Modify QMatrix4x4 and QQuaternion to use qreal internally

Some concerns were expressed about the float precision of QMatrix4x4,
which this change addresses by using qreal instead.

The QVector2D/3D/4D classes still use float internally, so that they
can be used directly in large arrays of vertex values to be uploaded
to an OpenGL server.

QQuaternion is a client-side class, and it should produce rotations
that are consistent with QMatrix4x4.  So its precision was changed too.

A consequence of this change is that the following no longer works
in a portable fashion:

    QMatrix4x4 mat;
    ...
    glLoadMatrixf(mat.constData());

The caller must now repack the argument to convert from qreal to GLfloat.

Reviewed-by: Michael Goddard
Reviewed-by: Andreas

8 files changed, 415 insertions, 460 deletions

diff --git a/src/gui/math3d/qgenericmatrix.cpp b/src/gui/math3d/qgenericmatrix.cpp
index 290c9c2..b5d8824 100644
--- a/src/gui/math3d/qgenericmatrix.cpp
+++ b/src/gui/math3d/qgenericmatrix.cpp
@@ -50,19 +50,14 @@ QT_BEGIN_NAMESPACE
     \ingroup painting
     \ingroup painting-3D
 
-    The QGenericMatrix template has four parameters:
+    The QGenericMatrix template has three parameters:
 
     \table
     \row \i N \i Number of columns.
     \row \i M \i Number of rows.
     \row \i T \i Element type that is visible to users of the class.
-    \row \i InnerT \i Element type that is used inside the class.
     \endtable
 
-    Normally T and InnerT are the same type; e.g. float or double.
-    But they can be different if the user wants to store elements
-    internally in a fixed-point format for the underlying hardware.
-
     \sa QMatrix4x4
 */
 
@@ -73,7 +68,7 @@ QT_BEGIN_NAMESPACE
 */
 
 /*!
-    \fn QGenericMatrix::QGenericMatrix(const QGenericMatrix<N, M, T, InnerT>& other)
+    \fn QGenericMatrix::QGenericMatrix(const QGenericMatrix<N, M, T>& other)
 
     Constructs a copy of \a other.
 */
@@ -89,13 +84,14 @@ QT_BEGIN_NAMESPACE
 */
 
 /*!
-    \fn T QGenericMatrix::operator()(int row, int column) const
+    \fn const T& QGenericMatrix::operator()(int row, int column) const
 
-    Returns the element at position (\a row, \a column) in this matrix.
+    Returns a constant reference to the element at position
+    (\a row, \a column) in this matrix.
 */
 
 /*!
-    \fn InnerT& QGenericMatrix::operator()(int row, int column)
+    \fn T& QGenericMatrix::operator()(int row, int column)
 
     Returns a reference to the element at position (\a row, \a column)
     in this matrix so that the element can be assigned to.
@@ -130,57 +126,57 @@ QT_BEGIN_NAMESPACE
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT>& QGenericMatrix::operator+=(const QGenericMatrix<N, M, T, InnerT>& other)
+    \fn QGenericMatrix<N, M, T>& QGenericMatrix::operator+=(const QGenericMatrix<N, M, T>& other)
 
     Adds the contents of \a other to this matrix.
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT>& QGenericMatrix::operator-=(const QGenericMatrix<N, M, T, InnerT>& other)
+    \fn QGenericMatrix<N, M, T>& QGenericMatrix::operator-=(const QGenericMatrix<N, M, T>& other)
 
     Subtracts the contents of \a other from this matrix.
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT>& QGenericMatrix::operator*=(T factor)
+    \fn QGenericMatrix<N, M, T>& QGenericMatrix::operator*=(T factor)
 
     Multiplies all elements of this matrix by \a factor.
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT>& QGenericMatrix::operator/=(T divisor)
+    \fn QGenericMatrix<N, M, T>& QGenericMatrix::operator/=(T divisor)
 
     Divides all elements of this matrix by \a divisor.
 */
 
 /*!
-    \fn bool QGenericMatrix::operator==(const QGenericMatrix<N, M, T, InnerT>& other) const
+    \fn bool QGenericMatrix::operator==(const QGenericMatrix<N, M, T>& other) const
 
     Returns true if this matrix is identical to \a other; false otherwise.
 */
 
 /*!
-    \fn bool QGenericMatrix::operator!=(const QGenericMatrix<N, M, T, InnerT>& other) const
+    \fn bool QGenericMatrix::operator!=(const QGenericMatrix<N, M, T>& other) const
 
     Returns true if this matrix is not identical to \a other; false otherwise.
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT> operator+(const QGenericMatrix<N, M, T, InnerT>& m1, const QGenericMatrix<N, M, T, InnerT>& m2)
+    \fn QGenericMatrix<N, M, T> operator+(const QGenericMatrix<N, M, T>& m1, const QGenericMatrix<N, M, T>& m2)
     \relates QGenericMatrix
 
     Returns the sum of \a m1 and \a m2.
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT> operator-(const QGenericMatrix<N, M, T, InnerT>& m1, const QGenericMatrix<N, M, T, InnerT>& m2)
+    \fn QGenericMatrix<N, M, T> operator-(const QGenericMatrix<N, M, T>& m1, const QGenericMatrix<N, M, T>& m2)
     \relates QGenericMatrix
 
     Returns the difference of \a m1 and \a m2.
 */
 
 /*!
-    \fn QGenericMatrix<M1, M2, T, InnerT> operator*(const QGenericMatrix<N, M2, T, InnerT>& m1, const QGenericMatrix<M1, N, T, InnerT>& m2)
+    \fn QGenericMatrix<M1, M2, T> operator*(const QGenericMatrix<N, M2, T>& m1, const QGenericMatrix<M1, N, T>& m2)
     \relates QGenericMatrix
 
     Returns the product of the NxM2 matrix \a m1 and the M1xN matrix \a m2
@@ -188,7 +184,7 @@ QT_BEGIN_NAMESPACE
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT> operator-(const QGenericMatrix<N, M, T, InnerT>& matrix)
+    \fn QGenericMatrix<N, M, T> operator-(const QGenericMatrix<N, M, T>& matrix)
     \overload
     \relates QGenericMatrix
 
@@ -196,21 +192,21 @@ QT_BEGIN_NAMESPACE
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT> operator*(T factor, const QGenericMatrix<N, M, T, InnerT>& matrix)
+    \fn QGenericMatrix<N, M, T> operator*(T factor, const QGenericMatrix<N, M, T>& matrix)
     \relates QGenericMatrix
 
     Returns the result of multiplying all elements of \a matrix by \a factor.
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT> operator*(const QGenericMatrix<N, M, T, InnerT>& matrix, T factor)
+    \fn QGenericMatrix<N, M, T> operator*(const QGenericMatrix<N, M, T>& matrix, T factor)
     \relates QGenericMatrix
 
     Returns the result of multiplying all elements of \a matrix by \a factor.
 */
 
 /*!
-    \fn QGenericMatrix<N, M, T, InnerT> operator/(const QGenericMatrix<N, M, T, InnerT>& matrix, T divisor)
+    \fn QGenericMatrix<N, M, T> operator/(const QGenericMatrix<N, M, T>& matrix, T divisor)
     \relates QGenericMatrix
 
     Returns the result of dividing all elements of \a matrix by \a divisor.
@@ -224,28 +220,25 @@ QT_BEGIN_NAMESPACE
 */
 
 /*!
-    \fn InnerT *QGenericMatrix::data()
+    \fn T *QGenericMatrix::data()
 
-    Returns a pointer to the raw data of this matrix.  This is intended
-    for use with raw GL functions.
+    Returns a pointer to the raw data of this matrix.
 
     \sa constData()
 */
 
 /*!
-    \fn const InnerT *QGenericMatrix::data() const
+    \fn const T *QGenericMatrix::data() const
 
     Returns a constant pointer to the raw data of this matrix.
-    This is intended for use with raw GL functions.
 
     \sa constData()
 */
 
 /*!
-    \fn const InnerT *QGenericMatrix::constData() const
+    \fn const T *QGenericMatrix::constData() const
 
     Returns a constant pointer to the raw data of this matrix.
-    This is intended for use with raw GL functions.
 
     \sa data()
 */
diff --git a/src/gui/math3d/qgenericmatrix.h b/src/gui/math3d/qgenericmatrix.h
index fe7ba5f..39c4ed8 100644
--- a/src/gui/math3d/qgenericmatrix.h
+++ b/src/gui/math3d/qgenericmatrix.h
@@ -51,103 +51,103 @@ QT_BEGIN_NAMESPACE
 
 QT_MODULE(Gui)
 
-template <int N, int M, typename T, typename InnerT = T>
+template <int N, int M, typename T>
 class QGenericMatrix
 {
 public:
     QGenericMatrix();
-    QGenericMatrix(const QGenericMatrix<N, M, T, InnerT>& other);
+    QGenericMatrix(const QGenericMatrix<N, M, T>& other);
     explicit QGenericMatrix(const T *values);
 
-    T operator()(int row, int column) const;
-    InnerT& operator()(int row, int column);
+    const T& operator()(int row, int column) const;
+    T& operator()(int row, int column);
 
     bool isIdentity() const;
     void setIdentity();
 
     void fill(T value);
 
-    QGenericMatrix<M, N, T, InnerT> transposed() const;
+    QGenericMatrix<M, N, T> transposed() const;
 
-    QGenericMatrix<N, M, T, InnerT>& operator+=(const QGenericMatrix<N, M, T, InnerT>& other);
-    QGenericMatrix<N, M, T, InnerT>& operator-=(const QGenericMatrix<N, M, T, InnerT>& other);
-    QGenericMatrix<N, M, T, InnerT>& operator*=(T factor);
-    QGenericMatrix<N, M, T, InnerT>& operator/=(T divisor);
-    bool operator==(const QGenericMatrix<N, M, T, InnerT>& other) const;
-    bool operator!=(const QGenericMatrix<N, M, T, InnerT>& other) const;
+    QGenericMatrix<N, M, T>& operator+=(const QGenericMatrix<N, M, T>& other);
+    QGenericMatrix<N, M, T>& operator-=(const QGenericMatrix<N, M, T>& other);
+    QGenericMatrix<N, M, T>& operator*=(T factor);
+    QGenericMatrix<N, M, T>& operator/=(T divisor);
+    bool operator==(const QGenericMatrix<N, M, T>& other) const;
+    bool operator!=(const QGenericMatrix<N, M, T>& other) const;
 
     void toValueArray(T *values);
 
