lib/ui/geometry.dart

// Copyright 2015 The Chromium 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 dimension, and the second the
  /// vertical dimension.
  const OffsetBase(this._dx, this._dy);

  final double _dx;
  final double _dy;

  /// Returns true if either dimension 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_ dimensions set to [double.INFINITY].
  bool get isInfinite => _dx >= double.INFINITY || _dy >= double.INFINITY;

  /// 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);
}

/// An immutable 2D floating-point offset.
///
/// An Offset represents a vector from an unspecified [Point].
///
/// Adding an offset to a [Point] returns the [Point] that is indicated by the
/// vector from that first point.
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);

  /// The x component of the offset.
  double get dx => _dx;

  /// The y component of the offset.
  double get dy => _dy;

  /// The magnitude of the offset.
  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;

  /// An offset with zero magnitude.
  static const Offset zero = const Offset(0.0, 0.0);

  /// An offset with infinite x and y components.
  static const Offset infinite = const Offset(double.INFINITY, double.INFINITY);

  /// Returns a new offset with the x component scaled by scaleX and the y component scaled by scaleY.
  Offset scale(double scaleX, double scaleY) => new Offset(dx * scaleX, dy * scaleY);

  /// Returns a new offset with translateX added to the x component and translateY added to the y component.
  Offset translate(double translateX, double translateY) => new Offset(dx + translateX, dy + translateY);

  /// Unary negation operator. Returns an offset with the coordinates negated.
  Offset operator -() => new 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].
  Offset operator -(Offset other) => new 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.
  Offset operator +(Offset other) => new 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).
  Offset operator *(double operand) => new 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).
  Offset operator /(double operand) => new 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) => new 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) => new 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: new Rect.fromLTWH(0.0, 0.0, 100.0, 100.0)
  /// ```
  ///
  /// See also: [Point.&]
  Rect operator &(Size other) => new Rect.fromLTWH(dx, dy, other.width, other.height);

  /// Returns the point at (0, 0) plus this offset.
  Point toPoint() => new Point(dx, dy);

  /// Linearly interpolate between two offsets.
  ///
  /// If either offset is null, this function interpolates from [Offset.zero].
  static Offset lerp(Offset a, Offset b, double t) {
    if (a == null && b == null)
      return null;
    if (a == null)
      return b * t;
    if (b == null)
      return a * (1.0 - t);
    return new Offset(lerpDouble(a.dx, b.dx, t), lerpDouble(a.dy, b.dy, t));
  }

  /// Compares two Offsets for equality.
  @override
  bool operator ==(dynamic other) => other is Offset && super == other;

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

/// Holds a 2D floating-point size.
///
/// You can think of this as a vector from Point(0,0) to Point(size.width,
/// size.height).
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.
  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.
  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;

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

  /// A size whose width and height are infinite.
  ///
  /// See also [isInfinite], which checks whether either dimension is infinite.
  static const Size infinite = const Size(double.INFINITY, double.INFINITY);

  /// 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.
  dynamic operator -(OffsetBase other) {
    if (other is Size)
      return new Offset(width - other.width, height - other.height);
    if (other is Offset)
      return new Size(width - other.dx, height - other.dy);
    throw new 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) => new 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) => new 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) => new 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) => new 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) => new Size(width % operand, height % operand);

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

  /// The lesser of the [width] and the [height].
  double get shortestSide {
    double w = width.abs();
    double h = height.abs();
    return w < h ? w : h;
  }

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

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

  /// The point at the center of the top edge of the rectangle described by the
  /// given point (which is interpreted as the top-left corner) and this size.
  ///
  /// See also [Rect.topCenter].
  Point topCenter(Point origin) => new Point(origin.x + width / 2.0, origin.y);

  /// The point at the intersection of the top and right edges of the rectangle
  /// described by the given point (which is interpreted as the top-left corner)
  /// and this size.
  ///
  /// See also [Rect.topRight].
  Point topRight(Point origin) => new Point(origin.x + width, origin.y);

  /// The point at the center of the left edge of the rectangle described by the
  /// given point (which is interpreted as the top-left corner) and this size.
  ///
  /// See also [Rect.centerLeft].
  Point centerLeft(Point origin) => new Point(origin.x, origin.y + height / 2.0);

