Clean up QVector2D/3D/4D

In random order:

* Remove code marked for removal in Qt 6.

* Inline as much as possible. This should give us a massive
speed boost in some simple operations where the function call
overhead as much as the cost of body of the function itself
(lengthSquared, dotProduct, etc.).

* Plaster constexpr and noexcept, as much as possible; follow
Lakos' rule.

* Unexport the classes; selectively export only the symbols
still defined out of line.

* Add [[nodiscard]] to any non-trivial mathematical operation
(e.g. calculate the length).

* To avoid circular dependencies, centralize their implementation
in one file. Leave the existing headers for compatibility with
existing #include statements.

* Change all the signatures of the classes' members to take
QVectorND, QPointF, etc. objects by value, not by const ref.
Usage in other classes (e.g. QMatrix4x4) has not been adjusted.

Change-Id: Iaf5a4b5289fcdf704e77656793390b8e772e94a5
Reviewed-by: Andy Nichols <andy.nichols@qt.io>

1 files changed, 1635 insertions, 0 deletions

diff --git a/src/gui/math3d/qvectornd.cpp b/src/gui/math3d/qvectornd.cpp
new file mode 100644
index 0000000000..5433e9bc6c
--- /dev/null
+++ b/src/gui/math3d/qvectornd.cpp
@@ -0,0 +1,1635 @@
+/****************************************************************************
+**
+** Copyright (C) 2016 The Qt Company Ltd.
+** Copyright (C) 2020 Klarälvdalens Datakonsult AB, a KDAB Group company, info@kdab.com, author Giuseppe D'Angelo <giuseppe.dangelo@kdab.com>
+** Contact: https://www.qt.io/licensing/
+**
+** This file is part of the QtGui module of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** Commercial License Usage
+** Licensees holding valid commercial Qt licenses may use this file in
+** accordance with the commercial license agreement provided with the
+** Software or, alternatively, in accordance with the terms contained in
+** a written agreement between you and The Qt Company. For licensing terms
+** and conditions see https://www.qt.io/terms-conditions. For further
+** information use the contact form at https://www.qt.io/contact-us.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 3 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL3 included in the
+** packaging of this file. Please review the following information to
+** ensure the GNU Lesser General Public License version 3 requirements
+** will be met: https://www.gnu.org/licenses/lgpl-3.0.html.
+**
+** GNU General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU
+** General Public License version 2.0 or (at your option) the GNU General
+** Public license version 3 or any later version approved by the KDE Free
+** Qt Foundation. The licenses are as published by the Free Software
+** Foundation and appearing in the file LICENSE.GPL2 and LICENSE.GPL3
+** included in the packaging of this file. Please review the following
+** information to ensure the GNU General Public License requirements will
+** be met: https://www.gnu.org/licenses/gpl-2.0.html and
+** https://www.gnu.org/licenses/gpl-3.0.html.
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+
+#include "qvectornd.h"
+#include <QtCore/qdatastream.h>
+#include <QtCore/qdebug.h>
+#include <QtCore/qvariant.h>
+#include <QtGui/qmatrix4x4.h>
+
+QT_BEGIN_NAMESPACE
+
+#ifndef QT_NO_VECTOR2D
+
+/*!
+    \class QVector2D
+    \brief The QVector2D class represents a vector or vertex in 2D space.
+    \since 4.6
+    \ingroup painting
+    \ingroup painting-3D
+    \inmodule QtGui
+
+    The QVector2D class can also be used to represent vertices in 2D space.
+    We therefore do not need to provide a separate vertex class.
+
+    \sa QVector3D, QVector4D, QQuaternion
+*/
+
+/*!
+    \fn QVector2D::QVector2D()
+
+    Constructs a null vector, i.e. with coordinates (0, 0).
+*/
+
+/*!
+    \fn QVector2D::QVector2D(Qt::Initialization)
+    \since 5.5
+    \internal
+
+    Constructs a vector without initializing the contents.
+*/
+
+/*!
+    \fn QVector2D::QVector2D(float xpos, float ypos)
+
+    Constructs a vector with coordinates (\a xpos, \a ypos).
+*/
+
+/*!
+    \fn QVector2D::QVector2D(QPoint point)
+
+    Constructs a vector with x and y coordinates from a 2D \a point.
+*/
+
+/*!
+    \fn QVector2D::QVector2D(QPointF point)
+
+    Constructs a vector with x and y coordinates from a 2D \a point.
+*/
+
+#ifndef QT_NO_VECTOR3D
+
+/*!
+    \fn QVector2D::QVector2D(QVector3D vector)
+
+    Constructs a vector with x and y coordinates from a 3D \a vector.
+    The z coordinate of \a vector is dropped.
+
+    \sa toVector3D()
+*/
+
+#endif
+
+#ifndef QT_NO_VECTOR4D
+
+/*!
+    \fn QVector2D::QVector2D(QVector4D vector)
+
+    Constructs a vector with x and y coordinates from a 3D \a vector.
+    The z and w coordinates of \a vector are dropped.
+
+    \sa toVector4D()
+*/
+
+#endif
+
+/*!
+    \fn bool QVector2D::isNull() const
+
+    Returns \c true if the x and y coordinates are set to 0.0,
+    otherwise returns \c false.
+*/
+
+/*!
+    \fn float QVector2D::x() const
+
+    Returns the x coordinate of this point.
+
+    \sa setX(), y()
+*/
+
+/*!
+    \fn float QVector2D::y() const
+
+    Returns the y coordinate of this point.
+
+    \sa setY(), x()
+*/
+
+/*!
+    \fn void QVector2D::setX(float x)
+
+    Sets the x coordinate of this point to the given \a x coordinate.
+
+    \sa x(), setY()
+*/
+
+/*!
+    \fn void QVector2D::setY(float y)
+
+    Sets the y coordinate of this point to the given \a y coordinate.
