// left-hand-side operand (a radius) multiplied by the scalar
  /// right-hand-side operand (a double).
  Radius operator *(double operand) => Radius.elliptical(x * operand, y * operand);

  /// Division operator.
  ///
  /// Returns a radius whose coordinates are the coordinates of the
  /// left-hand-side operand (a radius) divided by the scalar right-hand-side
  /// operand (a double).
  Radius operator /(double operand) => Radius.elliptical(x / operand, y / operand);

  /// Integer (truncating) division operator.
  ///
  /// Returns a radius whose coordinates are the coordinates of the
  /// left-hand-side operand (a radius) divided by the scalar right-hand-side
  /// operand (a double), rounded towards zero.
  Radius operator ~/(double operand) => Radius.elliptical((x ~/ operand).toDouble(), (y ~/ operand).toDouble());

  /// Modulo (remainder) operator.
  ///
  /// Returns a radius whose coordinates are the remainder of dividing the
  /// coordinates of the left-hand-side operand (a radius) by the scalar
  /// right-hand-side operand (a double).
  Radius operator %(double operand) => Radius.elliptical(x % operand, y % operand);

  /// Linearly interpolate between two radii.
  ///
  /// If either is null, this function substitutes [Radius.zero] instead.
  ///
  /// The `t` argument represents position on the timeline, with 0.0 meaning
  /// that the interpolation has not started, returning `a` (or something
  /// equivalent to `a`), 1.0 meaning that the interpolation has finished,
  /// returning `b` (or something equivalent to `b`), and values in between
  /// meaning that the interpolation is at the relevant point on the timeline
  /// between `a` and `b`. The interpolation can be extrapolated beyond 0.0 and
  /// 1.0, so negative values and values greater than 1.0 are valid (and can
  /// easily be generated by curves such as [Curves.elasticInOut]).
  ///
  /// Values for `t` are usually obtained from an [Animation<double>], such as
  /// an [AnimationController].
  static Radius lerp(Radius a, Radius b, double t) {
    assert(t != null);
    if (a == null && b == null)
      return null;
    if (a == null)
      return Radius.elliptical(b.x * t, b.y * t);
    if (b == null) {
      final double k = 1.0 - t;
      return Radius.elliptical(a.x * k, a.y * k);
    }
    return Radius.elliptical(
      lerpDouble(a.x, b.x, t),
      lerpDouble(a.y, b.y, t),
    );
  }

  @override
  bool operator ==(dynamic other) {
    if (identical(this, other))
      return true;
    if (runtimeType != other.runtimeType)
      return false;
    final Radius typedOther = other;
    return typedOther.x == x && typedOther.y == y;
  }

  @override
  int get hashCode => hashValues(x, y);

  @override
  String toString() {
    return x == y ? 'Radius.circular(${x.toStringAsFixed(1)})' :
                    'Radius.elliptical(${x.toStringAsFixed(1)}, '
                    '${y.toStringAsFixed(1)})';
  }
}

/// An immutable rounded rectangle with the custom radii for all four corners.
class RRect {
  /// Construct a rounded rectangle from its left, top, right, and bottom edges,
  /// and the same radii along its horizontal axis and its vertical axis.
  const RRect.fromLTRBXY(double left, double top, double right, double bottom,
                   double radiusX, double radiusY) : this._raw(
    top: top,
    left: left,
    right: right,
    bottom: bottom,
    tlRadiusX: radiusX,
    tlRadiusY: radiusY,
    trRadiusX: radiusX,
    trRadiusY: radiusY,
    blRadiusX: radiusX,
    blRadiusY: radiusY,
    brRadiusX: radiusX,
    brRadiusY: radiusY,
  );

  /// Construct a rounded rectangle from its left, top, right, and bottom edges,
  /// and the same radius in each corner.
  RRect.fromLTRBR(double left, double top, double right, double bottom,
                  Radius radius)
    : this._raw(
        top: top,
        left: left,
        right: right,
        bottom: bottom,
        tlRadiusX: radius.x,
        tlRadiusY: radius.y,
        trRadiusX: radius.x,
        trRadiusY: radius.y,
        blRadiusX: radius.x,
        blRadiusY: radius.y,
        brRadiusX: radius.x,
        brRadiusY: radius.y,
      );