-    InnerT *data() { return m[0]; }
-    const InnerT *data() const { return m[0]; }
-    const InnerT *constData() const { return m[0]; }
+    T *data() { return m[0]; }
+    const T *data() const { return m[0]; }
+    const T *constData() const { return m[0]; }
 
 #if !defined(Q_NO_TEMPLATE_FRIENDS)
-    template<int NN, int MM, typename TT, typename ITT>
-    friend QGenericMatrix<NN, MM, TT, ITT> operator+(const QGenericMatrix<NN, MM, TT, ITT>& m1, const QGenericMatrix<NN, MM, TT, ITT>& m2);
-    template<int NN, int MM, typename TT, typename ITT>
-    friend QGenericMatrix<NN, MM, TT, ITT> operator-(const QGenericMatrix<NN, MM, TT, ITT>& m1, const QGenericMatrix<NN, MM, TT, ITT>& m2);
-    template<int NN, int M1, int M2, typename TT, typename ITT>
-    friend QGenericMatrix<M1, M2, TT, ITT> operator*(const QGenericMatrix<NN, M2, TT, ITT>& m1, const QGenericMatrix<M1, NN, TT, ITT>& m2);
-    template<int NN, int MM, typename TT, typename ITT>
-    friend QGenericMatrix<NN, MM, TT, ITT> operator-(const QGenericMatrix<NN, MM, TT, ITT>& matrix);
-    template<int NN, int MM, typename TT, typename ITT>
-    friend QGenericMatrix<NN, MM, TT, ITT> operator*(TT factor, const QGenericMatrix<NN, MM, TT, ITT>& matrix);
-    template<int NN, int MM, typename TT, typename ITT>
-    friend QGenericMatrix<NN, MM, TT, ITT> operator*(const QGenericMatrix<NN, MM, TT, ITT>& matrix, TT factor);
-    template<int NN, int MM, typename TT, typename ITT>
-    friend QGenericMatrix<NN, MM, TT, ITT> operator/(const QGenericMatrix<NN, MM, TT, ITT>& matrix, TT divisor);
+    template<int NN, int MM, typename TT>
+    friend QGenericMatrix<NN, MM, TT> operator+(const QGenericMatrix<NN, MM, TT>& m1, const QGenericMatrix<NN, MM, TT>& m2);
+    template<int NN, int MM, typename TT>
+    friend QGenericMatrix<NN, MM, TT> operator-(const QGenericMatrix<NN, MM, TT>& m1, const QGenericMatrix<NN, MM, TT>& m2);
+    template<int NN, int M1, int M2, typename TT>
+    friend QGenericMatrix<M1, M2, TT> operator*(const QGenericMatrix<NN, M2, TT>& m1, const QGenericMatrix<M1, NN, TT>& m2);
+    template<int NN, int MM, typename TT>
+    friend QGenericMatrix<NN, MM, TT> operator-(const QGenericMatrix<NN, MM, TT>& matrix);
+    template<int NN, int MM, typename TT>
+    friend QGenericMatrix<NN, MM, TT> operator*(TT factor, const QGenericMatrix<NN, MM, TT>& matrix);
+    template<int NN, int MM, typename TT>
+    friend QGenericMatrix<NN, MM, TT> operator*(const QGenericMatrix<NN, MM, TT>& matrix, TT factor);
+    template<int NN, int MM, typename TT>
+    friend QGenericMatrix<NN, MM, TT> operator/(const QGenericMatrix<NN, MM, TT>& matrix, TT divisor);
 
 private:
 #endif
-    InnerT m[N][M];    // Column-major order to match OpenGL.
+    T m[N][M];    // Column-major order to match OpenGL.
 
     QGenericMatrix(int) {}       // Construct without initializing identity matrix.
 
 #if !defined(Q_NO_TEMPLATE_FRIENDS)
-    template <int NN, int MM, typename TT, typename ITT>
+    template <int NN, int MM, typename TT>
     friend class QGenericMatrix;
 #endif
 };
 
-template <int N, int M, typename T, typename InnerT>
-Q_INLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT>::QGenericMatrix()
+template <int N, int M, typename T>
+Q_INLINE_TEMPLATE QGenericMatrix<N, M, T>::QGenericMatrix()
 {
     setIdentity();
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_INLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT>::QGenericMatrix(const QGenericMatrix<N, M, T, InnerT>& other)
+template <int N, int M, typename T>
+Q_INLINE_TEMPLATE QGenericMatrix<N, M, T>::QGenericMatrix(const QGenericMatrix<N, M, T>& other)
 {
     for (int col = 0; col < N; ++col)
         for (int row = 0; row < M; ++row)
             m[col][row] = other.m[col][row];
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT>::QGenericMatrix(const T *values)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T>::QGenericMatrix(const T *values)
 {
     for (int col = 0; col < N; ++col)
         for (int row = 0; row < M; ++row)
             m[col][row] = values[row * N + col];
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_INLINE_TEMPLATE T QGenericMatrix<N, M, T, InnerT>::operator()(int row, int column) const
+template <int N, int M, typename T>
+Q_INLINE_TEMPLATE const T& QGenericMatrix<N, M, T>::operator()(int row, int column) const
 {
     Q_ASSERT(row >= 0 && row < M && column >= 0 && column < N);
-    return T(m[column][row]);
+    return m[column][row];
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_INLINE_TEMPLATE InnerT& QGenericMatrix<N, M, T, InnerT>::operator()(int row, int column)
+template <int N, int M, typename T>
+Q_INLINE_TEMPLATE T& QGenericMatrix<N, M, T>::operator()(int row, int column)
 {
     Q_ASSERT(row >= 0 && row < M && column >= 0 && column < N);
     return m[column][row];
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T, InnerT>::isIdentity() const
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T>::isIdentity() const
 {
     for (int col = 0; col < N; ++col) {
         for (int row = 0; row < M; ++row) {
@@ -163,8 +163,8 @@ Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T, InnerT>::isIdentity() const
     return true;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T, InnerT>::setIdentity()
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T>::setIdentity()
 {
     for (int col = 0; col < N; ++col) {
         for (int row = 0; row < M; ++row) {
@@ -176,51 +176,50 @@ Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T, InnerT>::setIdentity()
     }
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T, InnerT>::fill(T value)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T>::fill(T value)
 {
     for (int col = 0; col < N; ++col)
         for (int row = 0; row < M; ++row)
             m[col][row] = value;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<M, N, T, InnerT> QGenericMatrix<N, M, T, InnerT>::transposed() const
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<M, N, T> QGenericMatrix<N, M, T>::transposed() const
 {
-    QGenericMatrix<M, N, T, InnerT> result(1);
+    QGenericMatrix<M, N, T> result(1);
     for (int row = 0; row < M; ++row)
         for (int col = 0; col < N; ++col)
             result.m[row][col] = m[col][row];
     return result;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT>& QGenericMatrix<N, M, T, InnerT>::operator+=(const QGenericMatrix<N, M, T, InnerT>& other)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T>& QGenericMatrix<N, M, T>::operator+=(const QGenericMatrix<N, M, T>& other)
 {
     for (int index = 0; index < N * M; ++index)
         m[0][index] += other.m[0][index];
     return *this;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT>& QGenericMatrix<N, M, T, InnerT>::operator-=(const QGenericMatrix<N, M, T, InnerT>& other)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T>& QGenericMatrix<N, M, T>::operator-=(const QGenericMatrix<N, M, T>& other)
 {
     for (int index = 0; index < N * M; ++index)
         m[0][index] -= other.m[0][index];
     return *this;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT>& QGenericMatrix<N, M, T, InnerT>::operator*=(T factor)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T>& QGenericMatrix<N, M, T>::operator*=(T factor)
 {
-    InnerT f(factor);
     for (int index = 0; index < N * M; ++index)
-        m[0][index] *= f;
+        m[0][index] *= factor;
     return *this;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T, InnerT>::operator==(const QGenericMatrix<N, M, T, InnerT>& other) const
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T>::operator==(const QGenericMatrix<N, M, T>& other) const
 {
     for (int index = 0; index < N * M; ++index) {
         if (m[0][index] != other.m[0][index])
@@ -229,8 +228,8 @@ Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T, InnerT>::operator==(const QGen
     return true;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T, InnerT>::operator!=(const QGenericMatrix<N, M, T, InnerT>& other) const
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T>::operator!=(const QGenericMatrix<N, M, T>& other) const
 {
     for (int index = 0; index < N * M; ++index) {
         if (m[0][index] != other.m[0][index])
@@ -239,40 +238,39 @@ Q_OUTOFLINE_TEMPLATE bool QGenericMatrix<N, M, T, InnerT>::operator!=(const QGen
     return false;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT>& QGenericMatrix<N, M, T, InnerT>::operator/=(T divisor)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T>& QGenericMatrix<N, M, T>::operator/=(T divisor)
 {
-    InnerT d(divisor);
     for (int index = 0; index < N * M; ++index)
-        m[0][index] /= d;
+        m[0][index] /= divisor;
     return *this;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT> operator+(const QGenericMatrix<N, M, T, InnerT>& m1, const QGenericMatrix<N, M, T, InnerT>& m2)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T> operator+(const QGenericMatrix<N, M, T>& m1, const QGenericMatrix<N, M, T>& m2)
 {
-    QGenericMatrix<N, M, T, InnerT> result(1);
+    QGenericMatrix<N, M, T> result(1);
     for (int index = 0; index < N * M; ++index)
         result.m[0][index] = m1.m[0][index] + m2.m[0][index];
     return result;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT> operator-(const QGenericMatrix<N, M, T, InnerT>& m1, const QGenericMatrix<N, M, T, InnerT>& m2)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T> operator-(const QGenericMatrix<N, M, T>& m1, const QGenericMatrix<N, M, T>& m2)
 {
-    QGenericMatrix<N, M, T, InnerT> result(1);
+    QGenericMatrix<N, M, T> result(1);
     for (int index = 0; index < N * M; ++index)
         result.m[0][index] = m1.m[0][index] - m2.m[0][index];
     return result;
 }
 