+
+    \sa y(), setX()
+*/
+
+/*! \fn float &QVector2D::operator[](int i)
+    \since 5.2
+
+    Returns the component of the vector at index position \a i
+    as a modifiable reference.
+
+    \a i must be a valid index position in the vector (i.e., 0 <= \a i
+    < 2).
+*/
+
+/*! \fn float QVector2D::operator[](int i) const
+    \since 5.2
+
+    Returns the component of the vector at index position \a i.
+
+    \a i must be a valid index position in the vector (i.e., 0 <= \a i
+    < 2).
+*/
+
+/*!
+    \fn float QVector2D::length() const
+
+    Returns the length of the vector from the origin.
+
+    \sa lengthSquared(), normalized()
+*/
+
+/*!
+    \fn float QVector2D::lengthSquared() const
+
+    Returns the squared length of the vector from the origin.
+    This is equivalent to the dot product of the vector with itself.
+
+    \sa length(), dotProduct()
+*/
+
+/*!
+    \fn QVector2D QVector2D::normalized() const
+
+    Returns the normalized unit vector form of this vector.
+
+    If this vector is null, then a null vector is returned.  If the length
+    of the vector is very close to 1, then the vector will be returned as-is.
+    Otherwise the normalized form of the vector of length 1 will be returned.
+
+    \sa length(), normalize()
+*/
+
+/*!
+    \fn void QVector2D::normalize()
+
+    Normalizes the currect vector in place.  Nothing happens if this
+    vector is a null vector or the length of the vector is very close to 1.
+
+    \sa length(), normalized()
+*/
+
+/*!
+    \fn float QVector2D::distanceToPoint(QVector2D point) const
+    \since 5.1
+
+    Returns the distance from this vertex to a point defined by
+    the vertex \a point.
+
+    \sa distanceToLine()
+*/
+
+/*!
+    \fn float QVector2D::distanceToLine(QVector2D point, QVector2D direction) const
+    \since 5.1
+
+    Returns the distance that this vertex is from a line defined
+    by \a point and the unit vector \a direction.
+
+    If \a direction is a null vector, then it does not define a line.
+    In that case, the distance from \a point to this vertex is returned.
+
+    \sa distanceToPoint()
+*/
+
+/*!
+    \fn QVector2D &QVector2D::operator+=(QVector2D vector)
+
+    Adds the given \a vector to this vector and returns a reference to
+    this vector.
+
+    \sa operator-=()
+*/
+
+/*!
+    \fn QVector2D &QVector2D::operator-=(QVector2D vector)
+
+    Subtracts the given \a vector from this vector and returns a reference to
+    this vector.
+
+    \sa operator+=()
+*/
+
+/*!
+    \fn QVector2D &QVector2D::operator*=(float factor)
+
+    Multiplies this vector's coordinates by the given \a factor, and
+    returns a reference to this vector.
+
+    \sa operator/=()
+*/
+
+/*!
+    \fn QVector2D &QVector2D::operator*=(QVector2D vector)
+
+    Multiplies the components of this vector by the corresponding
+    components in \a vector.
+*/
+
+/*!
+    \fn QVector2D &QVector2D::operator/=(float divisor)
+
+    Divides this vector's coordinates by the given \a divisor, and
+    returns a reference to this vector.
+
+    \sa operator*=()
+*/
+
+/*!
+    \fn QVector2D &QVector2D::operator/=(QVector2D vector)
+    \since 5.5
+
+    Divides the components of this vector by the corresponding
+    components in \a vector.
+
+    \sa operator*=()
+*/
+
+/*!
+    \fn float QVector2D::dotProduct(QVector2D v1, QVector2D v2)
+
+    Returns the dot product of \a v1 and \a v2.
+*/
+
+/*!
+    \fn bool QVector2D::operator==(QVector2D v1, QVector2D v2)
+
+    Returns \c true if \a v1 is equal to \a v2; otherwise returns \c false.
+    This operator uses an exact floating-point comparison.
+*/
+
+/*!
+    \fn bool QVector2D::operator!=(QVector2D v1, QVector2D v2)
+
+    Returns \c true if \a v1 is not equal to \a v2; otherwise returns \c false.
+    This operator uses an exact floating-point comparison.
+*/
+
+/*!
+    \fn const QVector2D operator+(QVector2D v1, QVector2D v2)
+    \relates QVector2D
+
+    Returns a QVector2D object that is the sum of the given vectors, \a v1
+    and \a v2; each component is added separately.
+
+    \sa QVector2D::operator+=()
+*/
+
+/*!
+    \fn const QVector2D operator-(QVector2D v1, QVector2D v2)
+    \relates QVector2D
+
+    Returns a QVector2D object that is formed by subtracting \a v2 from \a v1;
+    each component is subtracted separately.
+
+    \sa QVector2D::operator-=()
+*/
+
+/*!
+    \fn const QVector2D operator*(float factor, QVector2D vector)
+    \relates QVector2D
+
+    Returns a copy of the given \a vector,  multiplied by the given \a factor.
+
+    \sa QVector2D::operator*=()
+*/
+
+/*!
+    \fn const QVector2D operator*(QVector2D vector, float factor)
+    \relates QVector2D
+
+    Returns a copy of the given \a vector,  multiplied by the given \a factor.
+
+    \sa QVector2D::operator*=()
+*/
+
+/*!
+    \fn const QVector2D operator*(QVector2D v1, QVector2D v2)
+    \relates QVector2D
+
+    Multiplies the components of \a v1 by the corresponding
+    components in \a v2.
+*/
+
+/*!
+    \fn const QVector2D operator-(QVector2D vector)
+    \relates QVector2D
+    \overload
+
+    Returns a QVector2D object that is formed by changing the sign of
+    the components of the given \a vector.
+
+    Equivalent to \c {QVector2D(0,0) - vector}.
