// Copyright (c) 2015, Google Inc. Please see the AUTHORS file for details.
// 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 vector_math;

/// 4D Matrix.
/// Values are stored in column major order.
class Matrix4 {
  final Float32List _m4storage;

  /// The components of the matrix.
  Float32List get storage => _m4storage;

  /// Solve [A] * [x] = [b].
  static void solve2(Matrix4 A, Vector2 x, Vector2 b) {
    final double a11 = A.entry(0, 0);
    final double a12 = A.entry(0, 1);
    final double a21 = A.entry(1, 0);
    final double a22 = A.entry(1, 1);
    final double bx = b.x - A._m4storage[8];
    final double by = b.y - A._m4storage[9];
    double det = a11 * a22 - a12 * a21;

    if (det != 0.0) {
      det = 1.0 / det;
    }

    x
      ..x = det * (a22 * bx - a12 * by)
      ..y = det * (a11 * by - a21 * bx);
  }

  /// Solve [A] * [x] = [b].
  static void solve3(Matrix4 A, Vector3 x, Vector3 b) {
    final double A0x = A.entry(0, 0);
    final double A0y = A.entry(1, 0);
    final double A0z = A.entry(2, 0);
    final double A1x = A.entry(0, 1);
    final double A1y = A.entry(1, 1);
    final double A1z = A.entry(2, 1);
    final double A2x = A.entry(0, 2);
    final double A2y = A.entry(1, 2);
    final double A2z = A.entry(2, 2);
    final double bx = b.x - A._m4storage[12];
    final double by = b.y - A._m4storage[13];
    final double bz = b.z - A._m4storage[14];
    double rx, ry, rz;
    double det;

    // Column1 cross Column 2
    rx = A1y * A2z - A1z * A2y;
    ry = A1z * A2x - A1x * A2z;
    rz = A1x * A2y - A1y * A2x;

    // A.getColumn(0).dot(x)
    det = A0x * rx + A0y * ry + A0z * rz;
    if (det != 0.0) {
      det = 1.0 / det;
    }

    // b dot [Column1 cross Column 2]
    final double x_ = det * (bx * rx + by * ry + bz * rz);

    // Column2 cross b
    rx = -(A2y * bz - A2z * by);
    ry = -(A2z * bx - A2x * bz);
    rz = -(A2x * by - A2y * bx);
    // Column0 dot -[Column2 cross b (Column3)]
    final double y_ = det * (A0x * rx + A0y * ry + A0z * rz);

    // b cross Column 1
    rx = -(by * A1z - bz * A1y);
    ry = -(bz * A1x - bx * A1z);
    rz = -(bx * A1y - by * A1x);
    // Column0 dot -[b cross Column 1]
    final double z_ = det * (A0x * rx + A0y * ry + A0z * rz);

    x
      ..x = x_
      ..y = y_
      ..z = z_;
  }

  /// Solve [A] * [x] = [b].
  static void solve(Matrix4 A, Vector4 x, Vector4 b) {
    final double a00 = A._m4storage[0];
    final double a01 = A._m4storage[1];
    final double a02 = A._m4storage[2];
    final double a03 = A._m4storage[3];
    final double a10 = A._m4storage[4];
    final double a11 = A._m4storage[5];
    final double a12 = A._m4storage[6];
    final double a13 = A._m4storage[7];
    final double a20 = A._m4storage[8];
    final double a21 = A._m4storage[9];
    final double a22 = A._m4storage[10];
    final double a23 = A._m4storage[11];
    final double a30 = A._m4storage[12];
    final double a31 = A._m4storage[13];
    final double a32 = A._m4storage[14];
    final double a33 = A._m4storage[15];
    final double b00 = a00 * a11 - a01 * a10;
    final double b01 = a00 * a12 - a02 * a10;
    final double b02 = a00 * a13 - a03 * a10;
    final double b03 = a01 * a12 - a02 * a11;
    final double b04 = a01 * a13 - a03 * a11;
    final double b05 = a02 * a13 - a03 * a12;
    final double b06 = a20 * a31 - a21 * a30;
    final double b07 = a20 * a32 - a22 * a30;
    final double b08 = a20 * a33 - a23 * a30;
    final double b09 = a21 * a32 - a22 * a31;
    final double b10 = a21 * a33 - a23 * a31;
    final double b11 = a22 * a33 - a23 * a32;

    final double bX = b.storage[0];
    final double bY = b.storage[1];
    final double bZ = b.storage[2];
    final double bW = b.storage[3];

    double det =
        b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

    if (det != 0.0) {
      det = 1.0 / det;
    }

    x
      ..x = det *
          ((a11 * b11 - a12 * b10 + a13 * b09) * bX -
              (a10 * b11 - a12 * b08 + a13 * b07) * bY +
              (a10 * b10 - a11 * b08 + a13 * b06) * bZ -
              (a10 * b09 - a11 * b07 + a12 * b06) * bW)
      ..y = det *
          -((a01 * b11 - a02 * b10 + a03 * b09) * bX -
              (a00 * b11 - a02 * b08 + a03 * b07) * bY +
              (a00 * b10 - a01 * b08 + a03 * b06) * bZ -
              (a00 * b09 - a01 * b07 + a02 * b06) * bW)
      ..z = det *
          ((a31 * b05 - a32 * b04 + a33 * b03) * bX -
              (a30 * b05 - a32 * b02 + a33 * b01) * bY +
              (a30 * b04 - a31 * b02 + a33 * b00) * bZ -
              (a30 * b03 - a31 * b01 + a32 * b00) * bW)
      ..w = det *
          -((a21 * b05 - a22 * b04 + a23 * b03) * bX -
              (a20 * b05 - a22 * b02 + a23 * b01) * bY +
              (a20 * b04 - a21 * b02 + a23 * b00) * bZ -
              (a20 * b03 - a21 * b01 + a22 * b00) * bW);
  }

  /// Return index in storage for [row], [col] value.
  int index(int row, int col) => (col * 4) + row;

  /// Value at [row], [col].
  double entry(int row, int col) {
    assert((row >= 0) && (row < dimension));
    assert((col >= 0) && (col < dimension));

    return _m4storage[index(row, col)];
  }

  /// Set value at [row], [col] to be [v].
  void setEntry(int row, int col, double v) {
    assert((row >= 0) && (row < dimension));
    assert((col >= 0) && (col < dimension));

    _m4storage[index(row, col)] = v;
  }

  /// Constructs a new mat4.
  factory Matrix4(
          double arg0,
          double arg1,
          double arg2,
          double arg3,
          double arg4,
          double arg5,
          double arg6,
          double arg7,
          double arg8,
          double arg9,
          double arg10,
          double arg11,
          double arg12,
          double arg13,
          double arg14,
          double arg15) =>
      new Matrix4.zero()
        ..setValues(arg0, arg1, arg2, arg3, arg4, arg5, arg6, arg7, arg8, arg9,
            arg10, arg11, arg12, arg13, arg14, arg15);

  /// New matrix from [values].
  factory Matrix4.fromList(List<double> values) => new Matrix4.zero()
    ..setValues(
        values[0],
        values[1],
        values[2],
        values[3],
        values[4],
        values[5],
        values[6],
        values[7],
        values[8],
        values[9],
        values[10],
        values[11],
        values[12],
        values[13],
        values[14],
        values[15]);

  /// Zero matrix.
  Matrix4.zero() : _m4storage = new Float32List(16);

  /// Identity matrix.
  factory Matrix4.identity() => new Matrix4.zero()..setIdentity();

  /// Copies values from [other].
  factory Matrix4.copy(Matrix4 other) => new Matrix4.zero()..setFrom(other);

  /// Constructs a matrix that is the inverse of [other].
  factory Matrix4.inverted(Matrix4 other) {
    final Matrix4 r = new Matrix4.zero();
    final double determinant = r.copyInverse(other);
    if (determinant == 0.0) {
      throw new ArgumentError.value(
          other, 'other', 'Matrix cannot be inverted');
    }
    return r;
  }

  /// Constructs a new mat4 from columns.
  factory Matrix4.columns(
          Vector4 arg0, Vector4 arg1, Vector4 arg2, Vector4 arg3) =>
      new Matrix4.zero()..setColumns(arg0, arg1, arg2, arg3);

  /// Outer product of [u] and [v].
  factory Matrix4.outer(Vector4 u, Vector4 v) =>
      new Matrix4.zero()..setOuter(u, v);

  /// Rotation of [radians_] around X.
  factory Matrix4.rotationX(double radians) => new Matrix4.zero()
    .._m4storage[15] = 1.0
    ..setRotationX(radians);

  /// Rotation of [radians_] around Y.
  factory Matrix4.rotationY(double radians) => new Matrix4.zero()
    .._m4storage[15] = 1.0
    ..setRotationY(radians);

  /// Rotation of [radians_] around Z.
  factory Matrix4.rotationZ(double radians) => new Matrix4.zero()
    .._m4storage[15] = 1.0
    ..setRotationZ(radians);

  /// Translation matrix.
  factory Matrix4.translation(Vector3 translation) => new Matrix4.zero()
    ..setIdentity()
    ..setTranslation(translation);

  /// Translation matrix.
  factory Matrix4.translationValues(double x, double y, double z) =>
      new Matrix4.zero()
        ..setIdentity()
        ..setTranslationRaw(x, y, z);

  /// Scale matrix.
  factory Matrix4.diagonal3(Vector3 scale) {
    final Matrix4 m = new Matrix4.zero();
    final Float32List mStorage = m._m4storage;
    final Float32List scaleStorage = scale._v3storage;
    mStorage[15] = 1.0;
    mStorage[10] = scaleStorage[2];
    mStorage[5] = scaleStorage[1];
    mStorage[0] = scaleStorage[0];
    return m;
  }

  /// Scale matrix.
  factory Matrix4.diagonal3Values(double x, double y, double z) =>
      new Matrix4.zero()
        .._m4storage[15] = 1.0
        .._m4storage[10] = z
        .._m4storage[5] = y
        .._m4storage[0] = x;

  /// Skew matrix around X axis
  factory Matrix4.skewX(double alpha) {
    final Matrix4 m = new Matrix4.identity();
    m._m4storage[4] = math.tan(alpha);
    return m;
  }

  /// Skew matrix around Y axis.
  factory Matrix4.skewY(double beta) {
    final Matrix4 m = new Matrix4.identity();
    m._m4storage[1] = math.tan(beta);
    return m;
  }