-template <int N, int M1, int M2, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<M1, M2, T, InnerT> operator*(const QGenericMatrix<N, M2, T, InnerT>& m1, const QGenericMatrix<M1, N, T, InnerT>& m2)
+template <int N, int M1, int M2, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<M1, M2, T> operator*(const QGenericMatrix<N, M2, T>& m1, const QGenericMatrix<M1, N, T>& m2)
 {
-    QGenericMatrix<M1, M2, T, InnerT> result(1);
+    QGenericMatrix<M1, M2, T> result(1);
     for (int row = 0; row < M2; ++row) {
         for (int col = 0; col < M1; ++col) {
-            InnerT sum(0.0f);
+            T sum(0.0f);
             for (int j = 0; j < N; ++j)
                 sum += m1.m[j][row] * m2.m[col][j];
             result.m[col][row] = sum;
@@ -281,47 +279,44 @@ Q_OUTOFLINE_TEMPLATE QGenericMatrix<M1, M2, T, InnerT> operator*(const QGenericM
     return result;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT> operator-(const QGenericMatrix<N, M, T, InnerT>& matrix)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T> operator-(const QGenericMatrix<N, M, T>& matrix)
 {
-    QGenericMatrix<N, M, T, InnerT> result(1);
+    QGenericMatrix<N, M, T> result(1);
     for (int index = 0; index < N * M; ++index)
         result.m[0][index] = -matrix.m[0][index];
     return result;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT> operator*(T factor, const QGenericMatrix<N, M, T, InnerT>& matrix)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T> operator*(T factor, const QGenericMatrix<N, M, T>& matrix)
 {
-    InnerT f(factor);
-    QGenericMatrix<N, M, T, InnerT> result(1);
+    QGenericMatrix<N, M, T> result(1);
     for (int index = 0; index < N * M; ++index)
-        result.m[0][index] = matrix.m[0][index] * f;
+        result.m[0][index] = matrix.m[0][index] * factor;
     return result;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT> operator*(const QGenericMatrix<N, M, T, InnerT>& matrix, T factor)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T> operator*(const QGenericMatrix<N, M, T>& matrix, T factor)
 {
-    InnerT f(factor);
-    QGenericMatrix<N, M, T, InnerT> result(1);
+    QGenericMatrix<N, M, T> result(1);
     for (int index = 0; index < N * M; ++index)
-        result.m[0][index] = matrix.m[0][index] * f;
+        result.m[0][index] = matrix.m[0][index] * factor;
     return result;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T, InnerT> operator/(const QGenericMatrix<N, M, T, InnerT>& matrix, T divisor)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE QGenericMatrix<N, M, T> operator/(const QGenericMatrix<N, M, T>& matrix, T divisor)
 {
-    InnerT d(divisor);
-    QGenericMatrix<N, M, T, InnerT> result(1);
+    QGenericMatrix<N, M, T> result(1);
     for (int index = 0; index < N * M; ++index)
-        result.m[0][index] = matrix.m[0][index] / d;
+        result.m[0][index] = matrix.m[0][index] / divisor;
     return result;
 }
 
-template <int N, int M, typename T, typename InnerT>
-Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T, InnerT>::toValueArray(T *values)
+template <int N, int M, typename T>
+Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T>::toValueArray(T *values)
 {
     for (int col = 0; col < N; ++col)
         for (int row = 0; row < M; ++row)
@@ -329,22 +324,22 @@ Q_OUTOFLINE_TEMPLATE void QGenericMatrix<N, M, T, InnerT>::toValueArray(T *value
 }
 
 // Define aliases for the useful variants of QGenericMatrix.
-typedef QGenericMatrix<2, 2, qreal, float> QMatrix2x2;
-typedef QGenericMatrix<2, 3, qreal, float> QMatrix2x3;
-typedef QGenericMatrix<2, 4, qreal, float> QMatrix2x4;
-typedef QGenericMatrix<3, 2, qreal, float> QMatrix3x2;
-typedef QGenericMatrix<3, 3, qreal, float> QMatrix3x3;
-typedef QGenericMatrix<3, 4, qreal, float> QMatrix3x4;
-typedef QGenericMatrix<4, 2, qreal, float> QMatrix4x2;
-typedef QGenericMatrix<4, 3, qreal, float> QMatrix4x3;
+typedef QGenericMatrix<2, 2, qreal> QMatrix2x2;
+typedef QGenericMatrix<2, 3, qreal> QMatrix2x3;
+typedef QGenericMatrix<2, 4, qreal> QMatrix2x4;
+typedef QGenericMatrix<3, 2, qreal> QMatrix3x2;
+typedef QGenericMatrix<3, 3, qreal> QMatrix3x3;
+typedef QGenericMatrix<3, 4, qreal> QMatrix3x4;
+typedef QGenericMatrix<4, 2, qreal> QMatrix4x2;
+typedef QGenericMatrix<4, 3, qreal> QMatrix4x3;
 
 #ifndef QT_NO_DEBUG_STREAM
 
-template <int N, int M, typename T, typename InnerT>
-QDebug operator<<(QDebug dbg, const QGenericMatrix<N, M, T, InnerT> &m)
+template <int N, int M, typename T>
+QDebug operator<<(QDebug dbg, const QGenericMatrix<N, M, T> &m)
 {
     dbg.nospace() << "QGenericMatrix<" << N << ", " << M
-        << ", " << QTypeInfo<T>::name() << ", " << QTypeInfo<InnerT>::name()
+        << ", " << QTypeInfo<T>::name()
         << ">(" << endl << qSetFieldWidth(10);
     for (int row = 0; row < M; ++row) {
         for (int col = 0; col < N; ++col)
diff --git a/src/gui/math3d/qmatrix4x4.cpp b/src/gui/math3d/qmatrix4x4.cpp
index eb5858c..2164aca 100644
--- a/src/gui/math3d/qmatrix4x4.cpp
+++ b/src/gui/math3d/qmatrix4x4.cpp
@@ -103,7 +103,7 @@ QMatrix4x4::QMatrix4x4(const qreal *values)
 #if !defined(QT_NO_MEMBER_TEMPLATES) || defined(Q_QDOC)
 
 /*!
-    \fn QMatrix4x4::QMatrix4x4(const QGenericMatrix<N, M, qreal, float>& matrix)
+    \fn QMatrix4x4::QMatrix4x4(const QGenericMatrix<N, M, qreal>& matrix)
 
     Constructs a 4x4 matrix from the left-most 4 columns and top-most
     4 rows of \a matrix.  If \a matrix has less than 4 columns or rows,
@@ -114,7 +114,7 @@ QMatrix4x4::QMatrix4x4(const qreal *values)
 */
 
 /*!
-    \fn QGenericMatrix<N, M, qreal, float> QMatrix4x4::toGenericMatrix() const
+    \fn QGenericMatrix<N, M, qreal> QMatrix4x4::toGenericMatrix() const
 
     Constructs a NxM generic matrix from the left-most N columns and
     top-most M rows of this 4x4 matrix.  If N or M is greater than 4,
@@ -127,7 +127,7 @@ QMatrix4x4::QMatrix4x4(const qreal *values)
 #endif
 
 /*!
-    \fn QMatrix4x4 qGenericMatrixToMatrix4x4(const QGenericMatrix<N, M, qreal, float>& matrix)
+    \fn QMatrix4x4 qGenericMatrixToMatrix4x4(const QGenericMatrix<N, M, qreal>& matrix)
     \relates QMatrix4x4
 
     Returns a 4x4 matrix constructed from the left-most 4 columns and
@@ -139,7 +139,7 @@ QMatrix4x4::QMatrix4x4(const qreal *values)
 */
 
 /*!
-    \fn QGenericMatrix<N, M, qreal, float> qGenericMatrixFromMatrix4x4(const QMatrix4x4& matrix)
+    \fn QGenericMatrix<N, M, qreal> qGenericMatrixFromMatrix4x4(const QMatrix4x4& matrix)
     \relates QMatrix4x4
 
     Returns a NxM generic matrix constructed from the left-most N columns
@@ -153,7 +153,7 @@ QMatrix4x4::QMatrix4x4(const qreal *values)
 /*!
     \internal
 */
-QMatrix4x4::QMatrix4x4(const float *values, int cols, int rows)
+QMatrix4x4::QMatrix4x4(const qreal *values, int cols, int rows)
 {
     for (int col = 0; col < 4; ++col) {
         for (int row = 0; row < 4; ++row) {
@@ -233,15 +233,16 @@ QMatrix4x4::QMatrix4x4(const QTransform& transform)
 }
 
 /*!
-    \fn qreal QMatrix4x4::operator()(int row, int column) const
+    \fn const qreal& QMatrix4x4::operator()(int row, int column) const
 
-    Returns the element at position (\a row, \a column) in this matrix.
+    Returns a constant reference to the element at position
+    (\a row, \a column) in this matrix.
 
     \sa column(), row()
 */
 
 /*!
-    \fn float& QMatrix4x4::operator()(int row, int column)
+    \fn qreal& QMatrix4x4::operator()(int row, int column)
 
     Returns a reference to the element at position (\a row, \a column)
     in this matrix so that the element can be assigned to.
@@ -312,8 +313,8 @@ QMatrix4x4::QMatrix4x4(const QTransform& transform)
 //     | A B C |
 // M = | D E F |   det(M) = A * (EI - HF) - B * (DI - GF) + C * (DH - GE)
 //     | G H I |
-static inline float matrixDet3
-    (const float m[4][4], int col0, int col1, int col2,
+static inline qreal matrixDet3
+    (const qreal m[4][4], int col0, int col1, int col2,
      int row0, int row1, int row2)
 {
     return m[col0][row0] *
@@ -328,9 +329,9 @@ static inline float matrixDet3
 }
 
 // Calculate the determinant of a 4x4 matrix.
-static inline float matrixDet4(const float m[4][4])
+static inline qreal matrixDet4(const qreal m[4][4])
 {
-    float det;
+    qreal det;
     det  = m[0][0] * matrixDet3(m, 1, 2, 3, 1, 2, 3);
     det -= m[1][0] * matrixDet3(m, 0, 2, 3, 1, 2, 3);
     det += m[2][0] * matrixDet3(m, 0, 1, 3, 1, 2, 3);
@@ -382,7 +383,7 @@ QMatrix4x4 QMatrix4x4::inverted(bool *invertible) const
 
     QMatrix4x4 inv(1); // The "1" says to not load the identity.
 
