gfx/2d/Matrix.h
author Kearwood (Kip) Gilbert <kgilbert@mozilla.com>
Tue, 21 Apr 2015 16:57:18 -0700
changeset 272445 61bd6e2c6e723fa9eb5fc5a6f1b4fe6a0de88032
parent 266935 b29617b91cb6940fabb4e29fd462c16a8b399ea5
child 272463 ab4eee1c6d7e262a8b4a616b79fbfda84293629d
permissions -rw-r--r--
Bug 1072898: Part 1 - Correct rendering of layers that are both in front and behind the w=0 plane. r=mattwoodrow - The BasicCompositor now transforms vertices prior to rendering in Skia, using a function that clips against frustum clipping planes in homogenous coordinate space.

/* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 2 -*-
 * This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

#ifndef MOZILLA_GFX_MATRIX_H_
#define MOZILLA_GFX_MATRIX_H_

#include "Types.h"
#include "Rect.h"
#include "Point.h"
#include <iosfwd>
#include <math.h>
#include "mozilla/Attributes.h"
#include "mozilla/DebugOnly.h"

namespace mozilla {
namespace gfx {

class Quaternion;

static bool FuzzyEqual(Float aV1, Float aV2) {
  // XXX - Check if fabs does the smart thing and just negates the sign bit.
  return fabs(aV2 - aV1) < 1e-6;
}

class Matrix
{
public:
  Matrix()
    : _11(1.0f), _12(0)
    , _21(0), _22(1.0f)
    , _31(0), _32(0)
  {}
  Matrix(Float a11, Float a12, Float a21, Float a22, Float a31, Float a32)
    : _11(a11), _12(a12)
    , _21(a21), _22(a22)
    , _31(a31), _32(a32)
  {}
  Float _11, _12;
  Float _21, _22;
  Float _31, _32;

  MOZ_ALWAYS_INLINE Matrix Copy() const
  {
    return Matrix(*this);
  }

  friend std::ostream& operator<<(std::ostream& aStream, const Matrix& aMatrix);

  Point operator *(const Point &aPoint) const
  {
    Point retPoint;

    retPoint.x = aPoint.x * _11 + aPoint.y * _21 + _31;
    retPoint.y = aPoint.x * _12 + aPoint.y * _22 + _32;

    return retPoint;
  }

  Size operator *(const Size &aSize) const
  {
    Size retSize;

    retSize.width = aSize.width * _11 + aSize.height * _21;
    retSize.height = aSize.width * _12 + aSize.height * _22;

    return retSize;
  }

  GFX2D_API Rect TransformBounds(const Rect& rect) const;

  static Matrix Translation(Float aX, Float aY)
  {
    return Matrix(1.0f, 0.0f, 0.0f, 1.0f, aX, aY);
  }

  static Matrix Translation(Point aPoint)
  {
    return Translation(aPoint.x, aPoint.y);
  }

  /**
   * Apply a translation to this matrix.
   *
   * The "Pre" in this method's name means that the translation is applied
   * -before- this matrix's existing transformation. That is, any vector that
   * is multiplied by the resulting matrix will first be translated, then be
   * transformed by the original transform.
   *
   * Calling this method will result in this matrix having the same value as
   * the result of:
   *
   *   Matrix::Translation(x, y) * this
   *
   * (Note that in performance critical code multiplying by the result of a
   * Translation()/Scaling() call is not recommended since that results in a
   * full matrix multiply involving 12 floating-point multiplications. Calling
   * this method would be preferred since it only involves four floating-point
   * multiplications.)
   */
  Matrix &PreTranslate(Float aX, Float aY)
  {
    _31 += _11 * aX + _21 * aY;
    _32 += _12 * aX + _22 * aY;

    return *this;
  }

  Matrix &PreTranslate(const Point &aPoint)
  {
    return PreTranslate(aPoint.x, aPoint.y);
  }

  /**
   * Similar to PreTranslate, but the translation is applied -after- this
   * matrix's existing transformation instead of before it.
   *
   * This method is generally less used than PreTranslate since typically code
   * want to adjust an existing user space to device space matrix to create a
   * transform to device space from a -new- user space (translated from the
   * previous user space). In that case consumers will need to use the Pre*
   * variants of the matrix methods rather than using the Post* methods, since
   * the Post* methods add a transform to the device space end of the
   * transformation.
   */
  Matrix &PostTranslate(Float aX, Float aY)
  {
    _31 += aX;
    _32 += aY;
    return *this;
  }