  /// Skew matrix around X axis (alpha) and Y axis (beta).
  factory Matrix4.skew(double alpha, double beta) {
    final Matrix4 m = new Matrix4.identity();
    m._m4storage[1] = math.tan(beta);
    m._m4storage[4] = math.tan(alpha);
    return m;
  }

  /// Constructs Matrix4 with given [Float32List] as [storage].
  Matrix4.fromFloat32List(this._m4storage);

  /// Constructs Matrix4 with a [storage] that views given [buffer] starting at
  /// [offset]. [offset] has to be multiple of [Float32List.BYTES_PER_ELEMENT].
  Matrix4.fromBuffer(ByteBuffer buffer, int offset)
      : _m4storage = new Float32List.view(buffer, offset, 16);

  /// Constructs Matrix4 from [translation], [rotation] and [scale].
  factory Matrix4.compose(
          Vector3 translation, Quaternion rotation, Vector3 scale) =>
      new Matrix4.zero()
        ..setFromTranslationRotationScale(translation, rotation, scale);

  /// Sets the diagonal to [arg].
  void splatDiagonal(double arg) {
    _m4storage[0] = arg;
    _m4storage[5] = arg;
    _m4storage[10] = arg;
    _m4storage[15] = arg;
  }

  /// Sets the matrix with specified values.
  void setValues(
      double arg0,
      double arg1,
      double arg2,
      double arg3,
      double arg4,
      double arg5,
      double arg6,
      double arg7,
      double arg8,
      double arg9,
      double arg10,
      double arg11,
      double arg12,
      double arg13,
      double arg14,
      double arg15) {
    _m4storage[15] = arg15;
    _m4storage[14] = arg14;
    _m4storage[13] = arg13;
    _m4storage[12] = arg12;
    _m4storage[11] = arg11;
    _m4storage[10] = arg10;
    _m4storage[9] = arg9;
    _m4storage[8] = arg8;
    _m4storage[7] = arg7;
    _m4storage[6] = arg6;
    _m4storage[5] = arg5;
    _m4storage[4] = arg4;
    _m4storage[3] = arg3;
    _m4storage[2] = arg2;
    _m4storage[1] = arg1;
    _m4storage[0] = arg0;
  }

  /// Sets the entire matrix to the column values.
  void setColumns(Vector4 arg0, Vector4 arg1, Vector4 arg2, Vector4 arg3) {
    final Float32List arg0Storage = arg0._v4storage;
    final Float32List arg1Storage = arg1._v4storage;
    final Float32List arg2Storage = arg2._v4storage;
    final Float32List arg3Storage = arg3._v4storage;
    _m4storage[0] = arg0Storage[0];
    _m4storage[1] = arg0Storage[1];
    _m4storage[2] = arg0Storage[2];
    _m4storage[3] = arg0Storage[3];
    _m4storage[4] = arg1Storage[0];
    _m4storage[5] = arg1Storage[1];
    _m4storage[6] = arg1Storage[2];
    _m4storage[7] = arg1Storage[3];
    _m4storage[8] = arg2Storage[0];
    _m4storage[9] = arg2Storage[1];
    _m4storage[10] = arg2Storage[2];
    _m4storage[11] = arg2Storage[3];
    _m4storage[12] = arg3Storage[0];
    _m4storage[13] = arg3Storage[1];
    _m4storage[14] = arg3Storage[2];
    _m4storage[15] = arg3Storage[3];
  }

  /// Sets the entire matrix to the matrix in [arg].
  void setFrom(Matrix4 arg) {
    final Float32List argStorage = arg._m4storage;
    _m4storage[15] = argStorage[15];
    _m4storage[14] = argStorage[14];
    _m4storage[13] = argStorage[13];
    _m4storage[12] = argStorage[12];
    _m4storage[11] = argStorage[11];
    _m4storage[10] = argStorage[10];
    _m4storage[9] = argStorage[9];
    _m4storage[8] = argStorage[8];
    _m4storage[7] = argStorage[7];
    _m4storage[6] = argStorage[6];
    _m4storage[5] = argStorage[5];
    _m4storage[4] = argStorage[4];
    _m4storage[3] = argStorage[3];
    _m4storage[2] = argStorage[2];
    _m4storage[1] = argStorage[1];
    _m4storage[0] = argStorage[0];
  }

  /// Sets the matrix from translation [arg0] and rotation [arg1].
  void setFromTranslationRotation(Vector3 arg0, Quaternion arg1) {
    final Float32List arg1Storage = arg1._qStorage;
    final double x = arg1Storage[0];
    final double y = arg1Storage[1];
    final double z = arg1Storage[2];
    final double w = arg1Storage[3];
    final double x2 = x + x;
    final double y2 = y + y;
    final double z2 = z + z;
    final double xx = x * x2;
    final double xy = x * y2;
    final double xz = x * z2;
    final double yy = y * y2;
    final double yz = y * z2;
    final double zz = z * z2;
    final double wx = w * x2;
    final double wy = w * y2;
    final double wz = w * z2;

    final Float32List arg0Storage = arg0._v3storage;
    _m4storage[0] = 1.0 - (yy + zz);
    _m4storage[1] = xy + wz;
    _m4storage[2] = xz - wy;
    _m4storage[3] = 0.0;
    _m4storage[4] = xy - wz;
    _m4storage[5] = 1.0 - (xx + zz);
    _m4storage[6] = yz + wx;
    _m4storage[7] = 0.0;
    _m4storage[8] = xz + wy;
    _m4storage[9] = yz - wx;
    _m4storage[10] = 1.0 - (xx + yy);
    _m4storage[11] = 0.0;
    _m4storage[12] = arg0Storage[0];
    _m4storage[13] = arg0Storage[1];
    _m4storage[14] = arg0Storage[2];
    _m4storage[15] = 1.0;
  }

  /// Sets the matrix from [translation], [rotation] and [scale].
  void setFromTranslationRotationScale(
      Vector3 translation, Quaternion rotation, Vector3 scale) {
    setFromTranslationRotation(translation, rotation);
    this.scale(scale);
  }

  /// Sets the upper 2x2 of the matrix to be [arg].
  void setUpper2x2(Matrix2 arg) {
    final Float32List argStorage = arg._m2storage;
    _m4storage[0] = argStorage[0];
    _m4storage[1] = argStorage[1];
    _m4storage[4] = argStorage[2];
    _m4storage[5] = argStorage[3];
  }

  /// Sets the diagonal of the matrix to be [arg].
  void setDiagonal(Vector4 arg) {
    final Float32List argStorage = arg._v4storage;
    _m4storage[0] = argStorage[0];
    _m4storage[5] = argStorage[1];
    _m4storage[10] = argStorage[2];
    _m4storage[15] = argStorage[3];
  }

  void setOuter(Vector4 u, Vector4 v) {
    final Float32List uStorage = u._v4storage;
    final Float32List vStorage = v._v4storage;
    _m4storage[0] = uStorage[0] * vStorage[0];
    _m4storage[1] = uStorage[0] * vStorage[1];
    _m4storage[2] = uStorage[0] * vStorage[2];
    _m4storage[3] = uStorage[0] * vStorage[3];
    _m4storage[4] = uStorage[1] * vStorage[0];
    _m4storage[5] = uStorage[1] * vStorage[1];
    _m4storage[6] = uStorage[1] * vStorage[2];
    _m4storage[7] = uStorage[1] * vStorage[3];
    _m4storage[8] = uStorage[2] * vStorage[0];
    _m4storage[9] = uStorage[2] * vStorage[1];
    _m4storage[10] = uStorage[2] * vStorage[2];
    _m4storage[11] = uStorage[2] * vStorage[3];
    _m4storage[12] = uStorage[3] * vStorage[0];
    _m4storage[13] = uStorage[3] * vStorage[1];
    _m4storage[14] = uStorage[3] * vStorage[2];
    _m4storage[15] = uStorage[3] * vStorage[3];
  }

  /// Returns a printable string
  @override
  String toString() => '[0] ${getRow(0)}\n[1] ${getRow(1)}\n'
      '[2] ${getRow(2)}\n[3] ${getRow(3)}\n';

  /// Dimension of the matrix.
  int get dimension => 4;

  /// Access the element of the matrix at the index [i].
  double operator [](int i) => _m4storage[i];

  /// Set the element of the matrix at the index [i].
  void operator []=(int i, double v) {
    _m4storage[i] = v;
  }

  /// Check if two matrices are the same.
  @override
  bool operator ==(Object other) =>
      (other is Matrix4) &&
      (_m4storage[0] == other._m4storage[0]) &&
      (_m4storage[1] == other._m4storage[1]) &&
      (_m4storage[2] == other._m4storage[2]) &&
      (_m4storage[3] == other._m4storage[3]) &&
      (_m4storage[4] == other._m4storage[4]) &&
      (_m4storage[5] == other._m4storage[5]) &&
      (_m4storage[6] == other._m4storage[6]) &&
      (_m4storage[7] == other._m4storage[7]) &&
      (_m4storage[8] == other._m4storage[8]) &&
      (_m4storage[9] == other._m4storage[9]) &&
      (_m4storage[10] == other._m4storage[10]) &&
      (_m4storage[11] == other._m4storage[11]) &&
      (_m4storage[12] == other._m4storage[12]) &&
      (_m4storage[13] == other._m4storage[13]) &&
      (_m4storage[14] == other._m4storage[14]) &&
      (_m4storage[15] == other._m4storage[15]);

  @override
  int get hashCode => quiver.hashObjects(_m4storage);

  /// Returns row 0
  Vector4 get row0 => getRow(0);

  /// Returns row 1
  Vector4 get row1 => getRow(1);

  /// Returns row 2
  Vector4 get row2 => getRow(2);

  /// Returns row 3
  Vector4 get row3 => getRow(3);

  /// Sets row 0 to [arg]
  set row0(Vector4 arg) => setRow(0, arg);

  /// Sets row 1 to [arg]
  set row1(Vector4 arg) => setRow(1, arg);

  /// Sets row 2 to [arg]
  set row2(Vector4 arg) => setRow(2, arg);

  /// Sets row 3 to [arg]
  set row3(Vector4 arg) => setRow(3, arg);