+*/
+
+/*!
+    \fn const QVector2D operator/(QVector2D vector, float divisor)
+    \relates QVector2D
+
+    Returns the QVector2D object formed by dividing all three components of
+    the given \a vector by the given \a divisor.
+
+    \sa QVector2D::operator/=()
+*/
+
+/*!
+    \fn const QVector2D operator/(QVector2D vector, QVector2D divisor)
+    \relates QVector2D
+    \since 5.5
+
+    Returns the QVector2D object formed by dividing components of the given
+    \a vector by a respective components of the given \a divisor.
+
+    \sa QVector2D::operator/=()
+*/
+
+/*!
+    \fn bool qFuzzyCompare(QVector2D v1, QVector2D v2)
+    \relates QVector2D
+
+    Returns \c true if \a v1 and \a v2 are equal, allowing for a small
+    fuzziness factor for floating-point comparisons; false otherwise.
+*/
+
+#ifndef QT_NO_VECTOR3D
+/*!
+    \fn QVector3D QVector2D::toVector3D() const
+
+    Returns the 3D form of this 2D vector, with the z coordinate set to zero.
+
+    \sa toVector4D(), toPoint()
+*/
+#endif
+
+#ifndef QT_NO_VECTOR4D
+/*!
+    \fn QVector4D QVector2D::toVector4D() const
+
+    Returns the 4D form of this 2D vector, with the z and w coordinates set to zero.
+
+    \sa toVector3D(), toPoint()
+*/
+#endif
+
+/*!
+    \fn QPoint QVector2D::toPoint() const
+
+    Returns the QPoint form of this 2D vector.
+
+    \sa toPointF(), toVector3D()
+*/
+
+/*!
+    \fn QPointF QVector2D::toPointF() const
+
+    Returns the QPointF form of this 2D vector.
+
+    \sa toPoint(), toVector3D()
+*/
+
+/*!
+    Returns the 2D vector as a QVariant.
+*/
+QVector2D::operator QVariant() const
+{
+    return QVariant::fromValue(*this);
+}
+
+#ifndef QT_NO_DEBUG_STREAM
+
+QDebug operator<<(QDebug dbg, QVector2D vector)
+{
+    QDebugStateSaver saver(dbg);
+    dbg.nospace() << "QVector2D(" << vector.x() << ", " << vector.y() << ')';
+    return dbg;
+}
+
+#endif
+
+#ifndef QT_NO_DATASTREAM
+
+/*!
+    \fn QDataStream &operator<<(QDataStream &stream, QVector2D vector)
+    \relates QVector2D
+
+    Writes the given \a vector to the given \a stream and returns a
+    reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator<<(QDataStream &stream, QVector2D vector)
+{
+    stream << vector.x() << vector.y();
+    return stream;
+}
+
+/*!
+    \fn QDataStream &operator>>(QDataStream &stream, QVector2D &vector)
+    \relates QVector2D
+
+    Reads a 2D vector from the given \a stream into the given \a vector
+    and returns a reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator>>(QDataStream &stream, QVector2D &vector)
+{
+    float x, y;
+    stream >> x;
+    stream >> y;
+    vector.setX(x);
+    vector.setY(y);
+    return stream;
+}
+
+#endif // QT_NO_DATASTREAM
+
+#endif // QT_NO_VECTOR2D
+
+
+
+#ifndef QT_NO_VECTOR3D
+
+/*!
+    \class QVector3D
+    \brief The QVector3D class represents a vector or vertex in 3D space.
+    \since 4.6
+    \ingroup painting-3D
+    \inmodule QtGui
+
+    Vectors are one of the main building blocks of 3D representation and
+    drawing.  They consist of three coordinates, traditionally called
+    x, y, and z.
+
+    The QVector3D class can also be used to represent vertices in 3D space.
+    We therefore do not need to provide a separate vertex class.
+
+    \sa QVector2D, QVector4D, QQuaternion
+*/
+
+/*!
+    \fn QVector3D::QVector3D()
+
+    Constructs a null vector, i.e. with coordinates (0, 0, 0).
+*/
+
+/*!
+    \fn QVector3D::QVector3D(Qt::Initialization)
+    \since 5.5
+    \internal
+
+    Constructs a vector without initializing the contents.
+*/
+
+/*!
+    \fn QVector3D::QVector3D(float xpos, float ypos, float zpos)
+
+    Constructs a vector with coordinates (\a xpos, \a ypos, \a zpos).
+*/
+
+/*!
+    \fn QVector3D::QVector3D(QPoint point)
+
+    Constructs a vector with x and y coordinates from a 2D \a point, and a
+    z coordinate of 0.
+*/
+
+/*!
+    \fn QVector3D::QVector3D(QPointF point)
+
+    Constructs a vector with x and y coordinates from a 2D \a point, and a
+    z coordinate of 0.
+*/
+
+#ifndef QT_NO_VECTOR2D
+
+/*!
+    \fn QVector3D::QVector3D(QVector2D vector)
+
+    Constructs a 3D vector from the specified 2D \a vector.  The z
+    coordinate is set to zero.
+
+    \sa toVector2D()
+*/
+
+/*!
+    QVector3D::QVector3D(QVector2D vector, float zpos)
+
+    Constructs a 3D vector from the specified 2D \a vector.  The z
+    coordinate is set to \a zpos.
+
+    \sa toVector2D()
+*/
+#endif
+
+#ifndef QT_NO_VECTOR4D
+
+/*!
+    \fn QVector3D::QVector3D(QVector4D vector)
+
+    Constructs a 3D vector from the specified 4D \a vector.  The w
+    coordinate is dropped.
+
+    \sa toVector4D()
+*/
+
+#endif
+
+/*!
+    \fn bool QVector3D::isNull() const
+
+    Returns \c true if the x, y, and z coordinates are set to 0.0,
+    otherwise returns \c false.