  Matrix &PostTranslate(const Point &aPoint)
  {
    return PostTranslate(aPoint.x, aPoint.y);
  }

  static Matrix Scaling(Float aScaleX, Float aScaleY)
  {
    return Matrix(aScaleX, 0.0f, 0.0f, aScaleY, 0.0f, 0.0f);
  }
  
  /**
   * Similar to PreTranslate, but applies a scale instead of a translation.
   */
  Matrix &PreScale(Float aX, Float aY)
  {
    _11 *= aX;
    _12 *= aX;
    _21 *= aY;
    _22 *= aY;

    return *this;
  }
  
  GFX2D_API static Matrix Rotation(Float aAngle);

  /**
   * Similar to PreTranslate, but applies a rotation instead of a translation.
   */
  Matrix &PreRotate(Float aAngle)
  {
    return *this = Matrix::Rotation(aAngle) * *this;
  }

  bool Invert()
  {
    // Compute co-factors.
    Float A = _22;
    Float B = -_21;
    Float C = _21 * _32 - _22 * _31;
    Float D = -_12;
    Float E = _11;
    Float F = _31 * _12 - _11 * _32;

    Float det = Determinant();

    if (!det) {
      return false;
    }

    Float inv_det = 1 / det;

    _11 = inv_det * A;
    _12 = inv_det * D;
    _21 = inv_det * B;
    _22 = inv_det * E;
    _31 = inv_det * C;
    _32 = inv_det * F;

    return true;
  }

  Matrix Inverse() const
  {
    Matrix clone = *this;
    DebugOnly<bool> inverted = clone.Invert();
    MOZ_ASSERT(inverted, "Attempted to get the inverse of a non-invertible matrix");
    return clone;
  }

  Float Determinant() const
  {
    return _11 * _22 - _12 * _21;
  }

  Matrix operator*(const Matrix &aMatrix) const
  {
    Matrix resultMatrix;

    resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21;
    resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22;
    resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21;
    resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22;
    resultMatrix._31 = this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + aMatrix._31;
    resultMatrix._32 = this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + aMatrix._32;

    return resultMatrix;
  }

  Matrix& operator*=(const Matrix &aMatrix)
  {
    *this = *this * aMatrix;
    return *this;
  }

  /**
   * Multiplies in the opposite order to operator=*.
   */
  Matrix &PreMultiply(const Matrix &aMatrix)
  {
    *this = aMatrix * *this;
    return *this;
  }

  /* Returns true if the other matrix is fuzzy-equal to this matrix.
   * Note that this isn't a cheap comparison!
   */
  bool operator==(const Matrix& other) const
  {
    return FuzzyEqual(_11, other._11) && FuzzyEqual(_12, other._12) &&
           FuzzyEqual(_21, other._21) && FuzzyEqual(_22, other._22) &&
           FuzzyEqual(_31, other._31) && FuzzyEqual(_32, other._32);
  }

  bool operator!=(const Matrix& other) const
  {
    return !(*this == other);
  }

  /* Returns true if the matrix is a rectilinear transformation (i.e.
   * grid-aligned rectangles are transformed to grid-aligned rectangles)
   */
  bool IsRectilinear() const {
    if (FuzzyEqual(_12, 0) && FuzzyEqual(_21, 0)) {
      return true;
    } else if (FuzzyEqual(_22, 0) && FuzzyEqual(_11, 0)) {
      return true;
    }

    return false;
  }

  /**
   * Returns true if the matrix is anything other than a straight
   * translation by integers.
  */
  bool HasNonIntegerTranslation() const {
    return HasNonTranslation() ||
      !FuzzyEqual(_31, floor(_31 + 0.5)) ||
      !FuzzyEqual(_32, floor(_32 + 0.5));
  }

  /**
   * Returns true if the matrix only has an integer translation.
   */
  bool HasOnlyIntegerTranslation() const {
    return !HasNonIntegerTranslation();
  }

  /**
   * Returns true if the matrix has any transform other
   * than a straight translation.
   */
  bool HasNonTranslation() const {
    return !FuzzyEqual(_11, 1.0) || !FuzzyEqual(_22, 1.0) ||
           !FuzzyEqual(_12, 0.0) || !FuzzyEqual(_21, 0.0);
  }

  /**
   * Returns true if the matrix has any transform other
   * than a translation or a -1 y scale (y axis flip)
   */
  bool HasNonTranslationOrFlip() const {
      return !FuzzyEqual(_11, 1.0) ||
             (!FuzzyEqual(_22, 1.0) && !FuzzyEqual(_22, -1.0)) ||
             !FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0);
  }

  /* Returns true if the matrix is an identity matrix.
   */
  bool IsIdentity() const
  {
    return _11 == 1.0f && _12 == 0.0f &&
           _21 == 0.0f && _22 == 1.0f &&
           _31 == 0.0f && _32 == 0.0f;
  }