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

  /// The point at the center of the right edge of the rectangle described by the
  /// given point (which is interpreted as the top-left corner) and this size.
  ///
  /// See also [Rect.centerLeft].
  Point centerRight(Point origin) => new Point(origin.x + width, origin.y + height / 2.0);

  /// The point at the intersection of the bottom and left edges of the
  /// rectangle described by the given point (which is interpreted as the
  /// top-left corner) and this size.
  ///
  /// See also [Rect.bottomLeft].
  Point bottomLeft(Point origin) => new Point(origin.x, origin.y + height);

  /// The point at the center of the bottom edge of the rectangle described by
  /// the given point (which is interpreted as the top-left corner) and this
  /// size.
  ///
  /// See also [Rect.bottomLeft].
  Point bottomCenter(Point origin) => new Point(origin.x + width / 2.0, origin.y + height);

  /// The point at the intersection of the bottom and right edges of the
  /// rectangle described by the given point (which is interpreted as the
  /// top-left corner) and this size.
  ///
  /// See also [Rect.bottomRight].
  Point bottomRight(Point origin) => new Point(origin.x + width, origin.y + height);

  /// Linearly interpolate between two sizes
  ///
  /// If either size is null, this function interpolates from [Offset.zero].
  static Size lerp(Size a, Size b, double t) {
    if (a == null && b == null)
      return null;
    if (a == null)
      return b * t;
    if (b == null)
      return a * (1.0 - t);
    return new Size(lerpDouble(a.width, b.width, t), lerpDouble(a.height, b.height, t));
  }

  /// Compares two Sizes for equality.
  @override
  bool operator ==(dynamic other) => other is Size && super == other;

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

/// An immutable 2D floating-point x,y coordinate pair.
///
/// A Point represents a specific position in Cartesian space.
///
/// Subtracting a point from another returns the [Offset] that represents the
/// vector between the two points.
class Point {
  /// Creates a point. The first argument sets [x], the horizontal component,
  /// and the second sets [y], the vertical component.
  const Point(this.x, this.y);

  /// The horizontal component of the point.
  final double x;

  /// The vertical component of the point.
  final double y;

  /// The point at the origin, (0, 0).
  static const Point origin = const Point(0.0, 0.0);

  /// Unary negation operator. Returns a point with the coordinates negated.
  Point operator -() => new Point(-x, -y);

  /// Binary subtraction operator. Returns an [Offset] representing the
  /// direction and distance from the other point (the right-hand-side operand)
  /// to this point (the left-hand-side operand).
  Offset operator -(Point other) => new Offset(x - other.x, y - other.y);

  /// Binary addition operator. Returns a point that is this point (the
  /// left-hand-side operand) plus a vector [Offset] (the right-hand-side
  /// operand).
  Point operator +(Offset other) => new Point(x + other.dx, y + other.dy);

  /// Rectangle constructor operator. Combines a point and a [Size] to form a
  /// [Rect] whose top-left coordinate is this point, the left-hand-side
  /// operand, and whose size is the right-hand-side operand.
  ///
  /// ```dart
  ///   Rect myRect = Point.origin & const Size(100.0, 100.0);
  ///   // same as: new Rect.fromLTWH(0.0, 0.0, 100.0, 100.0)
  /// ```
  ///
  /// See also: [Offset.&]
  Rect operator &(Size other) => new Rect.fromLTWH(x, y, other.width, other.height);

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

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

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

  /// Modulo (remainder) operator. Returns a point whose coordinates are the
  /// remainder of the coordinates of the left-hand-side operand (a point)
  /// divided by the scalar right-hand-side operand (a double).
  Point operator %(double operand) => new Point(x % operand, y % operand);

  /// Converts this point to an [Offset] with the same coordinates.
  // does the equivalent of "return this - Point.origin"
  Offset toOffset() => new Offset(x, y);

  /// Linearly interpolate between two points.
  ///
  /// If either point is null, this function interpolates from [Point.origin].
  static Point lerp(Point a, Point b, double t) {
    if (a == null && b == null)
      return null;
    if (a == null)
      return b * t;
    if (b == null)
      return a * (1.0 - t);
    return new Point(lerpDouble(a.x, b.x, t), lerpDouble(a.y, b.y, t));
  }