  /// Assigns the [row] of the matrix [arg]
  void setRow(int row, Vector4 arg) {
    final Float32List argStorage = arg._v4storage;
    _m4storage[index(row, 0)] = argStorage[0];
    _m4storage[index(row, 1)] = argStorage[1];
    _m4storage[index(row, 2)] = argStorage[2];
    _m4storage[index(row, 3)] = argStorage[3];
  }

  /// Gets the [row] of the matrix
  Vector4 getRow(int row) {
    final Vector4 r = new Vector4.zero();
    final Float32List rStorage = r._v4storage;
    rStorage[0] = _m4storage[index(row, 0)];
    rStorage[1] = _m4storage[index(row, 1)];
    rStorage[2] = _m4storage[index(row, 2)];
    rStorage[3] = _m4storage[index(row, 3)];
    return r;
  }

  /// Assigns the [column] of the matrix [arg]
  void setColumn(int column, Vector4 arg) {
    final int entry = column * 4;
    final Float32List argStorage = arg._v4storage;
    _m4storage[entry + 3] = argStorage[3];
    _m4storage[entry + 2] = argStorage[2];
    _m4storage[entry + 1] = argStorage[1];
    _m4storage[entry + 0] = argStorage[0];
  }

  /// Gets the [column] of the matrix
  Vector4 getColumn(int column) {
    final Vector4 r = new Vector4.zero();
    final Float32List rStorage = r._v4storage;
    final int entry = column * 4;
    rStorage[3] = _m4storage[entry + 3];
    rStorage[2] = _m4storage[entry + 2];
    rStorage[1] = _m4storage[entry + 1];
    rStorage[0] = _m4storage[entry + 0];
    return r;
  }

  /// Clone matrix.
  Matrix4 clone() => new Matrix4.copy(this);

  /// Copy into [arg].
  Matrix4 copyInto(Matrix4 arg) {
    final Float32List argStorage = arg._m4storage;
    argStorage[0] = _m4storage[0];
    argStorage[1] = _m4storage[1];
    argStorage[2] = _m4storage[2];
    argStorage[3] = _m4storage[3];
    argStorage[4] = _m4storage[4];
    argStorage[5] = _m4storage[5];
    argStorage[6] = _m4storage[6];
    argStorage[7] = _m4storage[7];
    argStorage[8] = _m4storage[8];
    argStorage[9] = _m4storage[9];
    argStorage[10] = _m4storage[10];
    argStorage[11] = _m4storage[11];
    argStorage[12] = _m4storage[12];
    argStorage[13] = _m4storage[13];
    argStorage[14] = _m4storage[14];
    argStorage[15] = _m4storage[15];
    return arg;
  }

  /// Returns new matrix -this
  Matrix4 operator -() => clone()..negate();

  /// Returns a new vector or matrix by multiplying [this] with [arg].
  dynamic operator *(dynamic arg) {
    if (arg is double) {
      return scaled(arg);
    }
    if (arg is Vector4) {
      return transformed(arg);
    }
    if (arg is Vector3) {
      return transformed3(arg);
    }
    if (arg is Matrix4) {
      return multiplied(arg);
    }
    throw new ArgumentError(arg);
  }

  /// Returns new matrix after component wise [this] + [arg]
  Matrix4 operator +(Matrix4 arg) => clone()..add(arg);

  /// Returns new matrix after component wise [this] - [arg]
  Matrix4 operator -(Matrix4 arg) => clone()..sub(arg);

  /// Translate this matrix by a [Vector3], [Vector4], or x,y,z
  void translate(dynamic x, [double y = 0.0, double z = 0.0]) {
    double tx;
    double ty;
    double tz;
    final double tw = x is Vector4 ? x.w : 1.0;
    if (x is Vector3) {
      tx = x.x;
      ty = x.y;
      tz = x.z;
    } else if (x is Vector3) {
      tx = x.x;
      ty = x.y;
      tz = x.z;
    } else if (x is double) {
      tx = x;
      ty = y;
      tz = z;
    }
    final double t1 = _m4storage[0] * tx +
        _m4storage[4] * ty +
        _m4storage[8] * tz +
        _m4storage[12] * tw;
    final double t2 = _m4storage[1] * tx +
        _m4storage[5] * ty +
        _m4storage[9] * tz +
        _m4storage[13] * tw;
    final double t3 = _m4storage[2] * tx +
        _m4storage[6] * ty +
        _m4storage[10] * tz +
        _m4storage[14] * tw;
    final double t4 = _m4storage[3] * tx +
        _m4storage[7] * ty +
        _m4storage[11] * tz +
        _m4storage[15] * tw;
    _m4storage[12] = t1;
    _m4storage[13] = t2;
    _m4storage[14] = t3;
    _m4storage[15] = t4;
  }

  /// Multiply [this] by a translation from the left.
  /// The translation can be specified with a  [Vector3], [Vector4], or x, y, z.
  void leftTranslate(dynamic x, [double y = 0.0, double z = 0.0]) {
    double tx;
    double ty;
    double tz;
    final double tw = x is Vector4 ? x.w : 1.0;
    if (x is Vector3) {
      tx = x.x;
      ty = x.y;
      tz = x.z;
    } else if (x is Vector4) {
      tx = x.x;
      ty = x.y;
      tz = x.z;
    } else if (x is double) {
      tx = x;
      ty = y;
      tz = z;
    }

    // Column 1
    _m4storage[0] += tx * _m4storage[3];
    _m4storage[1] += ty * _m4storage[3];
    _m4storage[2] += tz * _m4storage[3];
    _m4storage[3] = tw * _m4storage[3];

    // Column 2
    _m4storage[4] += tx * _m4storage[7];
    _m4storage[5] += ty * _m4storage[7];
    _m4storage[6] += tz * _m4storage[7];
    _m4storage[7] = tw * _m4storage[7];

    // Column 3
    _m4storage[8] += tx * _m4storage[11];
    _m4storage[9] += ty * _m4storage[11];
    _m4storage[10] += tz * _m4storage[11];
    _m4storage[11] = tw * _m4storage[11];

    // Column 4
    _m4storage[12] += tx * _m4storage[15];
    _m4storage[13] += ty * _m4storage[15];
    _m4storage[14] += tz * _m4storage[15];
    _m4storage[15] = tw * _m4storage[15];
  }

  /// Rotate this [angle] radians around [axis]
  void rotate(Vector3 axis, double angle) {
    final double len = axis.length;
    final Float32List axisStorage = axis._v3storage;
    final double x = axisStorage[0] / len;
    final double y = axisStorage[1] / len;
    final double z = axisStorage[2] / len;
    final double c = math.cos(angle);
    final double s = math.sin(angle);
    final double C = 1.0 - c;
    final double m11 = x * x * C + c;
    final double m12 = x * y * C - z * s;
    final double m13 = x * z * C + y * s;
    final double m21 = y * x * C + z * s;
    final double m22 = y * y * C + c;
    final double m23 = y * z * C - x * s;
    final double m31 = z * x * C - y * s;
    final double m32 = z * y * C + x * s;
    final double m33 = z * z * C + c;
    final double t1 =
        _m4storage[0] * m11 + _m4storage[4] * m21 + _m4storage[8] * m31;
    final double t2 =
        _m4storage[1] * m11 + _m4storage[5] * m21 + _m4storage[9] * m31;
    final double t3 =
        _m4storage[2] * m11 + _m4storage[6] * m21 + _m4storage[10] * m31;
    final double t4 =
        _m4storage[3] * m11 + _m4storage[7] * m21 + _m4storage[11] * m31;
    final double t5 =
        _m4storage[0] * m12 + _m4storage[4] * m22 + _m4storage[8] * m32;
    final double t6 =
        _m4storage[1] * m12 + _m4storage[5] * m22 + _m4storage[9] * m32;
    final double t7 =
        _m4storage[2] * m12 + _m4storage[6] * m22 + _m4storage[10] * m32;
    final double t8 =
        _m4storage[3] * m12 + _m4storage[7] * m22 + _m4storage[11] * m32;
    final double t9 =
        _m4storage[0] * m13 + _m4storage[4] * m23 + _m4storage[8] * m33;
    final double t10 =
        _m4storage[1] * m13 + _m4storage[5] * m23 + _m4storage[9] * m33;
    final double t11 =
        _m4storage[2] * m13 + _m4storage[6] * m23 + _m4storage[10] * m33;
    final double t12 =
        _m4storage[3] * m13 + _m4storage[7] * m23 + _m4storage[11] * m33;
    _m4storage[0] = t1;
    _m4storage[1] = t2;
    _m4storage[2] = t3;
    _m4storage[3] = t4;
    _m4storage[4] = t5;
    _m4storage[5] = t6;
    _m4storage[6] = t7;
    _m4storage[7] = t8;
    _m4storage[8] = t9;
    _m4storage[9] = t10;
    _m4storage[10] = t11;
    _m4storage[11] = t12;
  }

  /// Rotate this [angle] radians around X
  void rotateX(double angle) {
    final double cosAngle = math.cos(angle);
    final double sinAngle = math.sin(angle);
    final double t1 = _m4storage[4] * cosAngle + _m4storage[8] * sinAngle;
    final double t2 = _m4storage[5] * cosAngle + _m4storage[9] * sinAngle;
    final double t3 = _m4storage[6] * cosAngle + _m4storage[10] * sinAngle;
    final double t4 = _m4storage[7] * cosAngle + _m4storage[11] * sinAngle;
    final double t5 = _m4storage[4] * -sinAngle + _m4storage[8] * cosAngle;
    final double t6 = _m4storage[5] * -sinAngle + _m4storage[9] * cosAngle;
    final double t7 = _m4storage[6] * -sinAngle + _m4storage[10] * cosAngle;
    final double t8 = _m4storage[7] * -sinAngle + _m4storage[11] * cosAngle;
    _m4storage[4] = t1;
    _m4storage[5] = t2;
    _m4storage[6] = t3;
    _m4storage[7] = t4;
    _m4storage[8] = t5;
    _m4storage[9] = t6;
    _m4storage[10] = t7;
    _m4storage[11] = t8;
  }