  /* Returns true if the matrix is singular.
   */
  bool IsSingular() const
  {
    return Determinant() == 0;
  }

  GFX2D_API Matrix &NudgeToIntegers();

  bool IsTranslation() const
  {
    return FuzzyEqual(_11, 1.0f) && FuzzyEqual(_12, 0.0f) &&
           FuzzyEqual(_21, 0.0f) && FuzzyEqual(_22, 1.0f);
  }

  static bool FuzzyIsInteger(Float aValue)
  {
    return FuzzyEqual(aValue, floorf(aValue + 0.5f));
  }

  bool IsIntegerTranslation() const
  {
    return IsTranslation() && FuzzyIsInteger(_31) && FuzzyIsInteger(_32);
  }

  bool IsAllIntegers() const
  {
    return FuzzyIsInteger(_11) && FuzzyIsInteger(_12) &&
           FuzzyIsInteger(_21) && FuzzyIsInteger(_22) &&
           FuzzyIsInteger(_31) && FuzzyIsInteger(_32);
  }

  Point GetTranslation() const {
    return Point(_31, _32);
  }

  /**
   * Returns true if matrix is multiple of 90 degrees rotation with flipping,
   * scaling and translation.
   */
  bool PreservesAxisAlignedRectangles() const {
      return ((FuzzyEqual(_11, 0.0) && FuzzyEqual(_22, 0.0))
          || (FuzzyEqual(_12, 0.0) && FuzzyEqual(_21, 0.0)));
  }

  /**
   * Returns true if the matrix has any transform other
   * than a translation or scale; this is, if there is
   * no rotation.
   */
  bool HasNonAxisAlignedTransform() const {
      return !FuzzyEqual(_21, 0.0) || !FuzzyEqual(_12, 0.0);
  }
};

class Matrix4x4
{
public:
  Matrix4x4()
    : _11(1.0f), _12(0.0f), _13(0.0f), _14(0.0f)
    , _21(0.0f), _22(1.0f), _23(0.0f), _24(0.0f)
    , _31(0.0f), _32(0.0f), _33(1.0f), _34(0.0f)
    , _41(0.0f), _42(0.0f), _43(0.0f), _44(1.0f)
  {}

  Matrix4x4(Float a11, Float a12, Float a13, Float a14,
            Float a21, Float a22, Float a23, Float a24,
            Float a31, Float a32, Float a33, Float a34,
            Float a41, Float a42, Float a43, Float a44)
    : _11(a11), _12(a12), _13(a13), _14(a14)
    , _21(a21), _22(a22), _23(a23), _24(a24)
    , _31(a31), _32(a32), _33(a33), _34(a34)
    , _41(a41), _42(a42), _43(a43), _44(a44)
  {}

  Matrix4x4(const Matrix4x4& aOther)
  {
    memcpy(this, &aOther, sizeof(*this));
  }

  Float _11, _12, _13, _14;
  Float _21, _22, _23, _24;
  Float _31, _32, _33, _34;
  Float _41, _42, _43, _44;

  friend std::ostream& operator<<(std::ostream& aStream, const Matrix4x4& aMatrix);

  Point4D& operator[](int aIndex)
  {
      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
      return *reinterpret_cast<Point4D*>((&_11)+4*aIndex);
  }
  const Point4D& operator[](int aIndex) const
  {
      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
      return *reinterpret_cast<const Point4D*>((&_11)+4*aIndex);
  }

  /**
   * Returns true if the matrix is isomorphic to a 2D affine transformation.
   */
  bool Is2D() const
  {
    if (_13 != 0.0f || _14 != 0.0f ||
        _23 != 0.0f || _24 != 0.0f ||
        _31 != 0.0f || _32 != 0.0f || _33 != 1.0f || _34 != 0.0f ||
        _43 != 0.0f || _44 != 1.0f) {
      return false;
    }
    return true;
  }

  bool Is2D(Matrix* aMatrix) const {
    if (!Is2D()) {
      return false;
    }
    if (aMatrix) {
      aMatrix->_11 = _11;
      aMatrix->_12 = _12;
      aMatrix->_21 = _21;
      aMatrix->_22 = _22;
      aMatrix->_31 = _41;
      aMatrix->_32 = _42;
    }
    return true;
  }