  @override
  bool operator ==(dynamic other) {
    if (other is! Point)
      return false;
    final Point typedOther = other;
    return x == typedOther.x &&
           y == typedOther.y;
  }

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

  @override
  String toString() => "Point(${x?.toStringAsFixed(1)}, ${y?.toStringAsFixed(1)})";
}

/// An immutable 2D, axis-aligned, floating-point rectangle whose coordinates
/// are relative to an origin point.
class Rect {
  Rect._();

  /// Construct a rectangle from its left, top, right, and bottom edges.
  Rect.fromLTRB(double left, double top, double right, double bottom) {
    _value
      ..[0] = left
      ..[1] = top
      ..[2] = right
      ..[3] = bottom;
  }

  /// Construct a rectangle from its left and top edges, its width, and its height.
  ///
  /// To construct a [Rect] from a [Point] or [Offset] and a [Size], you can use
  /// the rectangle constructor operator `&`. See [Point.&] and [Offset.&].
  Rect.fromLTWH(double left, double top, double width, double height) {
    _value
      ..[0] = left
      ..[1] = top
      ..[2] = left + width
      ..[3] = top + height;
  }

  /// Construct a rectangle that bounds the given circle.
  Rect.fromCircle({ Point center, double radius }) {
    _value
      ..[0] = center.x - radius
      ..[1] = center.y - radius
      ..[2] = center.x + radius
      ..[3] = center.y + radius;
  }

  /// Construct the smallest rectangle that encloses the given points.
  Rect.fromPoints(Point a, Point b) {
    _value
      ..[0] = math.min(a.x, b.x)
      ..[1] = math.min(a.y, b.y)
      ..[2] = math.max(a.x, b.x)
      ..[3] = math.max(a.y, b.y);
  }

  static const int _kDataSize = 4;
  final Float32List _value = new Float32List(_kDataSize);

  /// The offset of the left edge of this rectangle from the x axis.
  double get left => _value[0];

  /// The offset of the top edge of this rectangle from the y axis.
  double get top => _value[1];

  /// The offset of the right edge of this rectangle from the x axis.
  double get right => _value[2];

  /// The offset of the bottom edge of this rectangle from the y axis.
  double get bottom => _value[3];

  /// A rectangle with left, top, right, and bottom edges all at zero.
  static final Rect zero = new Rect._();

  /// Returns a new rectangle translated by the given offset.
  Rect shift(Offset offset) {
    return new Rect.fromLTRB(left + offset.dx, top + offset.dy, right + offset.dx, bottom + offset.dy);
  }

  /// Returns a new rectangle with edges moved outwards by the given delta.
  Rect inflate(double delta) {
    return new 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 new Rect.fromLTRB(
      math.max(left, other.left),
      math.max(top, other.top),
      math.min(right, other.right),
      math.min(bottom, other.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 upper-left corner and the lower-right corner of this rectangle.
  Size get size => new Size(width, height);

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

  /// The lesser of the magnitudes of the width and the height of this
  /// rectangle.
  double get shortestSide {
    double w = width.abs();
    double h = height.abs();
    return w < h ? w : h;
  }


  /// The point at the intersection of the top and left edges of this rectangle.
  ///
  /// See also [Size.topLeft].
  Point get topLeft => new Point(left, top);

  /// The point at the center of the top edge of this rectangle.
  ///
  /// See also [Size.topCenter].
  Point get topCenter => new Point(left + width / 2.0, top);

  /// The point at the intersection of the top and right edges of this rectangle.
  ///
  /// See also [Size.topRight].
  Point get topRight => new Point(right, top);

  /// The point at the center of the left edge of this rectangle.
  ///
  /// See also [Size.centerLeft].
  Point get centerLeft => new Point(left, top + height / 2.0);

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

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

  /// The point at the intersection of the bottom and left edges of this rectangle.
  ///
  /// See also [Size.bottomLeft].
  Point get bottomLeft => new Point(left, bottom);