  /// Construct a rounded rectangle from its bounding box and the same radii
  /// along its horizontal axis and its vertical axis.
  RRect.fromRectXY(Rect rect, double radiusX, double radiusY)
    : this._raw(
        top: rect.top,
        left: rect.left,
        right: rect.right,
        bottom: rect.bottom,
        tlRadiusX: radiusX,
        tlRadiusY: radiusY,
        trRadiusX: radiusX,
        trRadiusY: radiusY,
        blRadiusX: radiusX,
        blRadiusY: radiusY,
        brRadiusX: radiusX,
        brRadiusY: radiusY,
      );

  /// Construct a rounded rectangle from its bounding box and a radius that is
  /// the same in each corner.
  RRect.fromRectAndRadius(Rect rect, Radius radius)
    : this._raw(
        top: rect.top,
        left: rect.left,
        right: rect.right,
        bottom: rect.bottom,
        tlRadiusX: radius.x,
        tlRadiusY: radius.y,
        trRadiusX: radius.x,
        trRadiusY: radius.y,
        blRadiusX: radius.x,
        blRadiusY: radius.y,
        brRadiusX: radius.x,
        brRadiusY: radius.y,
      );

  /// Construct a rounded rectangle from its left, top, right, and bottom edges,
  /// and topLeft, topRight, bottomRight, and bottomLeft radii.
  ///
  /// The corner radii default to [Radius.zero], i.e. right-angled corners.
  RRect.fromLTRBAndCorners(
    double left,
    double top,
    double right,
    double bottom, {
    Radius topLeft = Radius.zero,
    Radius topRight = Radius.zero,
    Radius bottomRight = Radius.zero,
    Radius bottomLeft = Radius.zero,
  }) : this._raw(
         top: top,
         left: left,
         right: right,
         bottom: bottom,
         tlRadiusX: topLeft.x,
         tlRadiusY: topLeft.y,
         trRadiusX: topRight.x,
         trRadiusY: topRight.y,
         blRadiusX: bottomLeft.x,
         blRadiusY: bottomLeft.y,
         brRadiusX: bottomRight.x,
         brRadiusY: bottomRight.y,
       );

  /// Construct a rounded rectangle from its bounding box and and topLeft,
  /// topRight, bottomRight, and bottomLeft radii.
  ///
  /// The corner radii default to [Radius.zero], i.e. right-angled corners
  RRect.fromRectAndCorners(
    Rect rect,
    {
      Radius topLeft = Radius.zero,
      Radius topRight = Radius.zero,
      Radius bottomRight = Radius.zero,
      Radius bottomLeft = Radius.zero
    }
  ) : this._raw(
        top: rect.top,
        left: rect.left,
        right: rect.right,
        bottom: rect.bottom,
        tlRadiusX: topLeft.x,
        tlRadiusY: topLeft.y,
        trRadiusX: topRight.x,
        trRadiusY: topRight.y,
        blRadiusX: bottomLeft.x,
        blRadiusY: bottomLeft.y,
        brRadiusX: bottomRight.x,
        brRadiusY: bottomRight.y,
      );

  const RRect._raw({
    this.left = 0.0,
    this.top = 0.0,
    this.right = 0.0,
    this.bottom = 0.0,
    this.tlRadiusX = 0.0,
    this.tlRadiusY = 0.0,
    this.trRadiusX = 0.0,
    this.trRadiusY = 0.0,
    this.brRadiusX = 0.0,
    this.brRadiusY = 0.0,
    this.blRadiusX = 0.0,
    this.blRadiusY = 0.0,
  }) : assert(left != null),
       assert(top != null),
       assert(right != null),
       assert(bottom != null),
       assert(tlRadiusX != null),
       assert(tlRadiusY != null),
       assert(trRadiusX != null),
       assert(trRadiusY != null),
       assert(brRadiusX != null),
       assert(brRadiusY != null),
       assert(blRadiusX != null),
       assert(blRadiusY != null);

  Float32List get _value32 => Float32List.fromList(<double>[
    left,
    top,
    right,
    bottom,
    tlRadiusX,
    tlRadiusY,
    trRadiusX,
    trRadiusY,
    brRadiusX,
    brRadiusY,
    blRadiusX,
    blRadiusY,
  ]);