-    float det = matrixDet4(m);
+    qreal det = matrixDet4(m);
     if (det == 0.0f) {
         if (invertible)
             *invertible = false;
@@ -436,12 +437,12 @@ QMatrix3x3 QMatrix4x4::normalMatrix() const
         return inv;
     }
 
-    float det = matrixDet3(m, 0, 1, 2, 0, 1, 2);
+    qreal det = matrixDet3(m, 0, 1, 2, 0, 1, 2);
     if (det == 0.0f)
         return inv;
     det = 1.0f / det;
 
-    float *invm = inv.data();
+    qreal *invm = inv.data();
 
     // Invert and transpose in a single step.
     invm[0 + 0 * 3] =  (m[1][1] * m[2][2] - m[2][1] * m[1][2]) * det;
@@ -697,9 +698,9 @@ QMatrix4x4 operator/(const QMatrix4x4& matrix, qreal divisor)
 */
 QMatrix4x4& QMatrix4x4::scale(const QVector3D& vector)
 {
-    float vx = vector.xp;
-    float vy = vector.yp;
-    float vz = vector.zp;
+    qreal vx = vector.x();
+    qreal vy = vector.y();
+    qreal vz = vector.z();
     if (flagBits == Identity) {
         m[0][0] = vx;
         m[1][1] = vy;
@@ -743,28 +744,26 @@ QMatrix4x4& QMatrix4x4::scale(const QVector3D& vector)
 */
 QMatrix4x4& QMatrix4x4::scale(qreal x, qreal y)
 {
-    float vx(x);
-    float vy(y);
     if (flagBits == Identity) {
-        m[0][0] = vx;
-        m[1][1] = vy;
+        m[0][0] = x;
+        m[1][1] = y;
         flagBits = Scale;
     } else if (flagBits == Scale || flagBits == (Scale | Translation)) {
-        m[0][0] *= vx;
-        m[1][1] *= vy;
+        m[0][0] *= x;
+        m[1][1] *= y;
     } else if (flagBits == Translation) {
-        m[0][0] = vx;
-        m[1][1] = vy;
+        m[0][0] = x;
+        m[1][1] = y;
         flagBits |= Scale;
     } else {
-        m[0][0] *= vx;
-        m[0][1] *= vx;
-        m[0][2] *= vx;
-        m[0][3] *= vx;
-        m[1][0] *= vy;
-        m[1][1] *= vy;
-        m[1][2] *= vy;
-        m[1][3] *= vy;
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[0][2] *= x;
+        m[0][3] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[1][2] *= y;
+        m[1][3] *= y;
         flagBits = General;
     }
     return *this;
@@ -780,36 +779,33 @@ QMatrix4x4& QMatrix4x4::scale(qreal x, qreal y)
 */
 QMatrix4x4& QMatrix4x4::scale(qreal x, qreal y, qreal z)
 {
-    float vx(x);
-    float vy(y);
-    float vz(z);
     if (flagBits == Identity) {
-        m[0][0] = vx;
-        m[1][1] = vy;
-        m[2][2] = vz;
+        m[0][0] = x;
+        m[1][1] = y;
+        m[2][2] = z;
         flagBits = Scale;
     } else if (flagBits == Scale || flagBits == (Scale | Translation)) {
-        m[0][0] *= vx;
-        m[1][1] *= vy;
-        m[2][2] *= vz;
+        m[0][0] *= x;
+        m[1][1] *= y;
+        m[2][2] *= z;
     } else if (flagBits == Translation) {
-        m[0][0] = vx;
-        m[1][1] = vy;
-        m[2][2] = vz;
+        m[0][0] = x;
+        m[1][1] = y;
+        m[2][2] = z;
         flagBits |= Scale;
     } else {
-        m[0][0] *= vx;
-        m[0][1] *= vx;
-        m[0][2] *= vx;
-        m[0][3] *= vx;
-        m[1][0] *= vy;
-        m[1][1] *= vy;
-        m[1][2] *= vy;
-        m[1][3] *= vy;
-        m[2][0] *= vz;
-        m[2][1] *= vz;
-        m[2][2] *= vz;
-        m[2][3] *= vz;
+        m[0][0] *= x;
+        m[0][1] *= x;
+        m[0][2] *= x;
+        m[0][3] *= x;
+        m[1][0] *= y;
+        m[1][1] *= y;
+        m[1][2] *= y;
+        m[1][3] *= y;
+        m[2][0] *= z;
+        m[2][1] *= z;
+        m[2][2] *= z;
+        m[2][3] *= z;
         flagBits = General;
     }
     return *this;
@@ -866,9 +862,9 @@ QMatrix4x4& QMatrix4x4::scale(qreal factor)
 */
 QMatrix4x4& QMatrix4x4::translate(const QVector3D& vector)
 {
-    float vx = vector.xp;
-    float vy = vector.yp;
-    float vz = vector.zp;
+    qreal vx = vector.x();
+    qreal vy = vector.y();
+    qreal vz = vector.z();
     if (flagBits == Identity) {
         m[3][0] = vx;
         m[3][1] = vy;
@@ -912,28 +908,26 @@ QMatrix4x4& QMatrix4x4::translate(const QVector3D& vector)
 */
 QMatrix4x4& QMatrix4x4::translate(qreal x, qreal y)
 {
-    float vx(x);
-    float vy(y);
     if (flagBits == Identity) {
-        m[3][0] = vx;
-        m[3][1] = vy;
+        m[3][0] = x;
+        m[3][1] = y;
         flagBits = Translation;
     } else if (flagBits == Translation) {
-        m[3][0] += vx;
-        m[3][1] += vy;
+        m[3][0] += x;
+        m[3][1] += y;
     } else if (flagBits == Scale) {
-        m[3][0] = m[0][0] * vx;
-        m[3][1] = m[1][1] * vy;
+        m[3][0] = m[0][0] * x;
+        m[3][1] = m[1][1] * y;
         m[3][2] = 0.;
         flagBits |= Translation;
     } else if (flagBits == (Scale | Translation)) {
-        m[3][0] += m[0][0] * vx;
-        m[3][1] += m[1][1] * vy;
+        m[3][0] += m[0][0] * x;
+        m[3][1] += m[1][1] * y;
     } else {
-        m[3][0] += m[0][0] * vx + m[1][0] * vy;
-        m[3][1] += m[0][1] * vx + m[1][1] * vy;
-        m[3][2] += m[0][2] * vx + m[1][2] * vy;
-        m[3][3] += m[0][3] * vx + m[1][3] * vy;
+        m[3][0] += m[0][0] * x + m[1][0] * y;
+        m[3][1] += m[0][1] * x + m[1][1] * y;
+        m[3][2] += m[0][2] * x + m[1][2] * y;
+        m[3][3] += m[0][3] * x + m[1][3] * y;
         if (flagBits == Rotation)
             flagBits |= Translation;
         else if (flagBits != (Rotation | Translation))
@@ -952,32 +946,29 @@ QMatrix4x4& QMatrix4x4::translate(qreal x, qreal y)
 */
 QMatrix4x4& QMatrix4x4::translate(qreal x, qreal y, qreal z)
 {
-    float vx(x);
-    float vy(y);
-    float vz(z);
     if (flagBits == Identity) {
-        m[3][0] = vx;
-        m[3][1] = vy;
-        m[3][2] = vz;
+        m[3][0] = x;
+        m[3][1] = y;
+        m[3][2] = z;
         flagBits = Translation;
     } else if (flagBits == Translation) {
-        m[3][0] += vx;
-        m[3][1] += vy;
-        m[3][2] += vz;
+        m[3][0] += x;
+        m[3][1] += y;
+        m[3][2] += z;
     } else if (flagBits == Scale) {
-        m[3][0] = m[0][0] * vx;
-        m[3][1] = m[1][1] * vy;
-        m[3][2] = m[2][2] * vz;
+        m[3][0] = m[0][0] * x;
+        m[3][1] = m[1][1] * y;
+        m[3][2] = m[2][2] * z;
         flagBits |= Translation;
     } else if (flagBits == (Scale | Translation)) {
-        m[3][0] += m[0][0] * vx;
-        m[3][1] += m[1][1] * vy;
-        m[3][2] += m[2][2] * vz;
+        m[3][0] += m[0][0] * x;
+        m[3][1] += m[1][1] * y;
+        m[3][2] += m[2][2] * z;
     } else {
-        m[3][0] += m[0][0] * vx + m[1][0] * vy + m[2][0] * vz;
-        m[3][1] += m[0][1] * vx + m[1][1] * vy + m[2][1] * vz;
-        m[3][2] += m[0][2] * vx + m[1][2] * vy + m[2][2] * vz;
-        m[3][3] += m[0][3] * vx + m[1][3] * vy + m[2][3] * vz;
+        m[3][0] += m[0][0] * x + m[1][0] * y + m[2][0] * z;
+        m[3][1] += m[0][1] * x + m[1][1] * y + m[2][1] * z;
+        m[3][2] += m[0][2] * x + m[1][2] * y + m[2][2] * z;
+        m[3][3] += m[0][3] * x + m[1][3] * y + m[2][3] * z;
         if (flagBits == Rotation)
             flagBits |= Translation;
         else if (flagBits != (Rotation | Translation))
@@ -1126,15 +1117,15 @@ QMatrix4x4& QMatrix4x4::rotate(const QQuaternion& quaternion)
     // Algorithm from:
     // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q54
     QMatrix4x4 m(1);
-    float xx = quaternion.xp * quaternion.xp;
-    float xy = quaternion.xp * quaternion.yp;
-    float xz = quaternion.xp * quaternion.zp;
-    float xw = quaternion.xp * quaternion.wp;
-    float yy = quaternion.yp * quaternion.yp;
-    float yz = quaternion.yp * quaternion.zp;
-    float yw = quaternion.yp * quaternion.wp;
-    float zz = quaternion.zp * quaternion.zp;
-    float zw = quaternion.zp * quaternion.wp;
+    qreal xx = quaternion.x() * quaternion.x();
+    qreal xy = quaternion.x() * quaternion.y();
+    qreal xz = quaternion.x() * quaternion.z();
+    qreal xw = quaternion.x() * quaternion.scalar();
+    qreal yy = quaternion.y() * quaternion.y();
+    qreal yz = quaternion.y() * quaternion.z();
+    qreal yw = quaternion.y() * quaternion.scalar();
+    qreal zz = quaternion.z() * quaternion.z();
+    qreal zw = quaternion.z() * quaternion.scalar();
     m.m[0][0] = 1.0f - 2 * (yy + zz);
     m.m[1][0] =        2 * (xy - zw);
     m.m[2][0] =        2 * (xz + yw);
@@ -1222,11 +1213,11 @@ QMatrix4x4& QMatrix4x4::ortho(qreal left, qreal right, qreal bottom, qreal top,
         translate(QVector3D
             (-(left + right) / width,
              -(top + bottom) / invheight,
-             0.0f, 1));
+             0.0f));
         scale(QVector3D
             (2.0f / width,
              2.0f / invheight,
-             -1.0f, 1));
+             -1.0f));
         return *this;
     }
 #endif
@@ -1356,17 +1347,17 @@ QMatrix4x4& QMatrix4x4::lookAt(const QVector3D& eye, const QVector3D& center, co
 