  /// Rotate this matrix [angle] radians around Y
  void rotateY(double angle) {
    final double cosAngle = math.cos(angle);
    final double sinAngle = math.sin(angle);
    final double t1 = _m4storage[0] * cosAngle + _m4storage[8] * -sinAngle;
    final double t2 = _m4storage[1] * cosAngle + _m4storage[9] * -sinAngle;
    final double t3 = _m4storage[2] * cosAngle + _m4storage[10] * -sinAngle;
    final double t4 = _m4storage[3] * cosAngle + _m4storage[11] * -sinAngle;
    final double t5 = _m4storage[0] * sinAngle + _m4storage[8] * cosAngle;
    final double t6 = _m4storage[1] * sinAngle + _m4storage[9] * cosAngle;
    final double t7 = _m4storage[2] * sinAngle + _m4storage[10] * cosAngle;
    final double t8 = _m4storage[3] * sinAngle + _m4storage[11] * cosAngle;
    _m4storage[0] = t1;
    _m4storage[1] = t2;
    _m4storage[2] = t3;
    _m4storage[3] = t4;
    _m4storage[8] = t5;
    _m4storage[9] = t6;
    _m4storage[10] = t7;
    _m4storage[11] = t8;
  }

  /// Rotate this matrix [angle] radians around Z
  void rotateZ(double angle) {
    final double cosAngle = math.cos(angle);
    final double sinAngle = math.sin(angle);
    final double t1 = _m4storage[0] * cosAngle + _m4storage[4] * sinAngle;
    final double t2 = _m4storage[1] * cosAngle + _m4storage[5] * sinAngle;
    final double t3 = _m4storage[2] * cosAngle + _m4storage[6] * sinAngle;
    final double t4 = _m4storage[3] * cosAngle + _m4storage[7] * sinAngle;
    final double t5 = _m4storage[0] * -sinAngle + _m4storage[4] * cosAngle;
    final double t6 = _m4storage[1] * -sinAngle + _m4storage[5] * cosAngle;
    final double t7 = _m4storage[2] * -sinAngle + _m4storage[6] * cosAngle;
    final double t8 = _m4storage[3] * -sinAngle + _m4storage[7] * cosAngle;
    _m4storage[0] = t1;
    _m4storage[1] = t2;
    _m4storage[2] = t3;
    _m4storage[3] = t4;
    _m4storage[4] = t5;
    _m4storage[5] = t6;
    _m4storage[6] = t7;
    _m4storage[7] = t8;
  }

  /// Scale this matrix by a [Vector3], [Vector4], or x,y,z
  void scale(dynamic x, [double y, double z]) {
    double sx;
    double sy;
    double sz;
    final double sw = x is Vector4 ? x.w : 1.0;
    if (x is Vector3) {
      sx = x.x;
      sy = x.y;
      sz = x.z;
    } else if (x is Vector4) {
      sx = x.x;
      sy = x.y;
      sz = x.z;
    } else if (x is double) {
      sx = x;
      sy = y == null ? x : y.toDouble();
      sz = z == null ? x : z.toDouble();
    }
    _m4storage[0] *= sx;
    _m4storage[1] *= sx;
    _m4storage[2] *= sx;
    _m4storage[3] *= sx;
    _m4storage[4] *= sy;
    _m4storage[5] *= sy;
    _m4storage[6] *= sy;
    _m4storage[7] *= sy;
    _m4storage[8] *= sz;
    _m4storage[9] *= sz;
    _m4storage[10] *= sz;
    _m4storage[11] *= sz;
    _m4storage[12] *= sw;
    _m4storage[13] *= sw;
    _m4storage[14] *= sw;
    _m4storage[15] *= sw;
  }

  /// Create a copy of [this] scaled by a [Vector3], [Vector4] or [x],[y], and
  /// [z].
  Matrix4 scaled(dynamic x, [double y = null, double z = null]) =>
      clone()..scale(x, y, z);

  /// Zeros [this].
  void setZero() {
    _m4storage[0] = 0.0;
    _m4storage[1] = 0.0;
    _m4storage[2] = 0.0;
    _m4storage[3] = 0.0;
    _m4storage[4] = 0.0;
    _m4storage[5] = 0.0;
    _m4storage[6] = 0.0;
    _m4storage[7] = 0.0;
    _m4storage[8] = 0.0;
    _m4storage[9] = 0.0;
    _m4storage[10] = 0.0;
    _m4storage[11] = 0.0;
    _m4storage[12] = 0.0;
    _m4storage[13] = 0.0;
    _m4storage[14] = 0.0;
    _m4storage[15] = 0.0;
  }

  /// Makes [this] into the identity matrix.
  void setIdentity() {
    _m4storage[0] = 1.0;
    _m4storage[1] = 0.0;
    _m4storage[2] = 0.0;
    _m4storage[3] = 0.0;
    _m4storage[4] = 0.0;
    _m4storage[5] = 1.0;
    _m4storage[6] = 0.0;
    _m4storage[7] = 0.0;
    _m4storage[8] = 0.0;
    _m4storage[9] = 0.0;
    _m4storage[10] = 1.0;
    _m4storage[11] = 0.0;
    _m4storage[12] = 0.0;
    _m4storage[13] = 0.0;
    _m4storage[14] = 0.0;
    _m4storage[15] = 1.0;
  }

  /// Returns the tranpose of this.
  Matrix4 transposed() => clone()..transpose();

  void transpose() {
    double temp;
    temp = _m4storage[4];
    _m4storage[4] = _m4storage[1];
    _m4storage[1] = temp;
    temp = _m4storage[8];
    _m4storage[8] = _m4storage[2];
    _m4storage[2] = temp;
    temp = _m4storage[12];
    _m4storage[12] = _m4storage[3];
    _m4storage[3] = temp;
    temp = _m4storage[9];
    _m4storage[9] = _m4storage[6];
    _m4storage[6] = temp;
    temp = _m4storage[13];
    _m4storage[13] = _m4storage[7];
    _m4storage[7] = temp;
    temp = _m4storage[14];
    _m4storage[14] = _m4storage[11];
    _m4storage[11] = temp;
  }

  /// Returns the component wise absolute value of this.
  Matrix4 absolute() {
    final Matrix4 r = new Matrix4.zero();
    final Float32List rStorage = r._m4storage;
    rStorage[0] = _m4storage[0].abs();
    rStorage[1] = _m4storage[1].abs();
    rStorage[2] = _m4storage[2].abs();
    rStorage[3] = _m4storage[3].abs();
    rStorage[4] = _m4storage[4].abs();
    rStorage[5] = _m4storage[5].abs();
    rStorage[6] = _m4storage[6].abs();
    rStorage[7] = _m4storage[7].abs();
    rStorage[8] = _m4storage[8].abs();
    rStorage[9] = _m4storage[9].abs();
    rStorage[10] = _m4storage[10].abs();
    rStorage[11] = _m4storage[11].abs();
    rStorage[12] = _m4storage[12].abs();
    rStorage[13] = _m4storage[13].abs();
    rStorage[14] = _m4storage[14].abs();
    rStorage[15] = _m4storage[15].abs();
    return r;
  }

  /// Returns the determinant of this matrix.
  double determinant() {
    final double det2_01_01 =
        _m4storage[0] * _m4storage[5] - _m4storage[1] * _m4storage[4];
    final double det2_01_02 =
        _m4storage[0] * _m4storage[6] - _m4storage[2] * _m4storage[4];
    final double det2_01_03 =
        _m4storage[0] * _m4storage[7] - _m4storage[3] * _m4storage[4];
    final double det2_01_12 =
        _m4storage[1] * _m4storage[6] - _m4storage[2] * _m4storage[5];
    final double det2_01_13 =
        _m4storage[1] * _m4storage[7] - _m4storage[3] * _m4storage[5];
    final double det2_01_23 =
        _m4storage[2] * _m4storage[7] - _m4storage[3] * _m4storage[6];
    final double det3_201_012 = _m4storage[8] * det2_01_12 -
        _m4storage[9] * det2_01_02 +
        _m4storage[10] * det2_01_01;
    final double det3_201_013 = _m4storage[8] * det2_01_13 -
        _m4storage[9] * det2_01_03 +
        _m4storage[11] * det2_01_01;
    final double det3_201_023 = _m4storage[8] * det2_01_23 -
        _m4storage[10] * det2_01_03 +
        _m4storage[11] * det2_01_02;
    final double det3_201_123 = _m4storage[9] * det2_01_23 -
        _m4storage[10] * det2_01_13 +
        _m4storage[11] * det2_01_12;
    return -det3_201_123 * _m4storage[12] +
        det3_201_023 * _m4storage[13] -
        det3_201_013 * _m4storage[14] +
        det3_201_012 * _m4storage[15];
  }

  /// Returns the dot product of row [i] and [v].
  double dotRow(int i, Vector4 v) {
    final Float32List vStorage = v._v4storage;
    return _m4storage[i] * vStorage[0] +
        _m4storage[4 + i] * vStorage[1] +
        _m4storage[8 + i] * vStorage[2] +
        _m4storage[12 + i] * vStorage[3];
  }

  /// Returns the dot product of column [j] and [v].
  double dotColumn(int j, Vector4 v) {
    final Float32List vStorage = v._v4storage;
    return _m4storage[j * 4] * vStorage[0] +
        _m4storage[j * 4 + 1] * vStorage[1] +
        _m4storage[j * 4 + 2] * vStorage[2] +
        _m4storage[j * 4 + 3] * vStorage[3];
  }

  /// Returns the trace of the matrix. The trace of a matrix is the sum of the
  /// diagonal entries.
  double trace() {
    double t = 0.0;
    t += _m4storage[0];
    t += _m4storage[5];
    t += _m4storage[10];
    t += _m4storage[15];
    return t;
  }

  /// Returns infinity norm of the matrix. Used for numerical analysis.
  double infinityNorm() {
    double norm = 0.0;
    {
      double row_norm = 0.0;
      row_norm += _m4storage[0].abs();
      row_norm += _m4storage[1].abs();
      row_norm += _m4storage[2].abs();
      row_norm += _m4storage[3].abs();
      norm = row_norm > norm ? row_norm : norm;
    }
    {
      double row_norm = 0.0;
      row_norm += _m4storage[4].abs();
      row_norm += _m4storage[5].abs();
      row_norm += _m4storage[6].abs();
      row_norm += _m4storage[7].abs();
      norm = row_norm > norm ? row_norm : norm;
    }
    {
      double row_norm = 0.0;
      row_norm += _m4storage[8].abs();
      row_norm += _m4storage[9].abs();
      row_norm += _m4storage[10].abs();
      row_norm += _m4storage[11].abs();
      norm = row_norm > norm ? row_norm : norm;
    }
    {
      double row_norm = 0.0;
      row_norm += _m4storage[12].abs();
      row_norm += _m4storage[13].abs();
      row_norm += _m4storage[14].abs();
      row_norm += _m4storage[15].abs();
      norm = row_norm > norm ? row_norm : norm;
    }
    return norm;
  }