  /// The offset of the left edge of this rectangle from the x axis.
  final double left;

  /// The offset of the top edge of this rectangle from the y axis.
  final double top;

  /// The offset of the right edge of this rectangle from the x axis.
  final double right;

  /// The offset of the bottom edge of this rectangle from the y axis.
  final double bottom;

  /// The top-left horizontal radius.
  final double tlRadiusX;

  /// The top-left vertical radius.
  final double tlRadiusY;

  /// The top-left [Radius].
  Radius get tlRadius => Radius.elliptical(tlRadiusX, tlRadiusY);

  /// The top-right horizontal radius.
  final double trRadiusX;

  /// The top-right vertical radius.
  final double trRadiusY;

  /// The top-right [Radius].
  Radius get trRadius => Radius.elliptical(trRadiusX, trRadiusY);

  /// The bottom-right horizontal radius.
  final double brRadiusX;

  /// The bottom-right vertical radius.
  final double brRadiusY;

  /// The bottom-right [Radius].
  Radius get brRadius => Radius.elliptical(brRadiusX, brRadiusY);

  /// The bottom-left horizontal radius.
  final double blRadiusX;

  /// The bottom-left vertical radius.
  final double blRadiusY;

  /// The bottom-left [Radius].
  Radius get blRadius => Radius.elliptical(blRadiusX, blRadiusY);

  /// A rounded rectangle with all the values set to zero.
  static const RRect zero = RRect._raw();

  /// Returns a new [RRect] translated by the given offset.
  RRect shift(Offset offset) {
    return RRect._raw(
      left: left + offset.dx,
      top: top + offset.dy,
      right: right + offset.dx,
      bottom: bottom + offset.dy,
      tlRadiusX: tlRadiusX,
      tlRadiusY: tlRadiusY,
      trRadiusX: trRadiusX,
      trRadiusY: trRadiusY,
      blRadiusX: blRadiusX,
      blRadiusY: blRadiusY,
      brRadiusX: brRadiusX,
      brRadiusY: brRadiusY,
    );
  }

  /// Returns a new [RRect] with edges and radii moved outwards by the given
  /// delta.
  RRect inflate(double delta) {
    return RRect._raw(
      left: left - delta,
      top: top - delta,
      right: right + delta,
      bottom: bottom + delta,
      tlRadiusX: tlRadiusX + delta,
      tlRadiusY: tlRadiusY + delta,
      trRadiusX: trRadiusX + delta,
      trRadiusY: trRadiusY + delta,
      blRadiusX: blRadiusX + delta,
      blRadiusY: blRadiusY + delta,
      brRadiusX: brRadiusX + delta,
      brRadiusY: brRadiusY + delta,
    );
  }

  /// Returns a new [RRect] with edges and radii moved inwards by the given delta.
  RRect deflate(double delta) => inflate(-delta);

  /// The distance between the left and right edges of this rectangle.
  double get width => right - left;

  /// The distance between the top and bottom edges of this rectangle.
  double get height => bottom - top;

  /// The bounding box of this rounded rectangle (the rectangle with no rounded corners).
  Rect get outerRect => Rect.fromLTRB(left, top, right, bottom);

  /// The non-rounded rectangle that is constrained by the smaller of the two
  /// diagonals, with each diagonal traveling through the middle of the curve
  /// corners. The middle of a corner is the intersection of the curve with its
  /// respective quadrant bisector.
  Rect get safeInnerRect {
    const double kInsetFactor = 0.29289321881; // 1-cos(pi/4)

    final double leftRadius = math.max(blRadiusX, tlRadiusX);
    final double topRadius = math.max(tlRadiusY, trRadiusY);
    final double rightRadius = math.max(trRadiusX, brRadiusX);
    final double bottomRadius = math.max(brRadiusY, blRadiusY);

    return Rect.fromLTRB(
      left + leftRadius * kInsetFactor,
      top + topRadius * kInsetFactor,
      right - rightRadius * kInsetFactor,
      bottom - bottomRadius * kInsetFactor
    );
  }