  Matrix As2D() const
  {
    MOZ_ASSERT(Is2D(), "Matrix is not a 2D affine transform");

    return Matrix(_11, _12, _21, _22, _41, _42);
  }

  bool CanDraw2D(Matrix* aMatrix = nullptr) const {
    if (_14 != 0.0f ||
        _24 != 0.0f ||
        _44 != 1.0f) {
      return false;
    }
    if (aMatrix) {
      aMatrix->_11 = _11;
      aMatrix->_12 = _12;
      aMatrix->_21 = _21;
      aMatrix->_22 = _22;
      aMatrix->_31 = _41;
      aMatrix->_32 = _42;
    }
    return true;
  }

  Matrix4x4& ProjectTo2D() {
    _31 = 0.0f;
    _32 = 0.0f;
    _13 = 0.0f;
    _23 = 0.0f;
    _33 = 1.0f;
    _43 = 0.0f;
    _34 = 0.0f;
    return *this;
  }

  Point4D ProjectPoint(const Point& aPoint) const {
    // Find a value for z that will transform to 0.

    // The transformed value of z is computed as:
    // z' = aPoint.x * _13 + aPoint.y * _23 + z * _33 + _43;

    // Solving for z when z' = 0 gives us:
    float z = -(aPoint.x * _13 + aPoint.y * _23 + _43) / _33;

    // Compute the transformed point
    return *this * Point4D(aPoint.x, aPoint.y, z, 1);
  }

  Rect ProjectRectBounds(const Rect& aRect, const Rect& aClip) const;

  /**
   * TransformAndClipRect projects a rectangle and clips against view frustum
   * clipping planes in homogenous space so that its projected vertices are
   * constrained within the 2d rectangle passed in aClip.
   * The resulting vertices are populated in aVerts.  aVerts must be
   * pre-allocated to hold at least kTransformAndClipRectMaxVerts Points.
   * The vertex count is returned by TransformAndClipRect.  It is possible to
   * emit fewer that 3 vertices, indicating that aRect will not be visible
   * within aClip.
   */
  size_t TransformAndClipRect(const Rect& aRect, const Rect& aClip, Point* aVerts) const;
  static const size_t kTransformAndClipRectMaxVerts = 32;

  static Matrix4x4 From2D(const Matrix &aMatrix) {
    Matrix4x4 matrix;
    matrix._11 = aMatrix._11;
    matrix._12 = aMatrix._12;
    matrix._21 = aMatrix._21;
    matrix._22 = aMatrix._22;
    matrix._41 = aMatrix._31;
    matrix._42 = aMatrix._32;
    return matrix;
  }

  bool Is2DIntegerTranslation() const
  {
    return Is2D() && As2D().IsIntegerTranslation();
  }

  Point4D TransposeTransform4D(const Point4D& aPoint) const
  {
      Float x = aPoint.x * _11 + aPoint.y * _12 + aPoint.z * _13 + aPoint.w * _14;
      Float y = aPoint.x * _21 + aPoint.y * _22 + aPoint.z * _23 + aPoint.w * _24;
      Float z = aPoint.x * _31 + aPoint.y * _32 + aPoint.z * _33 + aPoint.w * _34;
      Float w = aPoint.x * _41 + aPoint.y * _42 + aPoint.z * _43 + aPoint.w * _44;

      return Point4D(x, y, z, w);
  }

  Point4D operator *(const Point4D& aPoint) const
  {
    Point4D retPoint;

    retPoint.x = aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31 + _41;
    retPoint.y = aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32 + _42;
    retPoint.z = aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33 + _43;
    retPoint.w = aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34 + _44;

    return retPoint;
  }

  Point3D operator *(const Point3D& aPoint) const
  {
    Point4D temp(aPoint.x, aPoint.y, aPoint.z, 1);

    temp = *this * temp;
    temp /= temp.w;

    return Point3D(temp.x, temp.y, temp.z);
  }

  Point operator *(const Point &aPoint) const
  {
    Point4D temp(aPoint.x, aPoint.y, 0, 1);

    temp = *this * temp;
    temp /= temp.w;

    return Point(temp.x, temp.y);
  }

  GFX2D_API Rect TransformBounds(const Rect& rect) const;


  static Matrix4x4 Translation(Float aX, Float aY, Float aZ)
  {
    return Matrix4x4(1.0f, 0.0f, 0.0f, 0.0f,
                     0.0f, 1.0f, 0.0f, 0.0f,
                     0.0f, 0.0f, 1.0f, 0.0f,
                       aX,   aY,   aZ, 1.0f);
  }

  static Matrix4x4 Translation(const Point3D& aP)
  {
    return Translation(aP.x, aP.y, aP.z);
  }