+*/
+
+/*!
+    \fn float QVector3D::x() const
+
+    Returns the x coordinate of this point.
+
+    \sa setX(), y(), z()
+*/
+
+/*!
+    \fn float QVector3D::y() const
+
+    Returns the y coordinate of this point.
+
+    \sa setY(), x(), z()
+*/
+
+/*!
+    \fn float QVector3D::z() const
+
+    Returns the z coordinate of this point.
+
+    \sa setZ(), x(), y()
+*/
+
+/*!
+    \fn void QVector3D::setX(float x)
+
+    Sets the x coordinate of this point to the given \a x coordinate.
+
+    \sa x(), setY(), setZ()
+*/
+
+/*!
+    \fn void QVector3D::setY(float y)
+
+    Sets the y coordinate of this point to the given \a y coordinate.
+
+    \sa y(), setX(), setZ()
+*/
+
+/*!
+    \fn void QVector3D::setZ(float z)
+
+    Sets the z coordinate of this point to the given \a z coordinate.
+
+    \sa z(), setX(), setY()
+*/
+
+/*! \fn float &QVector3D::operator[](int i)
+    \since 5.2
+
+    Returns the component of the vector at index position \a i
+    as a modifiable reference.
+
+    \a i must be a valid index position in the vector (i.e., 0 <= \a i
+    < 3).
+*/
+
+/*! \fn float QVector3D::operator[](int i) const
+    \since 5.2
+
+    Returns the component of the vector at index position \a i.
+
+    \a i must be a valid index position in the vector (i.e., 0 <= \a i
+    < 3).
+*/
+
+/*!
+    \fn QVector3D QVector3D::normalized() const
+
+    Returns the normalized unit vector form of this vector.
+
+    If this vector is null, then a null vector is returned.  If the length
+    of the vector is very close to 1, then the vector will be returned as-is.
+    Otherwise the normalized form of the vector of length 1 will be returned.
+
+    \sa length(), normalize()
+*/
+
+/*!
+    \fn void QVector3D::normalize()
+
+    Normalizes the currect vector in place.  Nothing happens if this
+    vector is a null vector or the length of the vector is very close to 1.
+
+    \sa length(), normalized()
+*/
+
+/*!
+    \fn QVector3D &QVector3D::operator+=(QVector3D vector)
+
+    Adds the given \a vector to this vector and returns a reference to
+    this vector.
+
+    \sa operator-=()
+*/
+
+/*!
+    \fn QVector3D &QVector3D::operator-=(QVector3D vector)
+
+    Subtracts the given \a vector from this vector and returns a reference to
+    this vector.
+
+    \sa operator+=()
+*/
+
+/*!
+    \fn QVector3D &QVector3D::operator*=(float factor)
+
+    Multiplies this vector's coordinates by the given \a factor, and
+    returns a reference to this vector.
+
+    \sa operator/=()
+*/
+
+/*!
+    \fn QVector3D &QVector3D::operator*=(QVector3D vector)
+    \overload
+
+    Multiplies the components of this vector by the corresponding
+    components in \a vector.
+
+    Note: this is not the same as the crossProduct() of this
+    vector and \a vector.
+
+    \sa crossProduct()
+*/
+
+/*!
+    \fn QVector3D &QVector3D::operator/=(float divisor)
+
+    Divides this vector's coordinates by the given \a divisor, and
+    returns a reference to this vector.
+
+    \sa operator*=()
+*/
+
+/*!
+    \fn QVector3D &QVector3D::operator/=(QVector3D vector)
+    \since 5.5
+
+    Divides the components of this vector by the corresponding
+    components in \a vector.
+
+    \sa operator*=()
+*/
+
+/*!
+    \fn float QVector3D::dotProduct(QVector3D v1, QVector3D v2)
+
+    Returns the dot product of \a v1 and \a v2.
+*/
+
+/*!
+    \fn QVector3D QVector3D::crossProduct(QVector3D v1, QVector3D v2)
+
+    Returns the cross-product of vectors \a v1 and \a v2, which corresponds
+    to the normal vector of a plane defined by \a v1 and \a v2.
+
+    \sa normal()
+*/
+
+/*!
+    \fn QVector3D QVector3D::normal(QVector3D v1, QVector3D v2)
+
+    Returns the normal vector of a plane defined by vectors \a v1 and \a v2,
+    normalized to be a unit vector.
+
+    Use crossProduct() to compute the cross-product of \a v1 and \a v2 if you
+    do not need the result to be normalized to a unit vector.
+
+    \sa crossProduct(), distanceToPlane()
+*/
+
+/*!
+    \fn QVector3D QVector3D::normal(QVector3D v1, QVector3D v2, QVector3D v3)
+
+    Returns the normal vector of a plane defined by vectors
+    \a v2 - \a v1 and \a v3 - \a v1, normalized to be a unit vector.
+
+    Use crossProduct() to compute the cross-product of \a v2 - \a v1 and
+    \a v3 - \a v1 if you do not need the result to be normalized to a
+    unit vector.
+
+    \sa crossProduct(), distanceToPlane()
+*/
+
+/*!
+    \since 5.5
+
+    Returns the window coordinates of this vector initially in object/model
+    coordinates using the model view matrix \a modelView, the projection matrix
+    \a projection and the viewport dimensions \a viewport.
+
+    When transforming from clip to normalized space, a division by the w
+    component on the vector components takes place. To prevent dividing by 0 if
+    w equals to 0, it is set to 1.
+
+    \note the returned y coordinates are in OpenGL orientation. OpenGL expects
+    the bottom to be 0 whereas for Qt top is 0.