  /// The rectangle that would be formed using the axis-aligned intersection of
  /// the sides of the rectangle, i.e., the rectangle formed from the
  /// inner-most centers of the ellipses that form the corners. This is the
  /// intersection of the [wideMiddleRect] and the [tallMiddleRect]. If any of
  /// the intersections are void, the resulting [Rect] will have negative width
  /// or height.
  Rect get middleRect {
    final double leftRadius = math.max(blRadiusX, tlRadiusX);
    final double topRadius = math.max(tlRadiusY, trRadiusY);
    final double rightRadius = math.max(trRadiusX, brRadiusX);
    final double bottomRadius = math.max(brRadiusY, blRadiusY);
    return Rect.fromLTRB(
      left + leftRadius,
      top + topRadius,
      right - rightRadius,
      bottom - bottomRadius
    );
  }

  /// The biggest rectangle that is entirely inside the rounded rectangle and
  /// has the full width of the rounded rectangle. If the rounded rectangle does
  /// not have an axis-aligned intersection of its left and right side, the
  /// resulting [Rect] will have negative width or height.
  Rect get wideMiddleRect {
    final double topRadius = math.max(tlRadiusY, trRadiusY);
    final double bottomRadius = math.max(brRadiusY, blRadiusY);
    return Rect.fromLTRB(
      left,
      top + topRadius,
      right,
      bottom - bottomRadius
    );
  }

  /// The biggest rectangle that is entirely inside the rounded rectangle and
  /// has the full height of the rounded rectangle. If the rounded rectangle
  /// does not have an axis-aligned intersection of its top and bottom side, the
  /// resulting [Rect] will have negative width or height.
  Rect get tallMiddleRect {
    final double leftRadius = math.max(blRadiusX, tlRadiusX);
    final double rightRadius = math.max(trRadiusX, brRadiusX);
    return Rect.fromLTRB(
      left + leftRadius,
      top,
      right - rightRadius,
      bottom
    );
  }

  /// Whether this rounded rectangle encloses a non-zero area.
  /// Negative areas are considered empty.
  bool get isEmpty => left >= right || top >= bottom;

  /// Whether all coordinates of this rounded rectangle are finite.
  bool get isFinite => left.isFinite && top.isFinite && right.isFinite && bottom.isFinite;

  /// Whether this rounded rectangle is a simple rectangle with zero
  /// corner radii.
  bool get isRect {
    return (tlRadiusX == 0.0 || tlRadiusY == 0.0) &&
           (trRadiusX == 0.0 || trRadiusY == 0.0) &&
           (blRadiusX == 0.0 || blRadiusY == 0.0) &&
           (brRadiusX == 0.0 || brRadiusY == 0.0);
  }

  /// Whether this rounded rectangle has a side with no straight section.
  bool get isStadium {
    return tlRadius == trRadius
        && trRadius == brRadius
        && brRadius == blRadius
        && (width <= 2.0 * tlRadiusX || height <= 2.0 * tlRadiusY);
  }

  /// Whether this rounded rectangle has no side with a straight section.
  bool get isEllipse {
    return tlRadius == trRadius
        && trRadius == brRadius
        && brRadius == blRadius
        && width <= 2.0 * tlRadiusX
        && height <= 2.0 * tlRadiusY;
  }

  /// Whether this rounded rectangle would draw as a circle.
  bool get isCircle => width == height && isEllipse;

  /// The lesser of the magnitudes of the [width] and the [height] of this
  /// rounded rectangle.
  double get shortestSide => math.min(width.abs(), height.abs());

  /// The greater of the magnitudes of the [width] and the [height] of this
  /// rounded rectangle.
  double get longestSide => math.max(width.abs(), height.abs());

  /// Whether any of the dimensions are `NaN`.
  bool get hasNaN => left.isNaN || top.isNaN || right.isNaN || bottom.isNaN ||
                     trRadiusX.isNaN || trRadiusY.isNaN || tlRadiusX.isNaN || tlRadiusY.isNaN ||
                     brRadiusX.isNaN || brRadiusY.isNaN || blRadiusX.isNaN || blRadiusY.isNaN;

  /// The offset to the point halfway between the left and right and the top and
  /// bottom edges of this rectangle.
  Offset get center => Offset(left + width / 2.0, top + height / 2.0);

  // Returns the minimum between min and scale to which radius1 and radius2
  // should be scaled with in order not to exceed the limit.
  double _getMin(double min, double radius1, double radius2, double limit) {
    final double sum = radius1 + radius2;
    if (sum > limit && sum != 0.0)
      return math.min(min, limit / sum);
    return min;
  }