  /// Returns relative error between [this] and [correct]
  double relativeError(Matrix4 correct) {
    final Matrix4 diff = correct - this;
    final double correct_norm = correct.infinityNorm();
    final double diff_norm = diff.infinityNorm();
    return diff_norm / correct_norm;
  }

  /// Returns absolute error between [this] and [correct]
  double absoluteError(Matrix4 correct) {
    final double this_norm = infinityNorm();
    final double correct_norm = correct.infinityNorm();
    final double diff_norm = (this_norm - correct_norm).abs();
    return diff_norm;
  }

  /// Returns the translation vector from this homogeneous transformation matrix.
  Vector3 getTranslation() {
    final double z = _m4storage[14];
    final double y = _m4storage[13];
    final double x = _m4storage[12];
    return new Vector3(x, y, z);
  }

  /// Sets the translation vector in this homogeneous transformation matrix.
  void setTranslation(Vector3 t) {
    final Float32List tStorage = t._v3storage;
    final double z = tStorage[2];
    final double y = tStorage[1];
    final double x = tStorage[0];
    _m4storage[14] = z;
    _m4storage[13] = y;
    _m4storage[12] = x;
  }

  /// Sets the translation vector in this homogeneous transformation matrix.
  void setTranslationRaw(double x, double y, double z) {
    _m4storage[14] = z;
    _m4storage[13] = y;
    _m4storage[12] = x;
  }

  /// Returns the rotation matrix from this homogeneous transformation matrix.
  Matrix3 getRotation() {
    final Matrix3 r = new Matrix3.zero();
    copyRotation(r);
    return r;
  }

  /// Copies the rotation matrix from this homogeneous transformation matrix
  /// into [rotation].
  void copyRotation(Matrix3 rotation) {
    final Float32List rStorage = rotation._m3storage;
    rStorage[0] = _m4storage[0];
    rStorage[1] = _m4storage[1];
    rStorage[2] = _m4storage[2];
    rStorage[3] = _m4storage[4];
    rStorage[4] = _m4storage[5];
    rStorage[5] = _m4storage[6];
    rStorage[6] = _m4storage[8];
    rStorage[7] = _m4storage[9];
    rStorage[8] = _m4storage[10];
  }

  /// Sets the rotation matrix in this homogeneous transformation matrix.
  void setRotation(Matrix3 r) {
    final Float32List rStorage = r._m3storage;
    _m4storage[0] = rStorage[0];
    _m4storage[1] = rStorage[1];
    _m4storage[2] = rStorage[2];
    _m4storage[4] = rStorage[3];
    _m4storage[5] = rStorage[4];
    _m4storage[6] = rStorage[5];
    _m4storage[8] = rStorage[6];
    _m4storage[9] = rStorage[7];
    _m4storage[10] = rStorage[8];
  }

  /// Returns the normal matrix from this homogeneous transformation matrix. The normal
  /// matrix is the transpose of the inverse of the top-left 3x3 part of this 4x4 matrix.
  Matrix3 getNormalMatrix() => new Matrix3.identity()..copyNormalMatrix(this);

  /// Returns the max scale value of the 3 axes.
  double getMaxScaleOnAxis() {
    final double scaleXSq = _m4storage[0] * _m4storage[0] +
        _m4storage[1] * _m4storage[1] +
        _m4storage[2] * _m4storage[2];
    final double scaleYSq = _m4storage[4] * _m4storage[4] +
        _m4storage[5] * _m4storage[5] +
        _m4storage[6] * _m4storage[6];
    final double scaleZSq = _m4storage[8] * _m4storage[8] +
        _m4storage[9] * _m4storage[9] +
        _m4storage[10] * _m4storage[10];
    return math.sqrt(math.max(scaleXSq, math.max(scaleYSq, scaleZSq)));
  }

  /// Transposes just the upper 3x3 rotation matrix.
  void transposeRotation() {
    double temp;
    temp = _m4storage[1];
    _m4storage[1] = _m4storage[4];
    _m4storage[4] = temp;
    temp = _m4storage[2];
    _m4storage[2] = _m4storage[8];
    _m4storage[8] = temp;
    temp = _m4storage[4];
    _m4storage[4] = _m4storage[1];
    _m4storage[1] = temp;
    temp = _m4storage[6];
    _m4storage[6] = _m4storage[9];
    _m4storage[9] = temp;
    temp = _m4storage[8];
    _m4storage[8] = _m4storage[2];
    _m4storage[2] = temp;
    temp = _m4storage[9];
    _m4storage[9] = _m4storage[6];
    _m4storage[6] = temp;
  }

  /// Invert [this].
  double invert() => copyInverse(this);

  /// Set this matrix to be the inverse of [arg]
  double copyInverse(Matrix4 arg) {
    final Float32List argStorage = arg._m4storage;
    final double a00 = argStorage[0];
    final double a01 = argStorage[1];
    final double a02 = argStorage[2];
    final double a03 = argStorage[3];
    final double a10 = argStorage[4];
    final double a11 = argStorage[5];
    final double a12 = argStorage[6];
    final double a13 = argStorage[7];
    final double a20 = argStorage[8];
    final double a21 = argStorage[9];
    final double a22 = argStorage[10];
    final double a23 = argStorage[11];
    final double a30 = argStorage[12];
    final double a31 = argStorage[13];
    final double a32 = argStorage[14];
    final double a33 = argStorage[15];
    final double b00 = a00 * a11 - a01 * a10;
    final double b01 = a00 * a12 - a02 * a10;
    final double b02 = a00 * a13 - a03 * a10;
    final double b03 = a01 * a12 - a02 * a11;
    final double b04 = a01 * a13 - a03 * a11;
    final double b05 = a02 * a13 - a03 * a12;
    final double b06 = a20 * a31 - a21 * a30;
    final double b07 = a20 * a32 - a22 * a30;
    final double b08 = a20 * a33 - a23 * a30;
    final double b09 = a21 * a32 - a22 * a31;
    final double b10 = a21 * a33 - a23 * a31;
    final double b11 = a22 * a33 - a23 * a32;
    final double det =
        (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06);
    if (det == 0.0) {
      setFrom(arg);
      return 0.0;
    }
    final double invDet = 1.0 / det;
    _m4storage[0] = (a11 * b11 - a12 * b10 + a13 * b09) * invDet;
    _m4storage[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * invDet;
    _m4storage[2] = (a31 * b05 - a32 * b04 + a33 * b03) * invDet;
    _m4storage[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * invDet;
    _m4storage[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * invDet;
    _m4storage[5] = (a00 * b11 - a02 * b08 + a03 * b07) * invDet;
    _m4storage[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * invDet;
    _m4storage[7] = (a20 * b05 - a22 * b02 + a23 * b01) * invDet;
    _m4storage[8] = (a10 * b10 - a11 * b08 + a13 * b06) * invDet;
    _m4storage[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * invDet;
    _m4storage[10] = (a30 * b04 - a31 * b02 + a33 * b00) * invDet;
    _m4storage[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * invDet;
    _m4storage[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * invDet;
    _m4storage[13] = (a00 * b09 - a01 * b07 + a02 * b06) * invDet;
    _m4storage[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * invDet;
    _m4storage[15] = (a20 * b03 - a21 * b01 + a22 * b00) * invDet;
    return det;
  }

  double invertRotation() {
    final double det = determinant();
    if (det == 0.0) {
      return 0.0;
    }
    final double invDet = 1.0 / det;
    double ix;
    double iy;
    double iz;
    double jx;
    double jy;
    double jz;
    double kx;
    double ky;
    double kz;
    ix = invDet *
        (_m4storage[5] * _m4storage[10] - _m4storage[6] * _m4storage[9]);
    iy = invDet *
        (_m4storage[2] * _m4storage[9] - _m4storage[1] * _m4storage[10]);
    iz = invDet *
        (_m4storage[1] * _m4storage[6] - _m4storage[2] * _m4storage[5]);
    jx = invDet *
        (_m4storage[6] * _m4storage[8] - _m4storage[4] * _m4storage[10]);
    jy = invDet *
        (_m4storage[0] * _m4storage[10] - _m4storage[2] * _m4storage[8]);
    jz = invDet *
        (_m4storage[2] * _m4storage[4] - _m4storage[0] * _m4storage[6]);
    kx = invDet *
        (_m4storage[4] * _m4storage[9] - _m4storage[5] * _m4storage[8]);
    ky = invDet *
        (_m4storage[1] * _m4storage[8] - _m4storage[0] * _m4storage[9]);
    kz = invDet *
        (_m4storage[0] * _m4storage[5] - _m4storage[1] * _m4storage[4]);
    _m4storage[0] = ix;
    _m4storage[1] = iy;
    _m4storage[2] = iz;
    _m4storage[4] = jx;
    _m4storage[5] = jy;
    _m4storage[6] = jz;
    _m4storage[8] = kx;
    _m4storage[9] = ky;
    _m4storage[10] = kz;
    return det;
  }

  /// Sets the upper 3x3 to a rotation of [radians] around X
  void setRotationX(double radians) {
    final double c = math.cos(radians);
    final double s = math.sin(radians);
    _m4storage[0] = 1.0;
    _m4storage[1] = 0.0;
    _m4storage[2] = 0.0;
    _m4storage[4] = 0.0;
    _m4storage[5] = c;
    _m4storage[6] = s;
    _m4storage[8] = 0.0;
    _m4storage[9] = -s;
    _m4storage[10] = c;
    _m4storage[3] = 0.0;
    _m4storage[7] = 0.0;
    _m4storage[11] = 0.0;
  }

  /// Sets the upper 3x3 to a rotation of [radians] around Y
  void setRotationY(double radians) {
    final double c = math.cos(radians);
    final double s = math.sin(radians);
    _m4storage[0] = c;
    _m4storage[1] = 0.0;
    _m4storage[2] = -s;
    _m4storage[4] = 0.0;
    _m4storage[5] = 1.0;
    _m4storage[6] = 0.0;
    _m4storage[8] = s;
    _m4storage[9] = 0.0;
    _m4storage[10] = c;
    _m4storage[3] = 0.0;
    _m4storage[7] = 0.0;
    _m4storage[11] = 0.0;
  }