     QMatrix4x4 m(1);
 
-    m.m[0][0] = side.xp;
-    m.m[1][0] = side.yp;
-    m.m[2][0] = side.zp;
+    m.m[0][0] = side.x();
+    m.m[1][0] = side.y();
+    m.m[2][0] = side.z();
     m.m[3][0] = 0.0f;
-    m.m[0][1] = upVector.xp;
-    m.m[1][1] = upVector.yp;
-    m.m[2][1] = upVector.zp;
+    m.m[0][1] = upVector.x();
+    m.m[1][1] = upVector.y();
+    m.m[2][1] = upVector.z();
     m.m[3][1] = 0.0f;
-    m.m[0][2] = -forward.xp;
-    m.m[1][2] = -forward.yp;
-    m.m[2][2] = -forward.zp;
+    m.m[0][2] = -forward.x();
+    m.m[1][2] = -forward.y();
+    m.m[2][2] = -forward.z();
     m.m[3][2] = 0.0f;
     m.m[0][3] = 0.0f;
     m.m[1][3] = 0.0f;
@@ -1434,9 +1425,9 @@ void QMatrix4x4::toValueArray(qreal *values) const
 */
 QMatrix QMatrix4x4::toAffine() const
 {
-    return QMatrix(qreal(m[0][0]), qreal(m[0][1]),
-                   qreal(m[1][0]), qreal(m[1][1]),
-                   qreal(m[3][0]), qreal(m[3][1]));
+    return QMatrix(m[0][0], m[0][1],
+                   m[1][0], m[1][1],
+                   m[3][0], m[3][1]);
 }
 
 static const qreal inv_dist_to_plane = 1. / 1024.;
@@ -1462,15 +1453,12 @@ QTransform QMatrix4x4::toTransform(qreal distanceToPlane) const
 {
     if (distanceToPlane == 1024.0f) {
         // Optimize the common case with constants.
-        return QTransform(qreal(m[0][0]), qreal(m[0][1]),
-                                qreal(m[0][3]) - qreal(m[0][2]) *
-                                                 inv_dist_to_plane,
-                          qreal(m[1][0]), qreal(m[1][1]),
-                                qreal(m[1][3]) - qreal(m[1][2]) *
-                                                 inv_dist_to_plane,
-                          qreal(m[3][0]), qreal(m[3][1]),
-                                qreal(m[3][3]) - qreal(m[3][2]) *
-                                                 inv_dist_to_plane);
+        return QTransform(m[0][0], m[0][1],
+                                m[0][3] - m[0][2] * inv_dist_to_plane,
+                          m[1][0], m[1][1],
+                                m[1][3] - m[1][2] * inv_dist_to_plane,
+                          m[3][0], m[3][1],
+                                m[3][3] - m[3][2] * inv_dist_to_plane);
     } else if (distanceToPlane != 0.0f) {
         // The following projection matrix is pre-multiplied with "matrix":
         //      | 1 0 0 0 |
@@ -1480,17 +1468,14 @@ QTransform QMatrix4x4::toTransform(qreal distanceToPlane) const
         // where d = -1 / distanceToPlane.  After projection, row 3 and
         // column 3 are dropped to form the final QTransform.
         qreal d = 1.0f / distanceToPlane;
-        return QTransform(qreal(m[0][0]), qreal(m[0][1]),
-                                qreal(m[0][3]) - qreal(m[0][2]) * d,
-                          qreal(m[1][0]), qreal(m[1][1]),
-                                qreal(m[1][3]) - qreal(m[1][2]) * d,
-                          qreal(m[3][0]), qreal(m[3][1]),
-                                qreal(m[3][3]) - qreal(m[3][2]) * d);
+        return QTransform(m[0][0], m[0][1], m[0][3] - m[0][2] * d,
+                          m[1][0], m[1][1], m[1][3] - m[1][2] * d,
+                          m[3][0], m[3][1], m[3][3] - m[3][2] * d);
     } else {
         // Orthographic projection: drop row 3 and column 3.
-        return QTransform(qreal(m[0][0]), qreal(m[0][1]), qreal(m[0][3]),
-                          qreal(m[1][0]), qreal(m[1][1]), qreal(m[1][3]),
-                          qreal(m[3][0]), qreal(m[3][1]), qreal(m[3][3]));
+        return QTransform(m[0][0], m[0][1], m[0][3],
+                          m[1][0], m[1][1], m[1][3],
+                          m[3][0], m[3][1], m[3][3]);
     }
 }
 
@@ -1618,28 +1603,25 @@ QRectF QMatrix4x4::mapRect(const QRectF& rect) const
 }
 
 /*!
-    \fn float *QMatrix4x4::data()
+    \fn qreal *QMatrix4x4::data()
 
-    Returns a pointer to the raw data of this matrix.  This is intended
-    for use with raw GL functions.
+    Returns a pointer to the raw data of this matrix.
 
     \sa constData(), inferSpecialType()
 */
 
 /*!
-    \fn const float *QMatrix4x4::data() const
+    \fn const qreal *QMatrix4x4::data() const
 
     Returns a constant pointer to the raw data of this matrix.
-    This is intended for use with raw GL functions.
 
     \sa constData()
 */
 
 /*!
-    \fn const float *QMatrix4x4::constData() const
+    \fn const qreal *QMatrix4x4::constData() const
 
     Returns a constant pointer to the raw data of this matrix.
-    This is intended for use with raw GL functions.
 
     \sa data()
 */
@@ -1695,7 +1677,7 @@ void QMatrix4x4::extractAxisRotation(qreal &angle, QVector3D &axis) const
 {
     // Orientation is dependent on the upper 3x3 matrix; subtract the
     // homogeneous scaling element from the trace of the 4x4 matrix
-    float tr = m[0][0] + m[1][1] + m[2][2];
+    qreal tr = m[0][0] + m[1][1] + m[2][2];
     qreal cosa = qreal(0.5f * (tr - 1.0f));
     angle = acos(cosa) * 180.0f / M_PI;
 
@@ -1708,38 +1690,38 @@ void QMatrix4x4::extractAxisRotation(qreal &angle, QVector3D &axis) const
     }
 
     if (angle < 180.0f) {
-        axis.xp = m[1][2] - m[2][1];
-        axis.yp = m[2][0] - m[0][2];
-        axis.zp = m[0][1] - m[1][0];
+        axis.setX(m[1][2] - m[2][1]);
+        axis.setY(m[2][0] - m[0][2]);
+        axis.setZ(m[0][1] - m[1][0]);
         axis.normalize();
         return;
     }
 
     // rads == PI
-    float tmp;
+    qreal tmp;
 
     // r00 is maximum
     if ((m[0][0] >= m[2][2]) && (m[0][0] >= m[1][1])) {
-        axis.xp = 0.5f * qSqrt(m[0][0] - m[1][1] - m[2][2] + 1.0f);
+        axis.setX(0.5f * qSqrt(m[0][0] - m[1][1] - m[2][2] + 1.0f));
         tmp = 0.5f / axis.x();
-        axis.yp = m[1][0] * tmp;
-        axis.zp = m[2][0] * tmp;
+        axis.setY(m[1][0] * tmp);
+        axis.setZ(m[2][0] * tmp);
     }
 
     // r11 is maximum
     if ((m[1][1] >= m[2][2]) && (m[1][1] >= m[0][0])) {
-        axis.yp = 0.5f * qSqrt(m[1][1] - m[0][0] - m[2][2] + 1.0f);
+        axis.setY(0.5f * qSqrt(m[1][1] - m[0][0] - m[2][2] + 1.0f));
         tmp = 0.5f / axis.y();
-        axis.xp = tmp * m[1][0];
-        axis.zp = tmp * m[2][1];
+        axis.setX(tmp * m[1][0]);
+        axis.setZ(tmp * m[2][1]);
     }
 
     // r22 is maximum
     if ((m[2][2] >= m[1][1]) && (m[2][2] >= m[0][0])) {
-        axis.zp = 0.5f * qSqrt(m[2][2] - m[0][0] - m[1][1] + 1.0f);
+        axis.setZ(0.5f * qSqrt(m[2][2] - m[0][0] - m[1][1] + 1.0f));
         tmp = 0.5f / axis.z();
-        axis.xp = m[2][0]*tmp;
-        axis.yp = m[2][1]*tmp;
+        axis.setX(m[2][0]*tmp);
+        axis.setY(m[2][1]*tmp);
     }
 }
 