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

  /// The point at the intersection of the bottom and right edges of this rectangle.
  ///
  /// See also [Size.bottomRight].
  Point get bottomRight => new Point(right, bottom);


  /// Whether the given point 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(Point point) {
    return point.x >= left && point.x < right && point.y >= top && point.y < bottom;
  }

  /// Linearly interpolate between two rectangles.
  ///
  /// If either rect is null, [Rect.zero] is used as a substitute.
  static Rect lerp(Rect a, Rect b, double t) {
    if (a == null && b == null)
      return null;
    if (a == null)
      return new Rect.fromLTRB(b.left * t, b.top * t, b.right * t, b.bottom * t);
    if (b == null) {
      double k = 1.0 - t;
      return new Rect.fromLTRB(a.left * k, a.top * k, a.right * k, a.bottom * k);
    }
    return new 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 (other is! Rect)
      return false;
    final Rect typedOther = other;
    for (int i = 0; i < _kDataSize; i += 1) {
      if (_value[i] != typedOther._value[i])
        return false;
    }
    return true;
  }

  @override
  int get hashCode => hashList(_value);

  @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);

  /// 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 = const Radius.circular(0.0);

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

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

  /// Linearly interpolate between two radii.
  ///
  /// If either is null, this function substitutes [Radius.zero] instead.
  static Radius lerp(Radius a, Radius b, double t) {
    if (a == null && b == null)
      return null;
    if (a == null)
      return new Radius.elliptical(b.x * t, b.y * t);
    if (b == null) {
      double k = 1.0 - t;
      return new Radius.elliptical(a.x * k, a.y * k);
    }
    return new 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 (other is! Radius)
      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)})';
  }
}

/// A rounded rectangle with the custom radii for all four corners.
class RRect {
  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.
  RRect.fromLTRBXY(double left, double top, double right, double bottom,
                   double radiusX, double radiusY) {
    _value
      ..[0] = left
      ..[1] = top
      ..[2] = right
      ..[3] = bottom
      ..[4] = radiusX
      ..[5] = radiusY
      ..[6] = radiusX
      ..[7] = radiusY
      ..[8] = radiusX
      ..[9] = radiusY
      ..[10] = radiusX
      ..[11] = 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) {
    _value
      ..[0] = left
      ..[1] = top
      ..[2] = right
      ..[3] = bottom
      ..[4] = radius.x
      ..[5] = radius.y
      ..[6] = radius.x
      ..[7] = radius.y
      ..[8] = radius.x
      ..[9] = radius.y
      ..[10] = radius.x
      ..[11] = 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) {
    _value
      ..[0] = rect.left
      ..[1] = rect.top
      ..[2] = rect.right
      ..[3] = rect.bottom
      ..[4] = radiusX
      ..[5] = radiusY
      ..[6] = radiusX
      ..[7] = radiusY
      ..[8] = radiusX
      ..[9] = radiusY
      ..[10] = radiusX
      ..[11] = 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) {
    _value
      ..[0] = rect.left
      ..[1] = rect.top
      ..[2] = rect.right
      ..[3] = rect.bottom
      ..[4] = radius.x
      ..[5] = radius.y
      ..[6] = radius.x
      ..[7] = radius.y
      ..[8] = radius.x
      ..[9] = radius.y
      ..[10] = radius.x
      ..[11] = 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
    }
  ) {
    _value
      ..[0] = left
      ..[1] = top
      ..[2] = right
      ..[3] = bottom
      ..[4] = topLeft.x
      ..[5] = topLeft.y
      ..[6] = topRight.x
      ..[7] = topRight.y
      ..[8] = bottomRight.x
      ..[9] = bottomRight.y
      ..[10] = bottomLeft.x
      ..[11] = bottomLeft.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
    }
  ) {
    _value
      ..[0] = rect.left
      ..[1] = rect.top
      ..[2] = rect.right
      ..[3] = rect.bottom
      ..[4] = topLeft.x
      ..[5] = topLeft.y
      ..[6] = topRight.x
      ..[7] = topRight.y
      ..[8] = bottomRight.x
      ..[9] = bottomRight.y
      ..[10] = bottomLeft.x
      ..[11] = bottomLeft.y;
  }