  /// Sets the upper 3x3 to a rotation of [radians] around Z
  void setRotationZ(double radians) {
    final double c = math.cos(radians);
    final double s = math.sin(radians);
    _m4storage[0] = c;
    _m4storage[1] = s;
    _m4storage[2] = 0.0;
    _m4storage[4] = -s;
    _m4storage[5] = c;
    _m4storage[6] = 0.0;
    _m4storage[8] = 0.0;
    _m4storage[9] = 0.0;
    _m4storage[10] = 1.0;
    _m4storage[3] = 0.0;
    _m4storage[7] = 0.0;
    _m4storage[11] = 0.0;
  }

  /// Converts into Adjugate matrix and scales by [scale]
  void scaleAdjoint(double scale) {
    // Adapted from code by Richard Carling.
    final double a1 = _m4storage[0];
    final double b1 = _m4storage[4];
    final double c1 = _m4storage[8];
    final double d1 = _m4storage[12];
    final double a2 = _m4storage[1];
    final double b2 = _m4storage[5];
    final double c2 = _m4storage[9];
    final double d2 = _m4storage[13];
    final double a3 = _m4storage[2];
    final double b3 = _m4storage[6];
    final double c3 = _m4storage[10];
    final double d3 = _m4storage[14];
    final double a4 = _m4storage[3];
    final double b4 = _m4storage[7];
    final double c4 = _m4storage[11];
    final double d4 = _m4storage[15];
    _m4storage[0] = (b2 * (c3 * d4 - c4 * d3) -
            c2 * (b3 * d4 - b4 * d3) +
            d2 * (b3 * c4 - b4 * c3)) *
        scale;
    _m4storage[1] = -(a2 * (c3 * d4 - c4 * d3) -
            c2 * (a3 * d4 - a4 * d3) +
            d2 * (a3 * c4 - a4 * c3)) *
        scale;
    _m4storage[2] = (a2 * (b3 * d4 - b4 * d3) -
            b2 * (a3 * d4 - a4 * d3) +
            d2 * (a3 * b4 - a4 * b3)) *
        scale;
    _m4storage[3] = -(a2 * (b3 * c4 - b4 * c3) -
            b2 * (a3 * c4 - a4 * c3) +
            c2 * (a3 * b4 - a4 * b3)) *
        scale;
    _m4storage[4] = -(b1 * (c3 * d4 - c4 * d3) -
            c1 * (b3 * d4 - b4 * d3) +
            d1 * (b3 * c4 - b4 * c3)) *
        scale;
    _m4storage[5] = (a1 * (c3 * d4 - c4 * d3) -
            c1 * (a3 * d4 - a4 * d3) +
            d1 * (a3 * c4 - a4 * c3)) *
        scale;
    _m4storage[6] = -(a1 * (b3 * d4 - b4 * d3) -
            b1 * (a3 * d4 - a4 * d3) +
            d1 * (a3 * b4 - a4 * b3)) *
        scale;
    _m4storage[7] = (a1 * (b3 * c4 - b4 * c3) -
            b1 * (a3 * c4 - a4 * c3) +
            c1 * (a3 * b4 - a4 * b3)) *
        scale;
    _m4storage[8] = (b1 * (c2 * d4 - c4 * d2) -
            c1 * (b2 * d4 - b4 * d2) +
            d1 * (b2 * c4 - b4 * c2)) *
        scale;
    _m4storage[9] = -(a1 * (c2 * d4 - c4 * d2) -
            c1 * (a2 * d4 - a4 * d2) +
            d1 * (a2 * c4 - a4 * c2)) *
        scale;
    _m4storage[10] = (a1 * (b2 * d4 - b4 * d2) -
            b1 * (a2 * d4 - a4 * d2) +
            d1 * (a2 * b4 - a4 * b2)) *
        scale;
    _m4storage[11] = -(a1 * (b2 * c4 - b4 * c2) -
            b1 * (a2 * c4 - a4 * c2) +
            c1 * (a2 * b4 - a4 * b2)) *
        scale;
    _m4storage[12] = -(b1 * (c2 * d3 - c3 * d2) -
            c1 * (b2 * d3 - b3 * d2) +
            d1 * (b2 * c3 - b3 * c2)) *
        scale;
    _m4storage[13] = (a1 * (c2 * d3 - c3 * d2) -
            c1 * (a2 * d3 - a3 * d2) +
            d1 * (a2 * c3 - a3 * c2)) *
        scale;
    _m4storage[14] = -(a1 * (b2 * d3 - b3 * d2) -
            b1 * (a2 * d3 - a3 * d2) +
            d1 * (a2 * b3 - a3 * b2)) *
        scale;
    _m4storage[15] = (a1 * (b2 * c3 - b3 * c2) -
            b1 * (a2 * c3 - a3 * c2) +
            c1 * (a2 * b3 - a3 * b2)) *
        scale;
  }

  /// Rotates [arg] by the absolute rotation of [this]
  /// Returns [arg].
  /// Primarily used by AABB transformation code.
  Vector3 absoluteRotate(Vector3 arg) {
    final double m00 = _m4storage[0].abs();
    final double m01 = _m4storage[4].abs();
    final double m02 = _m4storage[8].abs();
    final double m10 = _m4storage[1].abs();
    final double m11 = _m4storage[5].abs();
    final double m12 = _m4storage[9].abs();
    final double m20 = _m4storage[2].abs();
    final double m21 = _m4storage[6].abs();
    final double m22 = _m4storage[10].abs();
    final Float32List argStorage = arg._v3storage;
    final double x = argStorage[0];
    final double y = argStorage[1];
    final double z = argStorage[2];
    argStorage[0] = x * m00 + y * m01 + z * m02 + 0.0 * 0.0;
    argStorage[1] = x * m10 + y * m11 + z * m12 + 0.0 * 0.0;
    argStorage[2] = x * m20 + y * m21 + z * m22 + 0.0 * 0.0;
    return arg;
  }

  /// Adds [o] to [this].
  void add(Matrix4 o) {
    final Float32List oStorage = o._m4storage;
    _m4storage[0] = _m4storage[0] + oStorage[0];
    _m4storage[1] = _m4storage[1] + oStorage[1];
    _m4storage[2] = _m4storage[2] + oStorage[2];
    _m4storage[3] = _m4storage[3] + oStorage[3];
    _m4storage[4] = _m4storage[4] + oStorage[4];
    _m4storage[5] = _m4storage[5] + oStorage[5];
    _m4storage[6] = _m4storage[6] + oStorage[6];
    _m4storage[7] = _m4storage[7] + oStorage[7];
    _m4storage[8] = _m4storage[8] + oStorage[8];
    _m4storage[9] = _m4storage[9] + oStorage[9];
    _m4storage[10] = _m4storage[10] + oStorage[10];
    _m4storage[11] = _m4storage[11] + oStorage[11];
    _m4storage[12] = _m4storage[12] + oStorage[12];
    _m4storage[13] = _m4storage[13] + oStorage[13];
    _m4storage[14] = _m4storage[14] + oStorage[14];
    _m4storage[15] = _m4storage[15] + oStorage[15];
  }

  /// Subtracts [o] from [this].
  void sub(Matrix4 o) {
    final Float32List oStorage = o._m4storage;
    _m4storage[0] = _m4storage[0] - oStorage[0];
    _m4storage[1] = _m4storage[1] - oStorage[1];
    _m4storage[2] = _m4storage[2] - oStorage[2];
    _m4storage[3] = _m4storage[3] - oStorage[3];
    _m4storage[4] = _m4storage[4] - oStorage[4];
    _m4storage[5] = _m4storage[5] - oStorage[5];
    _m4storage[6] = _m4storage[6] - oStorage[6];
    _m4storage[7] = _m4storage[7] - oStorage[7];
    _m4storage[8] = _m4storage[8] - oStorage[8];
    _m4storage[9] = _m4storage[9] - oStorage[9];
    _m4storage[10] = _m4storage[10] - oStorage[10];
    _m4storage[11] = _m4storage[11] - oStorage[11];
    _m4storage[12] = _m4storage[12] - oStorage[12];
    _m4storage[13] = _m4storage[13] - oStorage[13];
    _m4storage[14] = _m4storage[14] - oStorage[14];
    _m4storage[15] = _m4storage[15] - oStorage[15];
  }

  /// Negate [this].
  void negate() {
    _m4storage[0] = -_m4storage[0];
    _m4storage[1] = -_m4storage[1];
    _m4storage[2] = -_m4storage[2];
    _m4storage[3] = -_m4storage[3];
    _m4storage[4] = -_m4storage[4];
    _m4storage[5] = -_m4storage[5];
    _m4storage[6] = -_m4storage[6];
    _m4storage[7] = -_m4storage[7];
    _m4storage[8] = -_m4storage[8];
    _m4storage[9] = -_m4storage[9];
    _m4storage[10] = -_m4storage[10];
    _m4storage[11] = -_m4storage[11];
    _m4storage[12] = -_m4storage[12];
    _m4storage[13] = -_m4storage[13];
    _m4storage[14] = -_m4storage[14];
    _m4storage[15] = -_m4storage[15];
  }