  /// Scales all radii so that on each side their sum will not exceed the size
  /// of the width/height.
  ///
  /// Skia already handles RRects with radii that are too large in this way.
  /// Therefore, this method is only needed for RRect use cases that require
  /// the appropriately scaled radii values.
  ///
  /// See the [Skia scaling implementation](https://github.com/google/skia/blob/master/src/core/SkRRect.cpp)
  /// for more details.
  RRect scaleRadii() {
    double scale = 1.0;
    scale = _getMin(scale, blRadiusY, tlRadiusY, height);
    scale = _getMin(scale, tlRadiusX, trRadiusX, width);
    scale = _getMin(scale, trRadiusY, brRadiusY, height);
    scale = _getMin(scale, brRadiusX, blRadiusX, width);

    if (scale < 1.0) {
      return RRect._raw(
        top: top,
        left: left,
        right: right,
        bottom: bottom,
        tlRadiusX: tlRadiusX * scale,
        tlRadiusY: tlRadiusY * scale,
        trRadiusX: trRadiusX * scale,
        trRadiusY: trRadiusY * scale,
        blRadiusX: blRadiusX * scale,
        blRadiusY: blRadiusY * scale,
        brRadiusX: brRadiusX * scale,
        brRadiusY: brRadiusY * scale,
      );
    }

    return RRect._raw(
      top: top,
      left: left,
      right: right,
      bottom: bottom,
      tlRadiusX: tlRadiusX,
      tlRadiusY: tlRadiusY,
      trRadiusX: trRadiusX,
      trRadiusY: trRadiusY,
      blRadiusX: blRadiusX,
      blRadiusY: blRadiusY,
      brRadiusX: brRadiusX,
      brRadiusY: brRadiusY,
    );
  }

  /// Whether the point specified by the given offset (which is assumed to be
  /// relative to the origin) lies inside the rounded rectangle.
  ///
  /// This method may allocate (and cache) a copy of the object with normalized
  /// radii the first time it is called on a particular [RRect] instance. When
  /// using this method, prefer to reuse existing [RRect]s rather than
  /// recreating the object each time.
  bool contains(Offset point) {
    if (point.dx < left || point.dx >= right || point.dy < top || point.dy >= bottom)
      return false; // outside bounding box

    final RRect scaled = scaleRadii();

    double x;
    double y;
    double radiusX;
    double radiusY;
    // check whether point is in one of the rounded corner areas
    // x, y -> translate to ellipse center
    if (point.dx < left + scaled.tlRadiusX &&
        point.dy < top + scaled.tlRadiusY) {
      x = point.dx - left - scaled.tlRadiusX;
      y = point.dy - top - scaled.tlRadiusY;
      radiusX = scaled.tlRadiusX;
      radiusY = scaled.tlRadiusY;
    } else if (point.dx > right - scaled.trRadiusX &&
               point.dy < top + scaled.trRadiusY) {
      x = point.dx - right + scaled.trRadiusX;
      y = point.dy - top - scaled.trRadiusY;
      radiusX = scaled.trRadiusX;
      radiusY = scaled.trRadiusY;
    } else if (point.dx > right - scaled.brRadiusX &&
               point.dy > bottom - scaled.brRadiusY) {
      x = point.dx - right + scaled.brRadiusX;
      y = point.dy - bottom + scaled.brRadiusY;
      radiusX = scaled.brRadiusX;
      radiusY = scaled.brRadiusY;
    } else if (point.dx < left + scaled.blRadiusX &&
               point.dy > bottom - scaled.blRadiusY) {
      x = point.dx - left - scaled.blRadiusX;
      y = point.dy - bottom + scaled.blRadiusY;
      radiusX = scaled.blRadiusX;
      radiusY = scaled.blRadiusY;
    } else {
      return true; // inside and not within the rounded corner area
    }

    x = x / radiusX;
    y = y / radiusY;
    // check if the point is outside the unit circle
    if (x * x + y * y > 1.0)
      return false;
    return true;
  }