  RRect._fromList(List<double> list) {
    for (int i = 0; i < _kDataSize; i += 1)
      _value[i] = list[i];
  }

  static const int _kDataSize = 12;
  final Float32List _value = new Float32List(_kDataSize);
  RRect _scaled; // same RRect with scaled radii per side

  /// The offset of the left edge of this rectangle from the x axis.
  double get left => _value[0];

  /// The offset of the top edge of this rectangle from the y axis.
  double get top => _value[1];

  /// The offset of the right edge of this rectangle from the x axis.
  double get right => _value[2];

  /// The offset of the bottom edge of this rectangle from the y axis.
  double get bottom => _value[3];

  /// The top-left horizontal radius.
  double get tlRadiusX => _value[4];

  /// The top-left vertical radius.
  double get tlRadiusY => _value[5];

  /// The top-left [Radius].
  Radius get tlRadius => new Radius.elliptical(_value[4], _value[5]);

  /// The top-right horizontal radius.
  double get trRadiusX => _value[6];

  /// The top-right vertical radius.
  double get trRadiusY => _value[7];

  /// The top-right [Radius].
  Radius get trRadius => new Radius.elliptical(_value[6], _value[7]);

  /// The bottom-right horizontal radius.
  double get brRadiusX => _value[8];

  /// The bottom-right vertical radius.
  double get brRadiusY => _value[9];

  /// The bottom-right [Radius].
  Radius get brRadius => new Radius.elliptical(_value[8], _value[9]);

  /// The bottom-left horizontal radius.
  double get blRadiusX => _value[10];

  /// The bottom-left vertical radius.
  double get blRadiusY => _value[11];

  /// The bottom-left [Radius].
  Radius get blRadius => new Radius.elliptical(_value[10], _value[11]);

  /// A rounded rectangle with all the values set to zero.
  static final RRect zero = new RRect._();

  /// Returns a new RRect translated by the given offset.
  RRect shift(Offset offset) {
    return new RRect.fromLTRBAndCorners(
      _value[0] + offset.dx,
      _value[1] + offset.dy,
      _value[2] + offset.dx,
      _value[3] + offset.dy,
      topLeft: new Radius.elliptical(
        _value[4],
        _value[5]
      ),
      topRight: new Radius.elliptical(
        _value[6],
        _value[7]
      ),
      bottomRight: new Radius.elliptical(
        _value[8],
        _value[9]
      ),
      bottomLeft: new Radius.elliptical(
        _value[10],
        _value[11]
      )
    );
  }

  /// Returns a new RRect with edges and radii moved outwards by the given
  /// delta.
  RRect inflate(double delta) {
    return new RRect.fromLTRBAndCorners(
      _value[0] - delta,
      _value[1] - delta,
      _value[2] + delta,
      _value[3] + delta,
      topLeft: new Radius.elliptical(
        _value[4] + delta,
        _value[5] + delta
      ),
      topRight: new Radius.elliptical(
        _value[6] + delta,
        _value[7] + delta
      ),
      bottomRight: new Radius.elliptical(
        _value[8] + delta,
        _value[9] + delta
      ),
      bottomLeft: new Radius.elliptical(
        _value[10] + delta,
        _value[11] + 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 => new 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 new 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 new 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 new 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 new 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 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 {
    double w = width.abs();
    double h = height.abs();
    return w < h ? w : h;
  }

  /// The point halfway between the left and right and the top and bottom edges
  /// of this rectangle.
  Point get center => new Point(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) {
    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 pass the size of
  // the width/height.
  //
  // Inspired from:
  //   https://github.com/google/skia/blob/master/src/core/SkRRect.cpp#L164
  void _scaleRadii() {
    if (_scaled == null) {
      double scale = 1.0;
      final List<double> scaled = new List.from(_value);

      scale = _getMin(scale, scaled[11], scaled[5], height);
      scale = _getMin(scale, scaled[4], scaled[6], width);
      scale = _getMin(scale, scaled[7], scaled[9], height);
      scale = _getMin(scale, scaled[8], scaled[10], width);

      if (scale < 1.0) {
        for (int i = 4; i < _kDataSize; i += 1)
          scaled[i] *= scale;
      }