  /// Multiply [this] by [arg].
  void multiply(Matrix4 arg) {
    final double m00 = _m4storage[0];
    final double m01 = _m4storage[4];
    final double m02 = _m4storage[8];
    final double m03 = _m4storage[12];
    final double m10 = _m4storage[1];
    final double m11 = _m4storage[5];
    final double m12 = _m4storage[9];
    final double m13 = _m4storage[13];
    final double m20 = _m4storage[2];
    final double m21 = _m4storage[6];
    final double m22 = _m4storage[10];
    final double m23 = _m4storage[14];
    final double m30 = _m4storage[3];
    final double m31 = _m4storage[7];
    final double m32 = _m4storage[11];
    final double m33 = _m4storage[15];
    final Float32List argStorage = arg._m4storage;
    final double n00 = argStorage[0];
    final double n01 = argStorage[4];
    final double n02 = argStorage[8];
    final double n03 = argStorage[12];
    final double n10 = argStorage[1];
    final double n11 = argStorage[5];
    final double n12 = argStorage[9];
    final double n13 = argStorage[13];
    final double n20 = argStorage[2];
    final double n21 = argStorage[6];
    final double n22 = argStorage[10];
    final double n23 = argStorage[14];
    final double n30 = argStorage[3];
    final double n31 = argStorage[7];
    final double n32 = argStorage[11];
    final double n33 = argStorage[15];
    _m4storage[0] = (m00 * n00) + (m01 * n10) + (m02 * n20) + (m03 * n30);
    _m4storage[4] = (m00 * n01) + (m01 * n11) + (m02 * n21) + (m03 * n31);
    _m4storage[8] = (m00 * n02) + (m01 * n12) + (m02 * n22) + (m03 * n32);
    _m4storage[12] = (m00 * n03) + (m01 * n13) + (m02 * n23) + (m03 * n33);
    _m4storage[1] = (m10 * n00) + (m11 * n10) + (m12 * n20) + (m13 * n30);
    _m4storage[5] = (m10 * n01) + (m11 * n11) + (m12 * n21) + (m13 * n31);
    _m4storage[9] = (m10 * n02) + (m11 * n12) + (m12 * n22) + (m13 * n32);
    _m4storage[13] = (m10 * n03) + (m11 * n13) + (m12 * n23) + (m13 * n33);
    _m4storage[2] = (m20 * n00) + (m21 * n10) + (m22 * n20) + (m23 * n30);
    _m4storage[6] = (m20 * n01) + (m21 * n11) + (m22 * n21) + (m23 * n31);
    _m4storage[10] = (m20 * n02) + (m21 * n12) + (m22 * n22) + (m23 * n32);
    _m4storage[14] = (m20 * n03) + (m21 * n13) + (m22 * n23) + (m23 * n33);
    _m4storage[3] = (m30 * n00) + (m31 * n10) + (m32 * n20) + (m33 * n30);
    _m4storage[7] = (m30 * n01) + (m31 * n11) + (m32 * n21) + (m33 * n31);
    _m4storage[11] = (m30 * n02) + (m31 * n12) + (m32 * n22) + (m33 * n32);
    _m4storage[15] = (m30 * n03) + (m31 * n13) + (m32 * n23) + (m33 * n33);
  }

  /// Multiply a copy of [this] with [arg].
  Matrix4 multiplied(Matrix4 arg) => clone()..multiply(arg);

  /// Multiply a transposed [this] with [arg].
  void transposeMultiply(Matrix4 arg) {
    final double m00 = _m4storage[0];
    final double m01 = _m4storage[1];
    final double m02 = _m4storage[2];
    final double m03 = _m4storage[3];
    final double m10 = _m4storage[4];
    final double m11 = _m4storage[5];
    final double m12 = _m4storage[6];
    final double m13 = _m4storage[7];
    final double m20 = _m4storage[8];
    final double m21 = _m4storage[9];
    final double m22 = _m4storage[10];
    final double m23 = _m4storage[11];
    final double m30 = _m4storage[12];
    final double m31 = _m4storage[13];
    final double m32 = _m4storage[14];
    final double m33 = _m4storage[15];
    final Float32List argStorage = arg._m4storage;
    _m4storage[0] = (m00 * argStorage[0]) +
        (m01 * argStorage[1]) +
        (m02 * argStorage[2]) +
        (m03 * argStorage[3]);
    _m4storage[4] = (m00 * argStorage[4]) +
        (m01 * argStorage[5]) +
        (m02 * argStorage[6]) +
        (m03 * argStorage[7]);
    _m4storage[8] = (m00 * argStorage[8]) +
        (m01 * argStorage[9]) +
        (m02 * argStorage[10]) +
        (m03 * argStorage[11]);
    _m4storage[12] = (m00 * argStorage[12]) +
        (m01 * argStorage[13]) +
        (m02 * argStorage[14]) +
        (m03 * argStorage[15]);
    _m4storage[1] = (m10 * argStorage[0]) +
        (m11 * argStorage[1]) +
        (m12 * argStorage[2]) +
        (m13 * argStorage[3]);
    _m4storage[5] = (m10 * argStorage[4]) +
        (m11 * argStorage[5]) +
        (m12 * argStorage[6]) +
        (m13 * argStorage[7]);
    _m4storage[9] = (m10 * argStorage[8]) +
        (m11 * argStorage[9]) +
        (m12 * argStorage[10]) +
        (m13 * argStorage[11]);
    _m4storage[13] = (m10 * argStorage[12]) +
        (m11 * argStorage[13]) +
        (m12 * argStorage[14]) +
        (m13 * argStorage[15]);
    _m4storage[2] = (m20 * argStorage[0]) +
        (m21 * argStorage[1]) +
        (m22 * argStorage[2]) +
        (m23 * argStorage[3]);
    _m4storage[6] = (m20 * argStorage[4]) +
        (m21 * argStorage[5]) +
        (m22 * argStorage[6]) +
        (m23 * argStorage[7]);
    _m4storage[10] = (m20 * argStorage[8]) +
        (m21 * argStorage[9]) +
        (m22 * argStorage[10]) +
        (m23 * argStorage[11]);
    _m4storage[14] = (m20 * argStorage[12]) +
        (m21 * argStorage[13]) +
        (m22 * argStorage[14]) +
        (m23 * argStorage[15]);
    _m4storage[3] = (m30 * argStorage[0]) +
        (m31 * argStorage[1]) +
        (m32 * argStorage[2]) +
        (m33 * argStorage[3]);
    _m4storage[7] = (m30 * argStorage[4]) +
        (m31 * argStorage[5]) +
        (m32 * argStorage[6]) +
        (m33 * argStorage[7]);
    _m4storage[11] = (m30 * argStorage[8]) +
        (m31 * argStorage[9]) +
        (m32 * argStorage[10]) +
        (m33 * argStorage[11]);
    _m4storage[15] = (m30 * argStorage[12]) +
        (m31 * argStorage[13]) +
        (m32 * argStorage[14]) +
        (m33 * argStorage[15]);
  }

  /// Multiply [this] with a transposed [arg].
  void multiplyTranspose(Matrix4 arg) {
    final double m00 = _m4storage[0];
    final double m01 = _m4storage[4];
    final double m02 = _m4storage[8];
    final double m03 = _m4storage[12];
    final double m10 = _m4storage[1];
    final double m11 = _m4storage[5];
    final double m12 = _m4storage[9];
    final double m13 = _m4storage[13];
    final double m20 = _m4storage[2];
    final double m21 = _m4storage[6];
    final double m22 = _m4storage[10];
    final double m23 = _m4storage[14];
    final double m30 = _m4storage[3];
    final double m31 = _m4storage[7];
    final double m32 = _m4storage[11];
    final double m33 = _m4storage[15];
    final Float32List argStorage = arg._m4storage;
    _m4storage[0] = (m00 * argStorage[0]) +
        (m01 * argStorage[4]) +
        (m02 * argStorage[8]) +
        (m03 * argStorage[12]);
    _m4storage[4] = (m00 * argStorage[1]) +
        (m01 * argStorage[5]) +
        (m02 * argStorage[9]) +
        (m03 * argStorage[13]);
    _m4storage[8] = (m00 * argStorage[2]) +
        (m01 * argStorage[6]) +
        (m02 * argStorage[10]) +
        (m03 * argStorage[14]);
    _m4storage[12] = (m00 * argStorage[3]) +
        (m01 * argStorage[7]) +
        (m02 * argStorage[11]) +
        (m03 * argStorage[15]);
    _m4storage[1] = (m10 * argStorage[0]) +
        (m11 * argStorage[4]) +
        (m12 * argStorage[8]) +
        (m13 * argStorage[12]);
    _m4storage[5] = (m10 * argStorage[1]) +
        (m11 * argStorage[5]) +
        (m12 * argStorage[9]) +
        (m13 * argStorage[13]);
    _m4storage[9] = (m10 * argStorage[2]) +
        (m11 * argStorage[6]) +
        (m12 * argStorage[10]) +
        (m13 * argStorage[14]);
    _m4storage[13] = (m10 * argStorage[3]) +
        (m11 * argStorage[7]) +
        (m12 * argStorage[11]) +
        (m13 * argStorage[15]);
    _m4storage[2] = (m20 * argStorage[0]) +
        (m21 * argStorage[4]) +
        (m22 * argStorage[8]) +
        (m23 * argStorage[12]);
    _m4storage[6] = (m20 * argStorage[1]) +
        (m21 * argStorage[5]) +
        (m22 * argStorage[9]) +
        (m23 * argStorage[13]);
    _m4storage[10] = (m20 * argStorage[2]) +
        (m21 * argStorage[6]) +
        (m22 * argStorage[10]) +
        (m23 * argStorage[14]);
    _m4storage[14] = (m20 * argStorage[3]) +
        (m21 * argStorage[7]) +
        (m22 * argStorage[11]) +
        (m23 * argStorage[15]);
    _m4storage[3] = (m30 * argStorage[0]) +
        (m31 * argStorage[4]) +
        (m32 * argStorage[8]) +
        (m33 * argStorage[12]);
    _m4storage[7] = (m30 * argStorage[1]) +
        (m31 * argStorage[5]) +
        (m32 * argStorage[9]) +
        (m33 * argStorage[13]);
    _m4storage[11] = (m30 * argStorage[2]) +
        (m31 * argStorage[6]) +
        (m32 * argStorage[10]) +
        (m33 * argStorage[14]);
    _m4storage[15] = (m30 * argStorage[3]) +
        (m31 * argStorage[7]) +
        (m32 * argStorage[11]) +
        (m33 * argStorage[15]);
  }