+
+    \sa unproject()
+ */
+QVector3D QVector3D::project(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const
+{
+    QVector4D tmp(*this, 1.0f);
+    tmp = projection * modelView * tmp;
+    if (qFuzzyIsNull(tmp.w()))
+        tmp.setW(1.0f);
+    tmp /= tmp.w();
+
+    tmp = tmp * 0.5f + QVector4D(0.5f, 0.5f, 0.5f, 0.5f);
+    tmp.setX(tmp.x() * viewport.width() + viewport.x());
+    tmp.setY(tmp.y() * viewport.height() + viewport.y());
+
+    return tmp.toVector3D();
+}
+
+/*!
+    \since 5.5
+
+    Returns the object/model coordinates of this vector initially in window
+    coordinates using the model view matrix \a modelView, the projection matrix
+    \a projection and the viewport dimensions \a viewport.
+
+    When transforming from clip to normalized space, a division by the w
+    component of the vector components takes place. To prevent dividing by 0 if
+    w equals to 0, it is set to 1.
+
+    \note y coordinates in \a viewport should use OpenGL orientation. OpenGL
+    expects the bottom to be 0 whereas for Qt top is 0.
+
+    \sa project()
+ */
+QVector3D QVector3D::unproject(const QMatrix4x4 &modelView, const QMatrix4x4 &projection, const QRect &viewport) const
+{
+    QMatrix4x4 inverse = QMatrix4x4( projection * modelView ).inverted();
+
+    QVector4D tmp(*this, 1.0f);
+    tmp.setX((tmp.x() - float(viewport.x())) / float(viewport.width()));
+    tmp.setY((tmp.y() - float(viewport.y())) / float(viewport.height()));
+    tmp = tmp * 2.0f - QVector4D(1.0f, 1.0f, 1.0f, 1.0f);
+
+    QVector4D obj = inverse * tmp;
+    if (qFuzzyIsNull(obj.w()))
+        obj.setW(1.0f);
+    obj /= obj.w();
+    return obj.toVector3D();
+}
+
+/*!
+    \fn float QVector3D::distanceToPoint(QVector3D point) const
+
+    \since 5.1
+
+    Returns the distance from this vertex to a point defined by
+    the vertex \a point.
+
+    \sa distanceToPlane(), distanceToLine()
+*/
+
+/*!
+    \fn float QVector3D::distanceToPlane(QVector3D plane, QVector3D normal) const
+
+    Returns the distance from this vertex to a plane defined by
+    the vertex \a plane and a \a normal unit vector.  The \a normal
+    parameter is assumed to have been normalized to a unit vector.
+
+    The return value will be negative if the vertex is below the plane,
+    or zero if it is on the plane.
+
+    \sa normal(), distanceToLine()
+*/
+
+/*!
+    \fn float QVector3D::distanceToPlane(QVector3D plane1, QVector3D plane2, QVector3D plane3) const
+
+    Returns the distance from this vertex to a plane defined by
+    the vertices \a plane1, \a plane2 and \a plane3.
+
+    The return value will be negative if the vertex is below the plane,
+    or zero if it is on the plane.
+
+    The two vectors that define the plane are \a plane2 - \a plane1
+    and \a plane3 - \a plane1.
+
+    \sa normal(), distanceToLine()
+*/
+
+/*!
+    \fn float QVector3D::distanceToLine(QVector3D point, QVector3D direction) const
+
+    Returns the distance that this vertex is from a line defined
+    by \a point and the unit vector \a direction.
+
+    If \a direction is a null vector, then it does not define a line.
+    In that case, the distance from \a point to this vertex is returned.
+
+    \sa distanceToPlane()
+*/
+
+/*!
+    \fn bool QVector3D::operator==(QVector3D v1, QVector3D v2)
+
+    Returns \c true if \a v1 is equal to \a v2; otherwise returns \c false.
+    This operator uses an exact floating-point comparison.
+*/
+
+/*!
+    \fn bool QVector3D::operator!=(QVector3D v1, QVector3D v2)
+
+    Returns \c true if \a v1 is not equal to \a v2; otherwise returns \c false.
+    This operator uses an exact floating-point comparison.
+*/
+
+/*!
+    \fn const QVector3D operator+(QVector3D v1, QVector3D v2)
+    \relates QVector3D
+
+    Returns a QVector3D object that is the sum of the given vectors, \a v1
+    and \a v2; each component is added separately.
+
+    \sa QVector3D::operator+=()
+*/
+
+/*!
+    \fn const QVector3D operator-(QVector3D v1, QVector3D v2)
+    \relates QVector3D
+
+    Returns a QVector3D object that is formed by subtracting \a v2 from \a v1;
+    each component is subtracted separately.
+
+    \sa QVector3D::operator-=()
+*/
+
+/*!
+    \fn const QVector3D operator*(float factor, QVector3D vector)
+    \relates QVector3D
+
+    Returns a copy of the given \a vector,  multiplied by the given \a factor.
+
+    \sa QVector3D::operator*=()
+*/
+
+/*!
+    \fn const QVector3D operator*(QVector3D vector, float factor)
+    \relates QVector3D
+
+    Returns a copy of the given \a vector,  multiplied by the given \a factor.
+
+    \sa QVector3D::operator*=()
+*/
+
+/*!
+    \fn const QVector3D operator*(QVector3D v1, QVector3D v2)
+    \relates QVector3D
+
+    Multiplies the components of \a v1 by the corresponding components in \a v2.
+
+    Note: this is not the same as the crossProduct() of \a v1 and \a v2.
+
+    \sa QVector3D::crossProduct()
+*/
+
+/*!
+    \fn const QVector3D operator-(QVector3D vector)
+    \relates QVector3D
+    \overload
+
+    Returns a QVector3D object that is formed by changing the sign of
+    all three components of the given \a vector.
+
+    Equivalent to \c {QVector3D(0,0,0) - vector}.
+*/
+
+/*!
+    \fn const QVector3D operator/(QVector3D vector, float divisor)
+    \relates QVector3D
+
+    Returns the QVector3D object formed by dividing all three components of
+    the given \a vector by the given \a divisor.