@@ -1756,7 +1738,7 @@ QVector3D QMatrix4x4::extractTranslation() const
     return QVector3D
         (m[0][0] * m[3][0] + m[0][1] * m[3][1] + m[0][2] * m[3][2],
          m[1][0] * m[3][0] + m[1][1] * m[3][1] + m[1][2] * m[3][2],
-         m[2][0] * m[3][0] + m[2][1] * m[3][1] + m[2][2] * m[3][2], 1);
+         m[2][0] * m[3][0] + m[2][1] * m[3][1] + m[2][2] * m[3][2]);
 }
 #endif
 
@@ -1894,7 +1876,7 @@ QDataStream &operator>>(QDataStream &stream, QMatrix4x4 &matrix)
     for (int row = 0; row < 4; ++row) {
         for (int col = 0; col < 4; ++col) {
             stream >> x;
-            matrix(row, col) = float(x);
+            matrix(row, col) = qreal(x);
         }
     }
     matrix.inferSpecialType();
diff --git a/src/gui/math3d/qmatrix4x4.h b/src/gui/math3d/qmatrix4x4.h
index 4207bdf..8811027 100644
--- a/src/gui/math3d/qmatrix4x4.h
+++ b/src/gui/math3d/qmatrix4x4.h
@@ -71,14 +71,14 @@ public:
                       qreal m41, qreal m42, qreal m43, qreal m44);
 #if !defined(QT_NO_MEMBER_TEMPLATES) || defined(Q_QDOC)
     template <int N, int M>
-    explicit QMatrix4x4(const QGenericMatrix<N, M, qreal, float>& matrix);
+    explicit QMatrix4x4(const QGenericMatrix<N, M, qreal>& matrix);
 #endif
-    QMatrix4x4(const float *values, int cols, int rows);
+    QMatrix4x4(const qreal *values, int cols, int rows);
     QMatrix4x4(const QTransform& transform);
     QMatrix4x4(const QMatrix& matrix);
 
-    inline qreal operator()(int row, int column) const;
-    inline float& operator()(int row, int column);
+    inline const qreal& operator()(int row, int column) const;
+    inline qreal& operator()(int row, int column);
 
     inline QVector4D column(int index) const;
     inline void setColumn(int index, const QVector4D& value);
@@ -174,12 +174,12 @@ public:
 
 #if !defined(QT_NO_MEMBER_TEMPLATES) || defined(Q_QDOC)
     template <int N, int M>
-    QGenericMatrix<N, M, qreal, float> toGenericMatrix() const;
+    QGenericMatrix<N, M, qreal> toGenericMatrix() const;
 #endif
 
-    inline float *data();
-    inline const float *data() const { return m[0]; }
-    inline const float *constData() const { return m[0]; }
+    inline qreal *data();
+    inline const qreal *data() const { return m[0]; }
+    inline const qreal *constData() const { return m[0]; }
 
     void inferSpecialType();
 
@@ -190,7 +190,7 @@ public:
 #endif
 
 private:
-    float m[4][4];          // Column-major order to match OpenGL.
+    qreal m[4][4];          // Column-major order to match OpenGL.
     int flagBits;           // Flag bits from the enum below.
 
     enum {
@@ -224,9 +224,9 @@ inline QMatrix4x4::QMatrix4x4
 
 template <int N, int M>
 Q_INLINE_TEMPLATE QMatrix4x4::QMatrix4x4
-    (const QGenericMatrix<N, M, qreal, float>& matrix)
+    (const QGenericMatrix<N, M, qreal>& matrix)
 {
-    const float *values = matrix.constData();
+    const qreal *values = matrix.constData();
     for (int col = 0; col < 4; ++col) {
         for (int row = 0; row < 4; ++row) {
             if (col < N && row < M)
@@ -241,10 +241,10 @@ Q_INLINE_TEMPLATE QMatrix4x4::QMatrix4x4
 }
 
 template <int N, int M>
-QGenericMatrix<N, M, qreal, float> QMatrix4x4::toGenericMatrix() const
+QGenericMatrix<N, M, qreal> QMatrix4x4::toGenericMatrix() const
 {
-    QGenericMatrix<N, M, qreal, float> result;
-    float *values = result.data();
+    QGenericMatrix<N, M, qreal> result;
+    qreal *values = result.data();
     for (int col = 0; col < N; ++col) {
         for (int row = 0; row < M; ++row) {
             if (col < 4 && row < 4)
@@ -260,13 +260,13 @@ QGenericMatrix<N, M, qreal, float> QMatrix4x4::toGenericMatrix() const
 
 #endif
 
-inline qreal QMatrix4x4::operator()(int row, int column) const
+inline const qreal& QMatrix4x4::operator()(int row, int column) const
 {
     Q_ASSERT(row >= 0 && row < 4 && column >= 0 && column < 4);
-    return qreal(m[column][row]);
+    return m[column][row];
 }
 
-inline float& QMatrix4x4::operator()(int row, int column)
+inline qreal& QMatrix4x4::operator()(int row, int column)
 {
     Q_ASSERT(row >= 0 && row < 4 && column >= 0 && column < 4);
     flagBits = General;
@@ -276,32 +276,32 @@ inline float& QMatrix4x4::operator()(int row, int column)
 inline QVector4D QMatrix4x4::column(int index) const
 {
     Q_ASSERT(index >= 0 && index < 4);
-    return QVector4D(m[index][0], m[index][1], m[index][2], m[index][3], 1);
+    return QVector4D(m[index][0], m[index][1], m[index][2], m[index][3]);
 }
 
 inline void QMatrix4x4::setColumn(int index, const QVector4D& value)
 {
     Q_ASSERT(index >= 0 && index < 4);
-    m[index][0] = value.xp;
-    m[index][1] = value.yp;
-    m[index][2] = value.zp;
-    m[index][3] = value.wp;
+    m[index][0] = value.x();
+    m[index][1] = value.y();
+    m[index][2] = value.z();
+    m[index][3] = value.w();
     flagBits = General;
 }
 
 inline QVector4D QMatrix4x4::row(int index) const
 {
     Q_ASSERT(index >= 0 && index < 4);
-    return QVector4D(m[0][index], m[1][index], m[2][index], m[3][index], 1);
+    return QVector4D(m[0][index], m[1][index], m[2][index], m[3][index]);
 }
 
 inline void QMatrix4x4::setRow(int index, const QVector4D& value)
 {
     Q_ASSERT(index >= 0 && index < 4);
-    m[0][index] = value.xp;
-    m[1][index] = value.yp;
-    m[2][index] = value.zp;
-    m[3][index] = value.wp;
+    m[0][index] = value.x();
+    m[1][index] = value.y();
+    m[2][index] = value.z();
+    m[3][index] = value.w();
     flagBits = General;
 }
 
@@ -608,68 +608,68 @@ inline QMatrix4x4 operator*(const QMatrix4x4& m1, const QMatrix4x4& m2)
 
 inline QVector3D operator*(const QVector3D& vector, const QMatrix4x4& matrix)
 {
-    float x, y, z, w;
-    x = vector.xp * matrix.m[0][0] +
-        vector.yp * matrix.m[0][1] +
-        vector.zp * matrix.m[0][2] +
+    qreal x, y, z, w;
+    x = vector.x() * matrix.m[0][0] +
+        vector.y() * matrix.m[0][1] +
+        vector.z() * matrix.m[0][2] +
         matrix.m[0][3];
-    y = vector.xp * matrix.m[1][0] +
-        vector.yp * matrix.m[1][1] +
-        vector.zp * matrix.m[1][2] +
+    y = vector.x() * matrix.m[1][0] +
+        vector.y() * matrix.m[1][1] +
+        vector.z() * matrix.m[1][2] +
         matrix.m[1][3];
-    z = vector.xp * matrix.m[2][0] +
-        vector.yp * matrix.m[2][1] +
-        vector.zp * matrix.m[2][2] +
+    z = vector.x() * matrix.m[2][0] +
+        vector.y() * matrix.m[2][1] +
+        vector.z() * matrix.m[2][2] +
         matrix.m[2][3];
-    w = vector.xp * matrix.m[3][0] +
-        vector.yp * matrix.m[3][1] +
-        vector.zp * matrix.m[3][2] +
+    w = vector.x() * matrix.m[3][0] +
+        vector.y() * matrix.m[3][1] +
+        vector.z() * matrix.m[3][2] +
         matrix.m[3][3];
     if (w == 1.0f)
-        return QVector3D(x, y, z, 1);
+        return QVector3D(x, y, z);
     else
-        return QVector3D(x / w, y / w, z / w, 1);
+        return QVector3D(x / w, y / w, z / w);
 }
 