  /// Linearly interpolate between two rounded rectangles.
  ///
  /// If either is null, this function substitutes [RRect.zero] instead.
  ///
  /// The `t` argument represents position on the timeline, with 0.0 meaning
  /// that the interpolation has not started, returning `a` (or something
  /// equivalent to `a`), 1.0 meaning that the interpolation has finished,
  /// returning `b` (or something equivalent to `b`), and values in between
  /// meaning that the interpolation is at the relevant point on the timeline
  /// between `a` and `b`. The interpolation can be extrapolated beyond 0.0 and
  /// 1.0, so negative values and values greater than 1.0 are valid (and can
  /// easily be generated by curves such as [Curves.elasticInOut]).
  ///
  /// Values for `t` are usually obtained from an [Animation<double>], such as
  /// an [AnimationController].
  static RRect lerp(RRect a, RRect b, double t) {
    assert(t != null);
    if (a == null && b == null)
      return null;
    if (a == null) {
      return RRect._raw(
        left: b.left * t,
        top: b.top * t,
        right: b.right * t,
        bottom: b.bottom * t,
        tlRadiusX: b.tlRadiusX * t,
        tlRadiusY: b.tlRadiusY * t,
        trRadiusX: b.trRadiusX * t,
        trRadiusY: b.trRadiusY * t,
        brRadiusX: b.brRadiusX * t,
        brRadiusY: b.brRadiusY * t,
        blRadiusX: b.blRadiusX * t,
        blRadiusY: b.blRadiusY * t,
      );
    }
    if (b == null) {
      final double k = 1.0 - t;
      return RRect._raw(
        left: a.left * k,
        top: a.top * k,
        right: a.right * k,
        bottom: a.bottom * k,
        tlRadiusX: a.tlRadiusX * k,
        tlRadiusY: a.tlRadiusY * k,
        trRadiusX: a.trRadiusX * k,
        trRadiusY: a.trRadiusY * k,
        brRadiusX: a.brRadiusX * k,
        brRadiusY: a.brRadiusY * k,
        blRadiusX: a.blRadiusX * k,
        blRadiusY: a.blRadiusY * k,
      );
    }
    return RRect._raw(
      left: lerpDouble(a.left, b.left, t),
      top: lerpDouble(a.top, b.top, t),
      right: lerpDouble(a.right, b.right, t),
      bottom: lerpDouble(a.bottom, b.bottom, t),
      tlRadiusX: lerpDouble(a.tlRadiusX, b.tlRadiusX, t),
      tlRadiusY: lerpDouble(a.tlRadiusY, b.tlRadiusY, t),
      trRadiusX: lerpDouble(a.trRadiusX, b.trRadiusX, t),
      trRadiusY: lerpDouble(a.trRadiusY, b.trRadiusY, t),
      brRadiusX: lerpDouble(a.brRadiusX, b.brRadiusX, t),
      brRadiusY: lerpDouble(a.brRadiusY, b.brRadiusY, t),
      blRadiusX: lerpDouble(a.blRadiusX, b.blRadiusX, t),
      blRadiusY: lerpDouble(a.blRadiusY, b.blRadiusY, t),
    );
  }

  @override
  bool operator ==(dynamic other) {
    if (identical(this, other))
      return true;
    if (runtimeType != other.runtimeType)
      return false;
    final RRect typedOther = other;
    return left      == typedOther.left      &&
           top       == typedOther.top       &&
           right     == typedOther.right     &&
           bottom    == typedOther.bottom    &&
           tlRadiusX == typedOther.tlRadiusX &&
           tlRadiusY == typedOther.tlRadiusY &&
           trRadiusX == typedOther.trRadiusX &&
           trRadiusY == typedOther.trRadiusY &&
           blRadiusX == typedOther.blRadiusX &&
           blRadiusY == typedOther.blRadiusY &&
           brRadiusX == typedOther.brRadiusX &&
           brRadiusY == typedOther.brRadiusY;
  }

  @override
  int get hashCode => hashValues(left, top, right, bottom,
    tlRadiusX, tlRadiusY, trRadiusX, trRadiusY,
    blRadiusX, blRadiusY, brRadiusX, brRadiusY);