+
+    \sa QVector3D::operator/=()
+*/
+
+/*!
+    \fn const QVector3D operator/(QVector3D vector, QVector3D divisor)
+    \relates QVector3D
+    \since 5.5
+
+    Returns the QVector3D object formed by dividing components of the given
+    \a vector by a respective components of the given \a divisor.
+
+    \sa QVector3D::operator/=()
+*/
+
+/*!
+    \fn bool qFuzzyCompare(QVector3D v1, QVector3D v2)
+    \relates QVector3D
+
+    Returns \c true if \a v1 and \a v2 are equal, allowing for a small
+    fuzziness factor for floating-point comparisons; false otherwise.
+*/
+
+#ifndef QT_NO_VECTOR2D
+
+/*!
+    \fn QVector2D QVector3D::toVector2D() const
+
+    Returns the 2D vector form of this 3D vector, dropping the z coordinate.
+
+    \sa toVector4D(), toPoint()
+*/
+
+#endif
+
+#ifndef QT_NO_VECTOR4D
+
+/*!
+    \fn QVector4D QVector3D::toVector4D() const
+
+    Returns the 4D form of this 3D vector, with the w coordinate set to zero.
+
+    \sa toVector2D(), toPoint()
+*/
+
+#endif
+
+/*!
+    \fn QPoint QVector3D::toPoint() const
+
+    Returns the QPoint form of this 3D vector. The z coordinate
+    is dropped.
+
+    \sa toPointF(), toVector2D()
+*/
+
+/*!
+    \fn QPointF QVector3D::toPointF() const
+
+    Returns the QPointF form of this 3D vector. The z coordinate
+    is dropped.
+
+    \sa toPoint(), toVector2D()
+*/
+
+/*!
+    Returns the 3D vector as a QVariant.
+*/
+QVector3D::operator QVariant() const
+{
+    return QVariant::fromValue(*this);
+}
+
+/*!
+    \fn float QVector3D::length() const
+
+    Returns the length of the vector from the origin.
+
+    \sa lengthSquared(), normalized()
+*/
+
+/*!
+    \fn float QVector3D::lengthSquared() const
+
+    Returns the squared length of the vector from the origin.
+    This is equivalent to the dot product of the vector with itself.
+
+    \sa length(), dotProduct()
+*/
+
+#ifndef QT_NO_DEBUG_STREAM
+
+QDebug operator<<(QDebug dbg, QVector3D vector)
+{
+    QDebugStateSaver saver(dbg);
+    dbg.nospace() << "QVector3D("
+        << vector.x() << ", " << vector.y() << ", " << vector.z() << ')';
+    return dbg;
+}
+
+#endif
+
+#ifndef QT_NO_DATASTREAM
+
+/*!
+    \fn QDataStream &operator<<(QDataStream &stream, QVector3D vector)
+    \relates QVector3D
+
+    Writes the given \a vector to the given \a stream and returns a
+    reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator<<(QDataStream &stream, QVector3D vector)
+{
+    stream << vector.x() << vector.y() << vector.z();
+    return stream;
+}
+
+/*!
+    \fn QDataStream &operator>>(QDataStream &stream, QVector3D &vector)
+    \relates QVector3D
+
+    Reads a 3D vector from the given \a stream into the given \a vector
+    and returns a reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator>>(QDataStream &stream, QVector3D &vector)
+{
+    float x, y, z;
+    stream >> x;
+    stream >> y;
+    stream >> z;
+    vector.setX(x);
+    vector.setY(y);
+    vector.setZ(z);
+    return stream;
+}
+
+#endif // QT_NO_DATASTREAM
+
+#endif // QT_NO_VECTOR3D
+
+
+
+#ifndef QT_NO_VECTOR4D
+
+/*!
+    \class QVector4D
+    \brief The QVector4D class represents a vector or vertex in 4D space.
+    \since 4.6
+    \ingroup painting-3D
+    \inmodule QtGui
+
+    The QVector4D class can also be used to represent vertices in 4D space.
+    We therefore do not need to provide a separate vertex class.
+
+    \sa QQuaternion, QVector2D, QVector3D
+*/
+
+/*!
+    \fn QVector4D::QVector4D()
+
+    Constructs a null vector, i.e. with coordinates (0, 0, 0, 0).
+*/
+
+/*!
+    \fn QVector4D::QVector4D(Qt::Initialization)
+    \since 5.5
+    \internal
+
+    Constructs a vector without initializing the contents.
+*/
+
+/*!
+    \fn QVector4D::QVector4D(float xpos, float ypos, float zpos, float wpos)
+
+    Constructs a vector with coordinates (\a xpos, \a ypos, \a zpos, \a wpos).
+*/
+
+/*!
+    \fn QVector4D::QVector4D(QPoint point)
+
+    Constructs a vector with x and y coordinates from a 2D \a point, and
+    z and w coordinates of 0.
+*/
+
+/*!
+    \fn QVector4D::QVector4D(QPointF point)
+
+    Constructs a vector with x and y coordinates from a 2D \a point, and
+    z and w coordinates of 0.
+*/
+
+#ifndef QT_NO_VECTOR2D
+
+/*!
+    \fn QVector4D::QVector4D(QVector2D vector)
+
+    Constructs a 4D vector from the specified 2D \a vector.  The z
+    and w coordinates are set to zero.
+
+    \sa toVector2D()
+*/
+
+/*!
+    \fn QVector4D::QVector4D(QVector2D vector, float zpos, float wpos)
+
+    Constructs a 4D vector from the specified 2D \a vector.  The z
+    and w coordinates are set to \a zpos and \a wpos respectively.
+
+    \sa toVector2D()
+*/
+
+#endif
+
+#ifndef QT_NO_VECTOR3D
+
+/*!
+    \fn QVector4D::QVector4D(QVector3D vector)
+
+    Constructs a 4D vector from the specified 3D \a vector.  The w
+    coordinate is set to zero.