  /**
   * Apply a translation to this matrix.
   *
   * The "Pre" in this method's name means that the translation is applied
   * -before- this matrix's existing transformation. That is, any vector that
   * is multiplied by the resulting matrix will first be translated, then be
   * transformed by the original transform.
   *
   * Calling this method will result in this matrix having the same value as
   * the result of:
   *
   *   Matrix4x4::Translation(x, y) * this
   *
   * (Note that in performance critical code multiplying by the result of a
   * Translation()/Scaling() call is not recommended since that results in a
   * full matrix multiply involving 64 floating-point multiplications. Calling
   * this method would be preferred since it only involves 12 floating-point
   * multiplications.)
   */
  Matrix4x4 &PreTranslate(Float aX, Float aY, Float aZ)
  {
    _41 += aX * _11 + aY * _21 + aZ * _31;
    _42 += aX * _12 + aY * _22 + aZ * _32;
    _43 += aX * _13 + aY * _23 + aZ * _33;
    _44 += aX * _14 + aY * _24 + aZ * _34;

    return *this;
  }

  Matrix4x4 &PreTranslate(const Point3D& aPoint) {
    return PreTranslate(aPoint.x, aPoint.y, aPoint.z);
  }

  /**
   * Similar to PreTranslate, but the translation is applied -after- this
   * matrix's existing transformation instead of before it.
   *
   * This method is generally less used than PreTranslate since typically code
   * wants to adjust an existing user space to device space matrix to create a
   * transform to device space from a -new- user space (translated from the
   * previous user space). In that case consumers will need to use the Pre*
   * variants of the matrix methods rather than using the Post* methods, since
   * the Post* methods add a transform to the device space end of the
   * transformation.
   */
  Matrix4x4 &PostTranslate(Float aX, Float aY, Float aZ)
  {
    _11 += _14 * aX;
    _21 += _24 * aX;
    _31 += _34 * aX;
    _41 += _44 * aX;
    _12 += _14 * aY;
    _22 += _24 * aY;
    _32 += _34 * aY;
    _42 += _44 * aY;
    _13 += _14 * aZ;
    _23 += _24 * aZ;
    _33 += _34 * aZ;
    _43 += _44 * aZ;

    return *this;
  }

  Matrix4x4 &PostTranslate(const Point3D& aPoint) {
    return PostTranslate(aPoint.x, aPoint.y, aPoint.z);
  }

  static Matrix4x4 Scaling(Float aScaleX, Float aScaleY, float aScaleZ)
  {
    return Matrix4x4(aScaleX, 0.0f, 0.0f, 0.0f,
                     0.0f, aScaleY, 0.0f, 0.0f,
                     0.0f, 0.0f, aScaleZ, 0.0f,
                     0.0f, 0.0f, 0.0f, 1.0f);
  }

  /**
   * Similar to PreTranslate, but applies a scale instead of a translation.
   */
  Matrix4x4 &PreScale(Float aX, Float aY, Float aZ)
  {
    _11 *= aX;
    _12 *= aX;
    _13 *= aX;
    _21 *= aY;
    _22 *= aY;
    _23 *= aY;
    _31 *= aZ;
    _32 *= aZ;
    _33 *= aZ;

    return *this;
  }

  /**
   * Similar to PostTranslate, but applies a scale instead of a translation.
   */
  Matrix4x4 &PostScale(Float aScaleX, Float aScaleY, Float aScaleZ)
  {
    _11 *= aScaleX;
    _21 *= aScaleX;
    _31 *= aScaleX;
    _41 *= aScaleX;
    _12 *= aScaleY;
    _22 *= aScaleY;
    _32 *= aScaleY;
    _42 *= aScaleY;
    _13 *= aScaleZ;
    _23 *= aScaleZ;
    _33 *= aScaleZ;
    _43 *= aScaleZ;

    return *this;
  }

  void SkewXY(Float aSkew)
  {
    (*this)[1] += (*this)[0] * aSkew;
  }

  void SkewXZ(Float aSkew)
  {
      (*this)[2] += (*this)[0] * aSkew;
  }

  void SkewYZ(Float aSkew)
  {
      (*this)[2] += (*this)[1] * aSkew;
  }

  Matrix4x4 &ChangeBasis(Float aX, Float aY, Float aZ)
  {
    // Translate to the origin before applying this matrix
    PreTranslate(-aX, -aY, -aZ);