  /// Decomposes [this] into [translation], [rotation] and [scale] components.
  void decompose(Vector3 translation, Quaternion rotation, Vector3 scale) {
    final Vector3 v = new Vector3.zero();
    double sx =
        (v..setValues(_m4storage[0], _m4storage[1], _m4storage[2])).length;
    final double sy =
        (v..setValues(_m4storage[4], _m4storage[5], _m4storage[6])).length;
    final double sz =
        (v..setValues(_m4storage[8], _m4storage[9], _m4storage[10])).length;

    if (determinant() < 0) {
      sx = -sx;
    }

    translation._v3storage[0] = _m4storage[12];
    translation._v3storage[1] = _m4storage[13];
    translation._v3storage[2] = _m4storage[14];

    final double invSX = 1.0 / sx;
    final double invSY = 1.0 / sy;
    final double invSZ = 1.0 / sz;

    final Matrix4 m = new Matrix4.copy(this);
    m._m4storage[0] *= invSX;
    m._m4storage[1] *= invSX;
    m._m4storage[2] *= invSX;
    m._m4storage[4] *= invSY;
    m._m4storage[5] *= invSY;
    m._m4storage[6] *= invSY;
    m._m4storage[8] *= invSZ;
    m._m4storage[9] *= invSZ;
    m._m4storage[10] *= invSZ;

    rotation.setFromRotation(m.getRotation());

    scale._v3storage[0] = sx;
    scale._v3storage[1] = sy;
    scale._v3storage[2] = sz;
  }

  /// Rotate [arg] of type [Vector3] using the rotation defined by [this].
  Vector3 rotate3(Vector3 arg) {
    final Float32List argStorage = arg._v3storage;
    final double x_ = (_m4storage[0] * argStorage[0]) +
        (_m4storage[4] * argStorage[1]) +
        (_m4storage[8] * argStorage[2]);
    final double y_ = (_m4storage[1] * argStorage[0]) +
        (_m4storage[5] * argStorage[1]) +
        (_m4storage[9] * argStorage[2]);
    final double z_ = (_m4storage[2] * argStorage[0]) +
        (_m4storage[6] * argStorage[1]) +
        (_m4storage[10] * argStorage[2]);
    argStorage[0] = x_;
    argStorage[1] = y_;
    argStorage[2] = z_;
    return arg;
  }

  /// Rotate a copy of [arg] of type [Vector3] using the rotation defined by
  /// [this]. If a [out] parameter is supplied, the copy is stored in [out].
  Vector3 rotated3(Vector3 arg, [Vector3 out]) {
    if (out == null) {
      out = new Vector3.copy(arg);
    } else {
      out.setFrom(arg);
    }
    return rotate3(out);
  }

  /// Transform [arg] of type [Vector3] using the transformation defined by
  /// [this].
  Vector3 transform3(Vector3 arg) {
    final Float32List argStorage = arg._v3storage;
    final double x_ = (_m4storage[0] * argStorage[0]) +
        (_m4storage[4] * argStorage[1]) +
        (_m4storage[8] * argStorage[2]) +
        _m4storage[12];
    final double y_ = (_m4storage[1] * argStorage[0]) +
        (_m4storage[5] * argStorage[1]) +
        (_m4storage[9] * argStorage[2]) +
        _m4storage[13];
    final double z_ = (_m4storage[2] * argStorage[0]) +
        (_m4storage[6] * argStorage[1]) +
        (_m4storage[10] * argStorage[2]) +
        _m4storage[14];
    argStorage[0] = x_;
    argStorage[1] = y_;
    argStorage[2] = z_;
    return arg;
  }

  /// Transform a copy of [arg] of type [Vector3] using the transformation
  /// defined by [this]. If a [out] parameter is supplied, the copy is stored in
  /// [out].
  Vector3 transformed3(Vector3 arg, [Vector3 out]) {
    if (out == null) {
      out = new Vector3.copy(arg);
    } else {
      out.setFrom(arg);
    }
    return transform3(out);
  }

  /// Transform [arg] of type [Vector4] using the transformation defined by
  /// [this].
  Vector4 transform(Vector4 arg) {
    final Float32List argStorage = arg._v4storage;
    final double x_ = (_m4storage[0] * argStorage[0]) +
        (_m4storage[4] * argStorage[1]) +
        (_m4storage[8] * argStorage[2]) +
        (_m4storage[12] * argStorage[3]);
    final double y_ = (_m4storage[1] * argStorage[0]) +
        (_m4storage[5] * argStorage[1]) +
        (_m4storage[9] * argStorage[2]) +
        (_m4storage[13] * argStorage[3]);
    final double z_ = (_m4storage[2] * argStorage[0]) +
        (_m4storage[6] * argStorage[1]) +
        (_m4storage[10] * argStorage[2]) +
        (_m4storage[14] * argStorage[3]);
    final double w_ = (_m4storage[3] * argStorage[0]) +
        (_m4storage[7] * argStorage[1]) +
        (_m4storage[11] * argStorage[2]) +
        (_m4storage[15] * argStorage[3]);
    argStorage[0] = x_;
    argStorage[1] = y_;
    argStorage[2] = z_;
    argStorage[3] = w_;
    return arg;
  }

  /// Transform [arg] of type [Vector3] using the perspective transformation
  /// defined by [this].
  Vector3 perspectiveTransform(Vector3 arg) {
    final Float32List argStorage = arg._v3storage;
    final double x_ = (_m4storage[0] * argStorage[0]) +
        (_m4storage[4] * argStorage[1]) +
        (_m4storage[8] * argStorage[2]) +
        _m4storage[12];
    final double y_ = (_m4storage[1] * argStorage[0]) +
        (_m4storage[5] * argStorage[1]) +
        (_m4storage[9] * argStorage[2]) +
        _m4storage[13];
    final double z_ = (_m4storage[2] * argStorage[0]) +
        (_m4storage[6] * argStorage[1]) +
        (_m4storage[10] * argStorage[2]) +
        _m4storage[14];
    final double w_ = 1.0 /
        ((_m4storage[3] * argStorage[0]) +
            (_m4storage[7] * argStorage[1]) +
            (_m4storage[11] * argStorage[2]) +
            _m4storage[15]);
    argStorage[0] = x_ * w_;
    argStorage[1] = y_ * w_;
    argStorage[2] = z_ * w_;
    return arg;
  }

  /// Transform a copy of [arg] of type [Vector4] using the transformation
  /// defined by [this]. If a [out] parameter is supplied, the copy is stored in
  /// [out].
  Vector4 transformed(Vector4 arg, [Vector4 out]) {
    if (out == null) {
      out = new Vector4.copy(arg);
    } else {
      out.setFrom(arg);
    }
    return transform(out);
  }

  /// Copies [this] into [array] starting at [offset].
  void copyIntoArray(List<num> array, [int offset = 0]) {
    final int i = offset;
    array[i + 15] = _m4storage[15];
    array[i + 14] = _m4storage[14];
    array[i + 13] = _m4storage[13];
    array[i + 12] = _m4storage[12];
    array[i + 11] = _m4storage[11];
    array[i + 10] = _m4storage[10];
    array[i + 9] = _m4storage[9];
    array[i + 8] = _m4storage[8];
    array[i + 7] = _m4storage[7];
    array[i + 6] = _m4storage[6];
    array[i + 5] = _m4storage[5];
    array[i + 4] = _m4storage[4];
    array[i + 3] = _m4storage[3];
    array[i + 2] = _m4storage[2];
    array[i + 1] = _m4storage[1];
    array[i + 0] = _m4storage[0];
  }

  /// Copies elements from [array] into [this] starting at [offset].
  void copyFromArray(List<double> array, [int offset = 0]) {
    final int i = offset;
    _m4storage[15] = array[i + 15];
    _m4storage[14] = array[i + 14];
    _m4storage[13] = array[i + 13];
    _m4storage[12] = array[i + 12];
    _m4storage[11] = array[i + 11];
    _m4storage[10] = array[i + 10];
    _m4storage[9] = array[i + 9];
    _m4storage[8] = array[i + 8];
    _m4storage[7] = array[i + 7];
    _m4storage[6] = array[i + 6];
    _m4storage[5] = array[i + 5];
    _m4storage[4] = array[i + 4];
    _m4storage[3] = array[i + 3];
    _m4storage[2] = array[i + 2];
    _m4storage[1] = array[i + 1];
    _m4storage[0] = array[i + 0];
  }

  /// Multiply [this] to each set of xyz values in [array] starting at [offset].
  List<double> applyToVector3Array(List<double> array, [int offset = 0]) {
    for (int i = 0, j = offset; i < array.length; i += 3, j += 3) {
      final Vector3 v = new Vector3.array(array, j)..applyMatrix4(this);
      array[j] = v.storage[0];
      array[j + 1] = v.storage[1];
      array[j + 2] = v.storage[2];
    }

    return array;
  }

  Vector3 get right {
    final double x = _m4storage[0];
    final double y = _m4storage[1];
    final double z = _m4storage[2];
    return new Vector3(x, y, z);
  }

  Vector3 get up {
    final double x = _m4storage[4];
    final double y = _m4storage[5];
    final double z = _m4storage[6];
    return new Vector3(x, y, z);
  }

  Vector3 get forward {
    final double x = _m4storage[8];
    final double y = _m4storage[9];
    final double z = _m4storage[10];
    return new Vector3(x, y, z);
  }

  /// Is [this] the identity matrix?
  bool isIdentity() =>
      _m4storage[0] == 1.0 // col 1
      &&
      _m4storage[1] == 0.0 &&
      _m4storage[2] == 0.0 &&
      _m4storage[3] == 0.0 &&
      _m4storage[4] == 0.0 // col 2
      &&
      _m4storage[5] == 1.0 &&
      _m4storage[6] == 0.0 &&
      _m4storage[7] == 0.0 &&
      _m4storage[8] == 0.0 // col 3
      &&
      _m4storage[9] == 0.0 &&
      _m4storage[10] == 1.0 &&
      _m4storage[11] == 0.0 &&
      _m4storage[12] == 0.0 // col 4
      &&
      _m4storage[13] == 0.0 &&
      _m4storage[14] == 0.0 &&
      _m4storage[15] == 1.0;

  /// Is [this] the zero matrix?
  bool isZero() =>
      _m4storage[0] == 0.0 // col 1
      &&
      _m4storage[1] == 0.0 &&
      _m4storage[2] == 0.0 &&
      _m4storage[3] == 0.0 &&
      _m4storage[4] == 0.0 // col 2
      &&
      _m4storage[5] == 0.0 &&
      _m4storage[6] == 0.0 &&
      _m4storage[7] == 0.0 &&
      _m4storage[8] == 0.0 // col 3
      &&
      _m4storage[9] == 0.0 &&
      _m4storage[10] == 0.0 &&
      _m4storage[11] == 0.0 &&
      _m4storage[12] == 0.0 // col 4
      &&
      _m4storage[13] == 0.0 &&
      _m4storage[14] == 0.0 &&
      _m4storage[15] == 0.0;
}