+
+    \sa toVector3D()
+*/
+
+/*!
+    \fn QVector4D::QVector4D(QVector3D vector)
+
+    Constructs a 4D vector from the specified 3D \a vector.  The w
+    coordinate is set to \a wpos.
+
+    \sa toVector3D()
+*/
+
+#endif
+
+/*!
+    \fn bool QVector4D::isNull() const
+
+    Returns \c true if the x, y, z, and w coordinates are set to 0.0,
+    otherwise returns \c false.
+*/
+
+/*!
+    \fn float QVector4D::x() const
+
+    Returns the x coordinate of this point.
+
+    \sa setX(), y(), z(), w()
+*/
+
+/*!
+    \fn float QVector4D::y() const
+
+    Returns the y coordinate of this point.
+
+    \sa setY(), x(), z(), w()
+*/
+
+/*!
+    \fn float QVector4D::z() const
+
+    Returns the z coordinate of this point.
+
+    \sa setZ(), x(), y(), w()
+*/
+
+/*!
+    \fn float QVector4D::w() const
+
+    Returns the w coordinate of this point.
+
+    \sa setW(), x(), y(), z()
+*/
+
+/*!
+    \fn void QVector4D::setX(float x)
+
+    Sets the x coordinate of this point to the given \a x coordinate.
+
+    \sa x(), setY(), setZ(), setW()
+*/
+
+/*!
+    \fn void QVector4D::setY(float y)
+
+    Sets the y coordinate of this point to the given \a y coordinate.
+
+    \sa y(), setX(), setZ(), setW()
+*/
+
+/*!
+    \fn void QVector4D::setZ(float z)
+
+    Sets the z coordinate of this point to the given \a z coordinate.
+
+    \sa z(), setX(), setY(), setW()
+*/
+
+/*!
+    \fn void QVector4D::setW(float w)
+
+    Sets the w coordinate of this point to the given \a w coordinate.
+
+    \sa w(), setX(), setY(), setZ()
+*/
+
+/*! \fn float &QVector4D::operator[](int i)
+    \since 5.2
+
+    Returns the component of the vector at index position \a i
+    as a modifiable reference.
+
+    \a i must be a valid index position in the vector (i.e., 0 <= \a i
+    < 4).
+*/
+
+/*! \fn float QVector4D::operator[](int i) const
+    \since 5.2
+
+    Returns the component of the vector at index position \a i.
+
+    \a i must be a valid index position in the vector (i.e., 0 <= \a i
+    < 4).
+*/
+
+/*!
+    \fn float QVector4D::length() const
+
+    Returns the length of the vector from the origin.
+
+    \sa lengthSquared(), normalized()
+*/
+
+/*!
+    \fn float QVector4D::lengthSquared() const
+
+    Returns the squared length of the vector from the origin.
+    This is equivalent to the dot product of the vector with itself.
+
+    \sa length(), dotProduct()
+*/
+
+/*!
+    \fn QVector4D QVector4D::normalized() const
+
+    Returns the normalized unit vector form of this vector.
+
+    If this vector is null, then a null vector is returned.  If the length
+    of the vector is very close to 1, then the vector will be returned as-is.
+    Otherwise the normalized form of the vector of length 1 will be returned.
+
+    \sa length(), normalize()
+*/
+
+/*!
+    \fn void QVector4D::normalize()
+
+    Normalizes the currect vector in place.  Nothing happens if this
+    vector is a null vector or the length of the vector is very close to 1.
+
+    \sa length(), normalized()
+*/
+
+
+/*!
+    \fn QVector4D &QVector4D::operator+=(QVector4D vector)
+
+    Adds the given \a vector to this vector and returns a reference to
+    this vector.
+
+    \sa operator-=()
+*/
+
+/*!
+    \fn QVector4D &QVector4D::operator-=(QVector4D vector)
+
+    Subtracts the given \a vector from this vector and returns a reference to
+    this vector.
+
+    \sa operator+=()
+*/
+
+/*!
+    \fn QVector4D &QVector4D::operator*=(float factor)
+
+    Multiplies this vector's coordinates by the given \a factor, and
+    returns a reference to this vector.
+
+    \sa operator/=()
+*/
+
+/*!
+    \fn QVector4D &QVector4D::operator*=(QVector4D vector)
+
+    Multiplies the components of this vector by the corresponding
+    components in \a vector.
+*/
+
+/*!
+    \fn QVector4D &QVector4D::operator/=(float divisor)
+
+    Divides this vector's coordinates by the given \a divisor, and
+    returns a reference to this vector.
+
+    \sa operator*=()
+*/
+
+/*!
+    \fn QVector4D &QVector4D::operator/=(QVector4D vector)
+    \since 5.5
+
+    Divides the components of this vector by the corresponding
+    components in \a vector.
+
+    \sa operator*=()
+*/
+
+/*!
+    \fn float QVector4D::dotProduct(QVector4D v1, QVector4D v2)
+
+    Returns the dot product of \a v1 and \a v2.
+*/
+
+/*!
+    \fn bool QVector4D::operator==(QVector4D v1, QVector4D v2)
+
+    Returns \c true if \a v1 is equal to \a v2; otherwise returns \c false.
+    This operator uses an exact floating-point comparison.
+*/
+
+/*!
+    \fn bool QVector4D::operator!=(QVector4D v1, QVector4D v2)
+
+    Returns \c true if \a v1 is not equal to \a v2; otherwise returns \c false.
+    This operator uses an exact floating-point comparison.
+*/
+
+/*!
+    \fn const QVector4D operator+(QVector4D v1, QVector4D v2)
+    \relates QVector4D
+
+    Returns a QVector4D object that is the sum of the given vectors, \a v1
+    and \a v2; each component is added separately.
+
+    \sa QVector4D::operator+=()
+*/
+
+/*!