    // Translate back into position after applying this matrix
    PostTranslate(aX, aY, aZ);

    return *this;
  }

  Matrix4x4& Transpose() {
    std::swap(_12, _21);
    std::swap(_13, _31);
    std::swap(_14, _41);

    std::swap(_23, _32);
    std::swap(_24, _42);

    std::swap(_34, _43);

    return *this;
  }

  bool operator==(const Matrix4x4& o) const
  {
    // XXX would be nice to memcmp here, but that breaks IEEE 754 semantics
    return _11 == o._11 && _12 == o._12 && _13 == o._13 && _14 == o._14 &&
           _21 == o._21 && _22 == o._22 && _23 == o._23 && _24 == o._24 &&
           _31 == o._31 && _32 == o._32 && _33 == o._33 && _34 == o._34 &&
           _41 == o._41 && _42 == o._42 && _43 == o._43 && _44 == o._44;
  }

  bool operator!=(const Matrix4x4& o) const
  {
    return !((*this) == o);
  }

  Matrix4x4 operator*(const Matrix4x4 &aMatrix) const
  {
    Matrix4x4 matrix;

    matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21 + _13 * aMatrix._31 + _14 * aMatrix._41;
    matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21 + _23 * aMatrix._31 + _24 * aMatrix._41;
    matrix._31 = _31 * aMatrix._11 + _32 * aMatrix._21 + _33 * aMatrix._31 + _34 * aMatrix._41;
    matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + _43 * aMatrix._31 + _44 * aMatrix._41;
    matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22 + _13 * aMatrix._32 + _14 * aMatrix._42;
    matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22 + _23 * aMatrix._32 + _24 * aMatrix._42;
    matrix._32 = _31 * aMatrix._12 + _32 * aMatrix._22 + _33 * aMatrix._32 + _34 * aMatrix._42;
    matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + _43 * aMatrix._32 + _44 * aMatrix._42;
    matrix._13 = _11 * aMatrix._13 + _12 * aMatrix._23 + _13 * aMatrix._33 + _14 * aMatrix._43;
    matrix._23 = _21 * aMatrix._13 + _22 * aMatrix._23 + _23 * aMatrix._33 + _24 * aMatrix._43;
    matrix._33 = _31 * aMatrix._13 + _32 * aMatrix._23 + _33 * aMatrix._33 + _34 * aMatrix._43;
    matrix._43 = _41 * aMatrix._13 + _42 * aMatrix._23 + _43 * aMatrix._33 + _44 * aMatrix._43;
    matrix._14 = _11 * aMatrix._14 + _12 * aMatrix._24 + _13 * aMatrix._34 + _14 * aMatrix._44;
    matrix._24 = _21 * aMatrix._14 + _22 * aMatrix._24 + _23 * aMatrix._34 + _24 * aMatrix._44;
    matrix._34 = _31 * aMatrix._14 + _32 * aMatrix._24 + _33 * aMatrix._34 + _34 * aMatrix._44;
    matrix._44 = _41 * aMatrix._14 + _42 * aMatrix._24 + _43 * aMatrix._34 + _44 * aMatrix._44;

    return matrix;
  }

  Matrix4x4& operator*=(const Matrix4x4 &aMatrix)
  {
    *this = *this * aMatrix;
    return *this;
  }

  /* Returns true if the matrix is an identity matrix.
   */
  bool IsIdentity() const
  {
    return _11 == 1.0f && _12 == 0.0f && _13 == 0.0f && _14 == 0.0f &&
           _21 == 0.0f && _22 == 1.0f && _23 == 0.0f && _24 == 0.0f &&
           _31 == 0.0f && _32 == 0.0f && _33 == 1.0f && _34 == 0.0f &&
           _41 == 0.0f && _42 == 0.0f && _43 == 0.0f && _44 == 1.0f;
  }

  bool IsSingular() const
  {
    return Determinant() == 0.0;
  }

  Float Determinant() const
  {
    return _14 * _23 * _32 * _41
         - _13 * _24 * _32 * _41
         - _14 * _22 * _33 * _41
         + _12 * _24 * _33 * _41
         + _13 * _22 * _34 * _41
         - _12 * _23 * _34 * _41
         - _14 * _23 * _31 * _42
         + _13 * _24 * _31 * _42
         + _14 * _21 * _33 * _42
         - _11 * _24 * _33 * _42
         - _13 * _21 * _34 * _42
         + _11 * _23 * _34 * _42
         + _14 * _22 * _31 * _43
         - _12 * _24 * _31 * _43
         - _14 * _21 * _32 * _43
         + _11 * _24 * _32 * _43
         + _12 * _21 * _34 * _43
         - _11 * _22 * _34 * _43
         - _13 * _22 * _31 * _44
         + _12 * _23 * _31 * _44
         + _13 * _21 * _32 * _44
         - _11 * _23 * _32 * _44
         - _12 * _21 * _33 * _44
         + _11 * _22 * _33 * _44;
  }

  bool Invert();