      _scaled = new RRect._fromList(scaled);
    }
  }

  /// Whether the given point lies inside the rounded rectangle. This method
  /// works by normalizing the sizes of the radii in case they overflow the
  /// sizes of the side.
  bool contains(Point point) {
    if (point.x < left || point.x >= right || point.y < top || point.y >= bottom)
      return false; // outside bounding box

    _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.x < left + _scaled.tlRadiusX &&
        point.y < top + _scaled.tlRadiusY) {
      x = point.x - left - _scaled.tlRadiusX;
      y = point.y - top - _scaled.tlRadiusY;
      radiusX = _scaled.tlRadiusX;
      radiusY = _scaled.tlRadiusY;
    } else if (point.x > right - _scaled.trRadiusX &&
               point.y < top + _scaled.trRadiusY) {
      x = point.x - right + _scaled.trRadiusX;
      y = point.y - top - _scaled.trRadiusY;
      radiusX = _scaled.trRadiusX;
      radiusY = _scaled.trRadiusY;
    } else if (point.x > right - _scaled.brRadiusX &&
               point.y > bottom - _scaled.brRadiusY) {
      x = point.x - right + _scaled.brRadiusX;
      y = point.y - bottom + _scaled.brRadiusY;
      radiusX = _scaled.brRadiusX;
      radiusY = _scaled.brRadiusY;
    } else if (point.x < left + _scaled.blRadiusX &&
               point.y > bottom - _scaled.blRadiusY) {
      x = point.x - left - _scaled.blRadiusX;
      y = point.y - 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.
  static RRect lerp(RRect a, RRect b, double t) {
    if (a == null && b == null)
      return null;
    if (a == null) {
      return new RRect._fromList(<double>[
        b.left * t,
        b.top * t,
        b.right * t,
        b.bottom * t,
        b.tlRadiusX * t,
        b.tlRadiusY * t,
        b.trRadiusX * t,
        b.trRadiusY * t,
        b.brRadiusX * t,
        b.brRadiusY * t,
        b.blRadiusX * t,
        b.blRadiusY * t
      ]);
    }
    if (b == null) {
      double k = 1.0 - t;
      return new RRect._fromList(<double>[
        a.left * k,
        a.top * k,
        a.right * k,
        a.bottom * k,
        a.tlRadiusX * k,
        a.tlRadiusY * k,
        a.trRadiusX * k,
        a.trRadiusY * k,
        a.brRadiusX * k,
        a.brRadiusY * k,
        a.blRadiusX * k,
        a.blRadiusY * k
      ]);
    }
    return new RRect._fromList(<double>[
      lerpDouble(a.left, b.left, t),
      lerpDouble(a.top, b.top, t),
      lerpDouble(a.right, b.right, t),
      lerpDouble(a.bottom, b.bottom, t),
      lerpDouble(a.tlRadiusX, b.tlRadiusX, t),
      lerpDouble(a.tlRadiusY, b.tlRadiusY, t),
      lerpDouble(a.trRadiusX, b.trRadiusX, t),
      lerpDouble(a.trRadiusY, b.trRadiusY, t),
      lerpDouble(a.brRadiusX, b.brRadiusX, t),
      lerpDouble(a.brRadiusY, b.brRadiusY, t),
      lerpDouble(a.blRadiusX, b.blRadiusX, t),
      lerpDouble(a.blRadiusY, b.blRadiusY, t)
    ]);
  }

  @override
  bool operator ==(dynamic other) {
    if (identical(this, other))
      return true;
    if (other is! RRect)
      return false;
    final RRect typedOther = other;
    for (int i = 0; i < _kDataSize; i += 1) {
      if (_value[i] != typedOther._value[i])
        return false;
    }
    return true;
  }

  @override
  int get hashCode => hashList(_value);

  @override
  String toString() {
    return 'RRect.fromLTRBAndCorners(${left.toStringAsFixed(1)}, '
        '${top.toStringAsFixed(1)}, ${right.toStringAsFixed(1)}, '
        '${bottom.toStringAsFixed(1)}, '
        '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 [new 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 new RSTransform(scos, ssin, tx, ty);
  }

  final Float32List _value = new 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];
}