+    \fn const QVector4D operator-(QVector4D v1, QVector4D v2)
+    \relates QVector4D
+
+    Returns a QVector4D object that is formed by subtracting \a v2 from \a v1;
+    each component is subtracted separately.
+
+    \sa QVector4D::operator-=()
+*/
+
+/*!
+    \fn const QVector4D operator*(float factor, QVector4D vector)
+    \relates QVector4D
+
+    Returns a copy of the given \a vector,  multiplied by the given \a factor.
+
+    \sa QVector4D::operator*=()
+*/
+
+/*!
+    \fn const QVector4D operator*(QVector4D vector, float factor)
+    \relates QVector4D
+
+    Returns a copy of the given \a vector,  multiplied by the given \a factor.
+
+    \sa QVector4D::operator*=()
+*/
+
+/*!
+    \fn const QVector4D operator*(QVector4D v1, QVector4D v2)
+    \relates QVector4D
+
+    Returns the vector consisting of the multiplication of the
+    components from \a v1 and \a v2.
+
+    \sa QVector4D::operator*=()
+*/
+
+/*!
+    \fn const QVector4D operator-(QVector4D vector)
+    \relates QVector4D
+    \overload
+
+    Returns a QVector4D object that is formed by changing the sign of
+    all three components of the given \a vector.
+
+    Equivalent to \c {QVector4D(0,0,0,0) - vector}.
+*/
+
+/*!
+    \fn const QVector4D operator/(QVector4D vector, float divisor)
+    \relates QVector4D
+
+    Returns the QVector4D object formed by dividing all four components of
+    the given \a vector by the given \a divisor.
+
+    \sa QVector4D::operator/=()
+*/
+
+/*!
+    \fn const QVector4D operator/(QVector4D vector, QVector4D divisor)
+    \relates QVector4D
+    \since 5.5
+
+    Returns the QVector4D object formed by dividing components of the given
+    \a vector by a respective components of the given \a divisor.
+
+    \sa QVector4D::operator/=()
+*/
+
+/*!
+    \fn bool qFuzzyCompare(QVector4D v1, QVector4D v2)
+    \relates QVector4D
+
+    Returns \c true if \a v1 and \a v2 are equal, allowing for a small
+    fuzziness factor for floating-point comparisons; false otherwise.
+*/
+
+#ifndef QT_NO_VECTOR2D
+
+/*!
+    \fn QVector2D QVector4D::toVector2D() const
+
+    Returns the 2D vector form of this 4D vector, dropping the z and w coordinates.
+
+    \sa toVector2DAffine(), toVector3D(), toPoint()
+*/
+
+/*!
+    \fn QVector2D QVector4D::toVector2DAffine() const
+
+    Returns the 2D vector form of this 4D vector, dividing the x and y
+    coordinates by the w coordinate and dropping the z coordinate.
+    Returns a null vector if w is zero.
+
+    \sa toVector2D(), toVector3DAffine(), toPoint()
+*/
+
+#endif
+
+#ifndef QT_NO_VECTOR3D
+
+/*!
+    \fn QVector3D QVector4D::toVector3D() const
+
+    Returns the 3D vector form of this 4D vector, dropping the w coordinate.
+
+    \sa toVector3DAffine(), toVector2D(), toPoint()
+*/
+
+/*!
+    \fn QVector3D QVector4D::toVector3DAffine() const
+
+    Returns the 3D vector form of this 4D vector, dividing the x, y, and
+    z coordinates by the w coordinate.  Returns a null vector if w is zero.
+
+    \sa toVector3D(), toVector2DAffine(), toPoint()
+*/
+
+#endif
+
+/*!
+    \fn QPoint QVector4D::toPoint() const
+
+    Returns the QPoint form of this 4D vector. The z and w coordinates
+    are dropped.
+
+    \sa toPointF(), toVector2D()
+*/
+
+/*!
+    \fn QPointF QVector4D::toPointF() const
+
+    Returns the QPointF form of this 4D vector. The z and w coordinates
+    are dropped.
+
+    \sa toPoint(), toVector2D()
+*/
+
+/*!
+    Returns the 4D vector as a QVariant.
+*/
+QVector4D::operator QVariant() const
+{
+    return QVariant::fromValue(*this);
+}
+
+#ifndef QT_NO_DEBUG_STREAM
+
+QDebug operator<<(QDebug dbg, QVector4D vector)
+{
+    QDebugStateSaver saver(dbg);
+    dbg.nospace() << "QVector4D("
+        << vector.x() << ", " << vector.y() << ", "
+        << vector.z() << ", " << vector.w() << ')';
+    return dbg;
+}
+
+#endif
+
+#ifndef QT_NO_DATASTREAM
+
+/*!
+    \fn QDataStream &operator<<(QDataStream &stream, QVector4D vector)
+    \relates QVector4D
+
+    Writes the given \a vector to the given \a stream and returns a
+    reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator<<(QDataStream &stream, QVector4D vector)
+{
+    stream << vector.x() << vector.y()
+           << vector.z() << vector.w();
+    return stream;
+}
+
+/*!
+    \fn QDataStream &operator>>(QDataStream &stream, QVector4D &vector)
+    \relates QVector4D
+
+    Reads a 4D vector from the given \a stream into the given \a vector
+    and returns a reference to the stream.
+
+    \sa {Serializing Qt Data Types}
+*/
+
+QDataStream &operator>>(QDataStream &stream, QVector4D &vector)
+{
+    float x, y, z, w;
+    stream >> x;
+    stream >> y;
+    stream >> z;
+    stream >> w;
+    vector.setX(x);
+    vector.setY(y);
+    vector.setZ(z);
+    vector.setW(w);
+    return stream;
+}
+
+#endif // QT_NO_DATASTREAM
+
+#endif // QT_NO_VECTOR4D
+
+QT_END_NAMESPACE