  Matrix4x4 Inverse() const
  {
    Matrix4x4 clone = *this;
    DebugOnly<bool> inverted = clone.Invert();
    MOZ_ASSERT(inverted, "Attempted to get the inverse of a non-invertible matrix");
    return clone;
  }

  void Normalize()
  {
      for (int i = 0; i < 4; i++) {
          for (int j = 0; j < 4; j++) {
              (*this)[i][j] /= (*this)[3][3];
         }
      }
  }

  bool FuzzyEqual(const Matrix4x4& o) const
  {
    return gfx::FuzzyEqual(_11, o._11) && gfx::FuzzyEqual(_12, o._12) &&
           gfx::FuzzyEqual(_13, o._13) && gfx::FuzzyEqual(_14, o._14) &&
           gfx::FuzzyEqual(_21, o._21) && gfx::FuzzyEqual(_22, o._22) &&
           gfx::FuzzyEqual(_23, o._23) && gfx::FuzzyEqual(_24, o._24) &&
           gfx::FuzzyEqual(_31, o._31) && gfx::FuzzyEqual(_32, o._32) &&
           gfx::FuzzyEqual(_33, o._33) && gfx::FuzzyEqual(_34, o._34) &&
           gfx::FuzzyEqual(_41, o._41) && gfx::FuzzyEqual(_42, o._42) &&
           gfx::FuzzyEqual(_43, o._43) && gfx::FuzzyEqual(_44, o._44);
  }

  bool IsBackfaceVisible() const
  {
    // Inverse()._33 < 0;
    Float det = Determinant();
    Float __33 = _12*_24*_41 - _14*_22*_41 +
                _14*_21*_42 - _11*_24*_42 -
                _12*_21*_44 + _11*_22*_44;
    return (__33 * det) < 0;
  }

  Matrix4x4 &NudgeToIntegersFixedEpsilon()
  {
    NudgeToInteger(&_11);
    NudgeToInteger(&_12);
    NudgeToInteger(&_13);
    NudgeToInteger(&_14);
    NudgeToInteger(&_21);
    NudgeToInteger(&_22);
    NudgeToInteger(&_23);
    NudgeToInteger(&_24);
    NudgeToInteger(&_31);
    NudgeToInteger(&_32);
    NudgeToInteger(&_33);
    NudgeToInteger(&_34);
    static const float error = 1e-5f;
    NudgeToInteger(&_41, error);
    NudgeToInteger(&_42, error);
    NudgeToInteger(&_43, error);
    NudgeToInteger(&_44, error);
    return *this;
  }

  Point4D TransposedVector(int aIndex) const
  {
      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
      return Point4D(*((&_11)+aIndex), *((&_21)+aIndex), *((&_31)+aIndex), *((&_41)+aIndex));
  }

  void SetTransposedVector(int aIndex, Point4D &aVector)
  {
      MOZ_ASSERT(aIndex >= 0 && aIndex <= 3, "Invalid matrix array index");
      *((&_11)+aIndex) = aVector.x;
      *((&_21)+aIndex) = aVector.y;
      *((&_31)+aIndex) = aVector.z;
      *((&_41)+aIndex) = aVector.w;
  }

  // Sets this matrix to a rotation matrix given by aQuat.
  // This quaternion *MUST* be normalized!
  // Implemented in Quaternion.cpp
  void SetRotationFromQuaternion(const Quaternion& aQuat);

  // Set all the members of the matrix to NaN
  void SetNAN();
};

class Matrix5x4
{
public:
  Matrix5x4()
    : _11(1.0f), _12(0), _13(0), _14(0)
    , _21(0), _22(1.0f), _23(0), _24(0)
    , _31(0), _32(0), _33(1.0f), _34(0)
    , _41(0), _42(0), _43(0), _44(1.0f)
    , _51(0), _52(0), _53(0), _54(0)
  {}
  Matrix5x4(Float a11, Float a12, Float a13, Float a14,
         Float a21, Float a22, Float a23, Float a24,
         Float a31, Float a32, Float a33, Float a34,
         Float a41, Float a42, Float a43, Float a44,
         Float a51, Float a52, Float a53, Float a54)
    : _11(a11), _12(a12), _13(a13), _14(a14)
    , _21(a21), _22(a22), _23(a23), _24(a24)
    , _31(a31), _32(a32), _33(a33), _34(a34)
    , _41(a41), _42(a42), _43(a43), _44(a44)
    , _51(a51), _52(a52), _53(a53), _54(a54)
  {}

  bool operator==(const Matrix5x4 &o) const
  {
    return _11 == o._11 && _12 == o._12 && _13 == o._13 && _14 == o._14 &&
           _21 == o._21 && _22 == o._22 && _23 == o._23 && _24 == o._24 &&
           _31 == o._31 && _32 == o._32 && _33 == o._33 && _34 == o._34 &&
           _41 == o._41 && _42 == o._42 && _43 == o._43 && _44 == o._44 &&
           _51 == o._51 && _52 == o._52 && _53 == o._53 && _54 == o._54;
  }

  bool operator!=(const Matrix5x4 &aMatrix) const
  {
    return !(*this == aMatrix);
  }