 inline QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector)
 {
-    float x, y, z, w;
+    qreal x, y, z, w;
     if (matrix.flagBits == QMatrix4x4::Identity) {
         return vector;
     } else if (matrix.flagBits == QMatrix4x4::Translation) {
-        return QVector3D(vector.xp + matrix.m[3][0],
-                         vector.yp + matrix.m[3][1],
-                         vector.zp + matrix.m[3][2], 1);
+        return QVector3D(vector.x() + matrix.m[3][0],
+                         vector.y() + matrix.m[3][1],
+                         vector.z() + matrix.m[3][2]);
     } else if (matrix.flagBits ==
                     (QMatrix4x4::Translation | QMatrix4x4::Scale)) {
-        return QVector3D(vector.xp * matrix.m[0][0] + matrix.m[3][0],
-                         vector.yp * matrix.m[1][1] + matrix.m[3][1],
-                         vector.zp * matrix.m[2][2] + matrix.m[3][2], 1);
+        return QVector3D(vector.x() * matrix.m[0][0] + matrix.m[3][0],
+                         vector.y() * matrix.m[1][1] + matrix.m[3][1],
+                         vector.z() * matrix.m[2][2] + matrix.m[3][2]);
     } else if (matrix.flagBits == QMatrix4x4::Scale) {
-        return QVector3D(vector.xp * matrix.m[0][0],
-                         vector.yp * matrix.m[1][1],
-                         vector.zp * matrix.m[2][2], 1);
+        return QVector3D(vector.x() * matrix.m[0][0],
+                         vector.y() * matrix.m[1][1],
+                         vector.z() * matrix.m[2][2]);
     } else {
-        x = vector.xp * matrix.m[0][0] +
-            vector.yp * matrix.m[1][0] +
-            vector.zp * matrix.m[2][0] +
+        x = vector.x() * matrix.m[0][0] +
+            vector.y() * matrix.m[1][0] +
+            vector.z() * matrix.m[2][0] +
             matrix.m[3][0];
-        y = vector.xp * matrix.m[0][1] +
-            vector.yp * matrix.m[1][1] +
-            vector.zp * matrix.m[2][1] +
+        y = vector.x() * matrix.m[0][1] +
+            vector.y() * matrix.m[1][1] +
+            vector.z() * matrix.m[2][1] +
             matrix.m[3][1];
-        z = vector.xp * matrix.m[0][2] +
-            vector.yp * matrix.m[1][2] +
-            vector.zp * matrix.m[2][2] +
+        z = vector.x() * matrix.m[0][2] +
+            vector.y() * matrix.m[1][2] +
+            vector.z() * matrix.m[2][2] +
             matrix.m[3][2];
-        w = vector.xp * matrix.m[0][3] +
-            vector.yp * matrix.m[1][3] +
-            vector.zp * matrix.m[2][3] +
+        w = vector.x() * matrix.m[0][3] +
+            vector.y() * matrix.m[1][3] +
+            vector.z() * matrix.m[2][3] +
             matrix.m[3][3];
         if (w == 1.0f)
-            return QVector3D(x, y, z, 1);
+            return QVector3D(x, y, z);
         else
-            return QVector3D(x / w, y / w, z / w, 1);
+            return QVector3D(x / w, y / w, z / w);
     }
 }
 
@@ -679,54 +679,54 @@ inline QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector)
 
 inline QVector4D operator*(const QVector4D& vector, const QMatrix4x4& matrix)
 {
-    float x, y, z, w;
-    x = vector.xp * matrix.m[0][0] +
-        vector.yp * matrix.m[0][1] +
-        vector.zp * matrix.m[0][2] +
-        vector.wp * matrix.m[0][3];
-    y = vector.xp * matrix.m[1][0] +
-        vector.yp * matrix.m[1][1] +
-        vector.zp * matrix.m[1][2] +
-        vector.wp * matrix.m[1][3];
-    z = vector.xp * matrix.m[2][0] +
-        vector.yp * matrix.m[2][1] +
-        vector.zp * matrix.m[2][2] +
-        vector.wp * matrix.m[2][3];
-    w = vector.xp * matrix.m[3][0] +
-        vector.yp * matrix.m[3][1] +
-        vector.zp * matrix.m[3][2] +
-        vector.wp * matrix.m[3][3];
-    return QVector4D(x, y, z, w, 1);
+    qreal x, y, z, w;
+    x = vector.x() * matrix.m[0][0] +
+        vector.y() * matrix.m[0][1] +
+        vector.z() * matrix.m[0][2] +
+        vector.w() * matrix.m[0][3];
+    y = vector.x() * matrix.m[1][0] +
+        vector.y() * matrix.m[1][1] +
+        vector.z() * matrix.m[1][2] +
+        vector.w() * matrix.m[1][3];
+    z = vector.x() * matrix.m[2][0] +
+        vector.y() * matrix.m[2][1] +
+        vector.z() * matrix.m[2][2] +
+        vector.w() * matrix.m[2][3];
+    w = vector.x() * matrix.m[3][0] +
+        vector.y() * matrix.m[3][1] +
+        vector.z() * matrix.m[3][2] +
+        vector.w() * matrix.m[3][3];
+    return QVector4D(x, y, z, w);
 }
 
 inline QVector4D operator*(const QMatrix4x4& matrix, const QVector4D& vector)
 {
-    float x, y, z, w;
-    x = vector.xp * matrix.m[0][0] +
-        vector.yp * matrix.m[1][0] +
-        vector.zp * matrix.m[2][0] +
-        vector.wp * matrix.m[3][0];
-    y = vector.xp * matrix.m[0][1] +
-        vector.yp * matrix.m[1][1] +
-        vector.zp * matrix.m[2][1] +
-        vector.wp * matrix.m[3][1];
-    z = vector.xp * matrix.m[0][2] +
-        vector.yp * matrix.m[1][2] +
-        vector.zp * matrix.m[2][2] +
-        vector.wp * matrix.m[3][2];
-    w = vector.xp * matrix.m[0][3] +
-        vector.yp * matrix.m[1][3] +
-        vector.zp * matrix.m[2][3] +
-        vector.wp * matrix.m[3][3];
-    return QVector4D(x, y, z, w, 1);
+    qreal x, y, z, w;
+    x = vector.x() * matrix.m[0][0] +
+        vector.y() * matrix.m[1][0] +
+        vector.z() * matrix.m[2][0] +
+        vector.w() * matrix.m[3][0];
+    y = vector.x() * matrix.m[0][1] +
+        vector.y() * matrix.m[1][1] +
+        vector.z() * matrix.m[2][1] +
+        vector.w() * matrix.m[3][1];
+    z = vector.x() * matrix.m[0][2] +
+        vector.y() * matrix.m[1][2] +
+        vector.z() * matrix.m[2][2] +
+        vector.w() * matrix.m[3][2];
+    w = vector.x() * matrix.m[0][3] +
+        vector.y() * matrix.m[1][3] +
+        vector.z() * matrix.m[2][3] +
+        vector.w() * matrix.m[3][3];
+    return QVector4D(x, y, z, w);
 }
 
 #endif
 
 inline QPoint operator*(const QPoint& point, const QMatrix4x4& matrix)
 {
-    float xin, yin;
-    float x, y, w;
+    qreal xin, yin;
+    qreal x, y, w;
     xin = point.x();
     yin = point.y();
     x = xin * matrix.m[0][0] +
@@ -746,8 +746,8 @@ inline QPoint operator*(const QPoint& point, const QMatrix4x4& matrix)
 
 inline QPointF operator*(const QPointF& point, const QMatrix4x4& matrix)
 {
-    float xin, yin;
-    float x, y, w;
+    qreal xin, yin;
+    qreal x, y, w;
     xin = point.x();
     yin = point.y();
     x = xin * matrix.m[0][0] +
@@ -768,8 +768,8 @@ inline QPointF operator*(const QPointF& point, const QMatrix4x4& matrix)
 
 inline QPoint operator*(const QMatrix4x4& matrix, const QPoint& point)
 {
-    float xin, yin;
-    float x, y, w;
+    qreal xin, yin;
+    qreal x, y, w;
     xin = point.x();
     yin = point.y();
     if (matrix.flagBits == QMatrix4x4::Identity) {
@@ -803,8 +803,8 @@ inline QPoint operator*(const QMatrix4x4& matrix, const QPoint& point)
 
 inline QPointF operator*(const QMatrix4x4& matrix, const QPointF& point)
 {
-    float xin, yin;
-    float x, y, w;
+    qreal xin, yin;
+    qreal x, y, w;
     xin = point.x();
     yin = point.y();
     if (matrix.flagBits == QMatrix4x4::Identity) {
@@ -951,7 +951,7 @@ inline QVector4D QMatrix4x4::map(const QVector4D& point) const
 
 #endif
 
-inline float *QMatrix4x4::data()
+inline qreal *QMatrix4x4::data()
 {
     // We have to assume that the caller will modify the matrix elements,
     // so we flip it over to "General" mode.
@@ -969,17 +969,17 @@ Q_GUI_EXPORT QDataStream &operator>>(QDataStream &, QMatrix4x4 &);
 #endif
 
 template <int N, int M>
-QMatrix4x4 qGenericMatrixToMatrix4x4(const QGenericMatrix<N, M, qreal, float>& matrix)
+QMatrix4x4 qGenericMatrixToMatrix4x4(const QGenericMatrix<N, M, qreal>& matrix)
 {
     return QMatrix4x4(matrix.constData(), N, M);
 }
 
 template <int N, int M>
-QGenericMatrix<N, M, qreal, float> qGenericMatrixFromMatrix4x4(const QMatrix4x4& matrix)
+QGenericMatrix<N, M, qreal> qGenericMatrixFromMatrix4x4(const QMatrix4x4& matrix)
 {
-    QGenericMatrix<N, M, qreal, float> result;
-    const float *m = matrix.constData();
-    float *values = result.data();
+    QGenericMatrix<N, M, qreal> result;
+    const qreal *m = matrix.constData();
+    qreal *values = result.data();
     for (int col = 0; col < N; ++col) {
         for (int row = 0; row < M; ++row) {
             if (col < 4 && row < 4)
diff --git a/src/gui/math3d/qquaternion.cpp b/src/gui/math3d/qquaternion.cpp
index ece4482..7206e9a 100644
--- a/src/gui/math3d/qquaternion.cpp
+++ b/src/gui/math3d/qquaternion.cpp
@@ -353,7 +353,7 @@ QQuaternion QQuaternion::fromAxisAndAngle(const QVector3D& axis, qreal angle)
     qreal s = qSin(a);
     qreal c = qCos(a);
     QVector3D ax = axis.normalized();
-    return QQuaternion(c, ax.xp * s, ax.yp * s, ax.zp * s, 1).normalized();
+    return QQuaternion(c, ax.x() * s, ax.y() * s, ax.z() * s).normalized();
 }
 
 #endif
@@ -365,19 +365,16 @@ QQuaternion QQuaternion::fromAxisAndAngle(const QVector3D& axis, qreal angle)
 QQuaternion QQuaternion::fromAxisAndAngle
         (qreal x, qreal y, qreal z, qreal angle)
 {
-    float xp = x;
-    float yp = y;
-    float zp = z;
-    qreal length = qSqrt(xp * xp + yp * yp + zp * zp);
-    if (!qIsNull(length)) {
-        xp /= length;
-        yp /= length;
-        zp /= length;
+    qreal length = qSqrt(x * x + y * y + z * z);
+    if (!qFuzzyIsNull(length - 1.0f) && !qFuzzyIsNull(length)) {
+        x /= length;
+        y /= length;
+        z /= length;
     }
     qreal a = (angle / 2.0f) * M_PI / 180.0f;
     qreal s = qSin(a);
     qreal c = qCos(a);
-    return QQuaternion(c, xp * s, yp * s, zp * s, 1).normalized();
+    return QQuaternion(c, x * s, y * s, z * s).normalized();
 }
 