  @override
  String toString() {
    final String rect = '${left.toStringAsFixed(1)}, '
                        '${top.toStringAsFixed(1)}, '
                        '${right.toStringAsFixed(1)}, '
                        '${bottom.toStringAsFixed(1)}';
    if (tlRadius == trRadius &&
        trRadius == brRadius &&
        brRadius == blRadius) {
      if (tlRadius.x == tlRadius.y)
        return 'RRect.fromLTRBR($rect, ${tlRadius.x.toStringAsFixed(1)})';
      return 'RRect.fromLTRBXY($rect, ${tlRadius.x.toStringAsFixed(1)}, ${tlRadius.y.toStringAsFixed(1)})';
    }
    return 'RRect.fromLTRBAndCorners('
             '$rect, '
             'topLeft: $tlRadius, '
             'topRight: $trRadius, '
             'bottomRight: $brRadius, '
             'bottomLeft: $blRadius'
           ')';
  }
}

/// A transform consisting of a translation, a rotation, and a uniform scale.
///
/// Used by [Canvas.drawAtlas]. This is a more efficient way to represent these
/// simple transformations than a full matrix.
// Modeled after Skia's SkRSXform.
class RSTransform {
  /// Creates an RSTransform.
  ///
  /// An [RSTransform] expresses the combination of a translation, a rotation
  /// around a particular point, and a scale factor.
  ///
  /// The first argument, `scos`, is the cosine of the rotation, multiplied by
  /// the scale factor.
  ///
  /// The second argument, `ssin`, is the sine of the rotation, multiplied by
  /// that same scale factor.
  ///
  /// The third argument is the x coordinate of the translation, minus the
  /// `scos` argument multiplied by the x-coordinate of the rotation point, plus
  /// the `ssin` argument multiplied by the y-coordinate of the rotation point.
  ///
  /// The fourth argument is the y coordinate of the translation, minus the `ssin`
  /// argument multiplied by the x-coordinate of the rotation point, minus the
  /// `scos` argument multiplied by the y-coordinate of the rotation point.
  ///
  /// The [RSTransform.fromComponents] method may be a simpler way to
  /// construct these values. However, if there is a way to factor out the
  /// computations of the sine and cosine of the rotation so that they can be
  /// reused over multiple calls to this constructor, it may be more efficient
  /// to directly use this constructor instead.
  RSTransform(double scos, double ssin, double tx, double ty) {
    _value
      ..[0] = scos
      ..[1] = ssin
      ..[2] = tx
      ..[3] = ty;
  }

  /// Creates an RSTransform from its individual components.
  ///
  /// The `rotation` parameter gives the rotation in radians.
  ///
  /// The `scale` parameter describes the uniform scale factor.
  ///
  /// The `anchorX` and `anchorY` parameters give the coordinate of the point
  /// around which to rotate.
  ///
  /// The `translateX` and `translateY` parameters give the coordinate of the
  /// offset by which to translate.
  ///
  /// This constructor computes the arguments of the [new RSTransform]
  /// constructor and then defers to that constructor to actually create the
  /// object. If many [RSTransform] objects are being created and there is a way
  /// to factor out the computations of the sine and cosine of the rotation
  /// (which are computed each time this constructor is called) and reuse them
  /// over multiple [RSTransform] objects, it may be more efficient to directly
  /// use the more direct [new RSTransform] constructor instead.
  factory RSTransform.fromComponents({
    double rotation,
    double scale,
    double anchorX,
    double anchorY,
    double translateX,
    double translateY
  }) {
    final double scos = math.cos(rotation) * scale;
    final double ssin = math.sin(rotation) * scale;
    final double tx = translateX + -scos * anchorX + ssin * anchorY;
    final double ty = translateY + -ssin * anchorX - scos * anchorY;
    return RSTransform(scos, ssin, tx, ty);
  }

  final Float32List _value = Float32List(4);

  /// The cosine of the rotation multiplied by the scale factor.
  double get scos => _value[0];

  /// The sine of the rotation multiplied by that same scale factor.
  double get ssin => _value[1];

  /// The x coordinate of the translation, minus [scos] multiplied by the
  /// x-coordinate of the rotation point, plus [ssin] multiplied by the
  /// y-coordinate of the rotation point.
  double get tx => _value[2];

  /// The y coordinate of the translation, minus [ssin] multiplied by the
  /// x-coordinate of the rotation point, minus [scos] multiplied by the
  /// y-coordinate of the rotation point.
  double get ty => _value[3];
}