  Matrix5x4 operator*(const Matrix5x4 &aMatrix) const
  {
    Matrix5x4 resultMatrix;

    resultMatrix._11 = this->_11 * aMatrix._11 + this->_12 * aMatrix._21 + this->_13 * aMatrix._31 + this->_14 * aMatrix._41;
    resultMatrix._12 = this->_11 * aMatrix._12 + this->_12 * aMatrix._22 + this->_13 * aMatrix._32 + this->_14 * aMatrix._42;
    resultMatrix._13 = this->_11 * aMatrix._13 + this->_12 * aMatrix._23 + this->_13 * aMatrix._33 + this->_14 * aMatrix._43;
    resultMatrix._14 = this->_11 * aMatrix._14 + this->_12 * aMatrix._24 + this->_13 * aMatrix._34 + this->_14 * aMatrix._44;
    resultMatrix._21 = this->_21 * aMatrix._11 + this->_22 * aMatrix._21 + this->_23 * aMatrix._31 + this->_24 * aMatrix._41;
    resultMatrix._22 = this->_21 * aMatrix._12 + this->_22 * aMatrix._22 + this->_23 * aMatrix._32 + this->_24 * aMatrix._42;
    resultMatrix._23 = this->_21 * aMatrix._13 + this->_22 * aMatrix._23 + this->_23 * aMatrix._33 + this->_24 * aMatrix._43;
    resultMatrix._24 = this->_21 * aMatrix._14 + this->_22 * aMatrix._24 + this->_23 * aMatrix._34 + this->_24 * aMatrix._44;
    resultMatrix._31 = this->_31 * aMatrix._11 + this->_32 * aMatrix._21 + this->_33 * aMatrix._31 + this->_34 * aMatrix._41;
    resultMatrix._32 = this->_31 * aMatrix._12 + this->_32 * aMatrix._22 + this->_33 * aMatrix._32 + this->_34 * aMatrix._42;
    resultMatrix._33 = this->_31 * aMatrix._13 + this->_32 * aMatrix._23 + this->_33 * aMatrix._33 + this->_34 * aMatrix._43;
    resultMatrix._34 = this->_31 * aMatrix._14 + this->_32 * aMatrix._24 + this->_33 * aMatrix._34 + this->_34 * aMatrix._44;
    resultMatrix._41 = this->_41 * aMatrix._11 + this->_42 * aMatrix._21 + this->_43 * aMatrix._31 + this->_44 * aMatrix._41;
    resultMatrix._42 = this->_41 * aMatrix._12 + this->_42 * aMatrix._22 + this->_43 * aMatrix._32 + this->_44 * aMatrix._42;
    resultMatrix._43 = this->_41 * aMatrix._13 + this->_42 * aMatrix._23 + this->_43 * aMatrix._33 + this->_44 * aMatrix._43;
    resultMatrix._44 = this->_41 * aMatrix._14 + this->_42 * aMatrix._24 + this->_43 * aMatrix._34 + this->_44 * aMatrix._44;
    resultMatrix._51 = this->_51 * aMatrix._11 + this->_52 * aMatrix._21 + this->_53 * aMatrix._31 + this->_54 * aMatrix._41 + aMatrix._51;
    resultMatrix._52 = this->_51 * aMatrix._12 + this->_52 * aMatrix._22 + this->_53 * aMatrix._32 + this->_54 * aMatrix._42 + aMatrix._52;
    resultMatrix._53 = this->_51 * aMatrix._13 + this->_52 * aMatrix._23 + this->_53 * aMatrix._33 + this->_54 * aMatrix._43 + aMatrix._53;
    resultMatrix._54 = this->_51 * aMatrix._14 + this->_52 * aMatrix._24 + this->_53 * aMatrix._34 + this->_54 * aMatrix._44 + aMatrix._54;

    return resultMatrix;
  }

  Matrix5x4& operator*=(const Matrix5x4 &aMatrix)
  {
    *this = *this * aMatrix;
    return *this;
  }

  Float _11, _12, _13, _14;
  Float _21, _22, _23, _24;
  Float _31, _32, _33, _34;
  Float _41, _42, _43, _44;
  Float _51, _52, _53, _54;
};

}
}

#endif /* MOZILLA_GFX_MATRIX_H_ */