 /*!
diff --git a/src/gui/math3d/qquaternion.h b/src/gui/math3d/qquaternion.h
index 12576d2..f243c42 100644
--- a/src/gui/math3d/qquaternion.h
+++ b/src/gui/math3d/qquaternion.h
@@ -133,11 +133,7 @@ public:
         (const QQuaternion& q1, const QQuaternion& q2, qreal t);
 
 private:
-    float wp, xp, yp, zp;
-
-    friend class QMatrix4x4;
-
-    QQuaternion(float scalar, float xpos, float ypos, float zpos, int dummy);
+    qreal wp, xp, yp, zp;
 };
 
 inline QQuaternion::QQuaternion() : wp(1.0f), xp(0.0f), yp(0.0f), zp(0.0f) {}
@@ -145,8 +141,6 @@ inline QQuaternion::QQuaternion() : wp(1.0f), xp(0.0f), yp(0.0f), zp(0.0f) {}
 inline QQuaternion::QQuaternion(qreal scalar, qreal xpos, qreal ypos, qreal zpos) : wp(scalar), xp(xpos), yp(ypos), zp(zpos) {}
 
 
-inline QQuaternion::QQuaternion(float scalar, float xpos, float ypos, float zpos, int) : wp(scalar), xp(xpos), yp(ypos), zp(zpos) {}
-
 inline bool QQuaternion::isNull() const
 {
     return qIsNull(xp) && qIsNull(yp) && qIsNull(zp) && qIsNull(wp);
@@ -169,7 +163,7 @@ inline void QQuaternion::setScalar(qreal scalar) { wp = scalar; }
 
 inline QQuaternion QQuaternion::conjugate() const
 {
-    return QQuaternion(wp, -xp, -yp, -zp, 1);
+    return QQuaternion(wp, -xp, -yp, -zp);
 }
 
 inline QQuaternion &QQuaternion::operator+=(const QQuaternion &quaternion)
@@ -201,18 +195,18 @@ inline QQuaternion &QQuaternion::operator*=(qreal factor)
 
 inline const QQuaternion operator*(const QQuaternion &q1, const QQuaternion& q2)
 {
-    float ww = (q1.zp + q1.xp) * (q2.xp + q2.yp);
-    float yy = (q1.wp - q1.yp) * (q2.wp + q2.zp);
-    float zz = (q1.wp + q1.yp) * (q2.wp - q2.zp);
-    float xx = ww + yy + zz;
-    float qq = 0.5 * (xx + (q1.zp - q1.xp) * (q2.xp - q2.yp));
-
-    float w = qq - ww + (q1.zp - q1.yp) * (q2.yp - q2.zp);
-    float x = qq - xx + (q1.xp + q1.wp) * (q2.xp + q2.wp);
-    float y = qq - yy + (q1.wp - q1.xp) * (q2.yp + q2.zp);
-    float z = qq - zz + (q1.zp + q1.yp) * (q2.wp - q2.xp);
-
-    return QQuaternion(w, x, y, z, 1);
+    qreal ww = (q1.zp + q1.xp) * (q2.xp + q2.yp);
+    qreal yy = (q1.wp - q1.yp) * (q2.wp + q2.zp);
+    qreal zz = (q1.wp + q1.yp) * (q2.wp - q2.zp);
+    qreal xx = ww + yy + zz;
+    qreal qq = 0.5 * (xx + (q1.zp - q1.xp) * (q2.xp - q2.yp));
+
+    qreal w = qq - ww + (q1.zp - q1.yp) * (q2.yp - q2.zp);
+    qreal x = qq - xx + (q1.xp + q1.wp) * (q2.xp + q2.wp);
+    qreal y = qq - yy + (q1.wp - q1.xp) * (q2.yp + q2.zp);
+    qreal z = qq - zz + (q1.zp + q1.yp) * (q2.wp - q2.xp);
+
+    return QQuaternion(w, x, y, z);
 }
 
 inline QQuaternion &QQuaternion::operator*=(const QQuaternion &quaternion)
@@ -242,32 +236,32 @@ inline bool operator!=(const QQuaternion &q1, const QQuaternion &q2)
 
 inline const QQuaternion operator+(const QQuaternion &q1, const QQuaternion &q2)
 {
-    return QQuaternion(q1.wp + q2.wp, q1.xp + q2.xp, q1.yp + q2.yp, q1.zp + q2.zp, 1);
+    return QQuaternion(q1.wp + q2.wp, q1.xp + q2.xp, q1.yp + q2.yp, q1.zp + q2.zp);
 }
 
 inline const QQuaternion operator-(const QQuaternion &q1, const QQuaternion &q2)
 {
-    return QQuaternion(q1.wp - q2.wp, q1.xp - q2.xp, q1.yp - q2.yp, q1.zp - q2.zp, 1);
+    return QQuaternion(q1.wp - q2.wp, q1.xp - q2.xp, q1.yp - q2.yp, q1.zp - q2.zp);
 }
 
 inline const QQuaternion operator*(qreal factor, const QQuaternion &quaternion)
 {
-    return QQuaternion(quaternion.wp * factor, quaternion.xp * factor, quaternion.yp * factor, quaternion.zp * factor, 1);
+    return QQuaternion(quaternion.wp * factor, quaternion.xp * factor, quaternion.yp * factor, quaternion.zp * factor);
 }
 
 inline const QQuaternion operator*(const QQuaternion &quaternion, qreal factor)
 {
-    return QQuaternion(quaternion.wp * factor, quaternion.xp * factor, quaternion.yp * factor, quaternion.zp * factor, 1);
+    return QQuaternion(quaternion.wp * factor, quaternion.xp * factor, quaternion.yp * factor, quaternion.zp * factor);
 }
 
 inline const QQuaternion operator-(const QQuaternion &quaternion)
 {
-    return QQuaternion(-quaternion.wp, -quaternion.xp, -quaternion.yp, -quaternion.zp, 1);
+    return QQuaternion(-quaternion.wp, -quaternion.xp, -quaternion.yp, -quaternion.zp);
 }
 
 inline const QQuaternion operator/(const QQuaternion &quaternion, qreal divisor)
 {
-    return QQuaternion(quaternion.wp / divisor, quaternion.xp / divisor, quaternion.yp / divisor, quaternion.zp / divisor, 1);
+    return QQuaternion(quaternion.wp / divisor, quaternion.xp / divisor, quaternion.yp / divisor, quaternion.zp / divisor);
 }
 
 inline bool qFuzzyCompare(const QQuaternion& q1, const QQuaternion& q2)
@@ -281,18 +275,18 @@ inline bool qFuzzyCompare(const QQuaternion& q1, const QQuaternion& q2)
 #ifndef QT_NO_VECTOR3D
 
 inline QQuaternion::QQuaternion(qreal scalar, const QVector3D& vector)
-    : wp(scalar), xp(vector.xp), yp(vector.yp), zp(vector.zp) {}
+    : wp(scalar), xp(vector.x()), yp(vector.y()), zp(vector.z()) {}
 
 inline void QQuaternion::setVector(const QVector3D& vector)
 {
-    xp = vector.xp;
-    yp = vector.yp;
-    zp = vector.zp;
+    xp = vector.x();
+    yp = vector.y();
+    zp = vector.z();
 }
 
 inline QVector3D QQuaternion::vector() const
 {
-    return QVector3D(xp, yp, zp, 1);
+    return QVector3D(xp, yp, zp);
 }
 
 #endif
@@ -307,11 +301,11 @@ inline void QQuaternion::setVector(qreal x, qreal y, qreal z)
 #ifndef QT_NO_VECTOR4D
 
 inline QQuaternion::QQuaternion(const QVector4D& vector)
-    : wp(vector.wp), xp(vector.xp), yp(vector.yp), zp(vector.zp) {}
+    : wp(vector.w()), xp(vector.x()), yp(vector.y()), zp(vector.z()) {}
 
 inline QVector4D QQuaternion::toVector4D() const
 {
-    return QVector4D(xp, yp, zp, wp, 1);
+    return QVector4D(xp, yp, zp, wp);
 }
 
 #endif
diff --git a/src/gui/math3d/qvector3d.h b/src/gui/math3d/qvector3d.h
index 767517e..1e95865 100644
--- a/src/gui/math3d/qvector3d.h
+++ b/src/gui/math3d/qvector3d.h
@@ -54,7 +54,6 @@ QT_MODULE(Gui)
 class QMatrix4x4;
 class QVector2D;
 class QVector4D;
-class QQuaternion;
 
 #ifndef QT_NO_VECTOR3D
 
@@ -136,8 +135,6 @@ private:
 
     friend class QVector2D;
     friend class QVector4D;
-    friend class QQuaternion;
-    friend class QMatrix4x4;
 #ifndef QT_NO_MATRIX4X4
     friend QVector3D operator*(const QVector3D& vector, const QMatrix4x4& matrix);
     friend QVector3D operator*(const QMatrix4x4& matrix, const QVector3D& vector);
diff --git a/src/gui/math3d/qvector4d.h b/src/gui/math3d/qvector4d.h
index 4bd6639..520319a 100644
--- a/src/gui/math3d/qvector4d.h
+++ b/src/gui/math3d/qvector4d.h
@@ -54,7 +54,6 @@ QT_MODULE(Gui)
 class QMatrix4x4;
 class QVector2D;
 class QVector3D;
-class QQuaternion;
 
 #ifndef QT_NO_VECTOR4D
 
@@ -133,8 +132,6 @@ private:
 
     friend class QVector2D;
     friend class QVector3D;
-    friend class QQuaternion;
-    friend class QMatrix4x4;
 #ifndef QT_NO_MATRIX4X4
     friend QVector4D operator*(const QVector4D& vector, const QMatrix4x4& matrix);
     friend QVector4D operator*(const QMatrix4x4& matrix, const QVector4D& vector);