/****************************************************************************+
−
**+
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** Copyright (C) 2010 Nokia Corporation and/or its subsidiary(-ies).+
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** All rights reserved.+
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** Contact: Nokia Corporation (qt-info@nokia.com)+
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**+
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** This file is part of the QtGui module of the Qt Toolkit.+
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**+
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** $QT_BEGIN_LICENSE:LGPL$+
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** No Commercial Usage+
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** This file contains pre-release code and may not be distributed.+
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** You may use this file in accordance with the terms and conditions+
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** contained in the Technology Preview License Agreement accompanying+
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** this package.+
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**+
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** GNU Lesser General Public License Usage+
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** Alternatively, this file may be used under the terms of the GNU Lesser+
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** General Public License version 2.1 as published by the Free Software+
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** Foundation and appearing in the file LICENSE.LGPL included in the+
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** packaging of this file.  Please review the following information to+
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** ensure the GNU Lesser General Public License version 2.1 requirements+
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** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.+
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**+
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** In addition, as a special exception, Nokia gives you certain additional+
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** rights.  These rights are described in the Nokia Qt LGPL Exception+
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** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.+
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**+
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** If you have questions regarding the use of this file, please contact+
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** Nokia at qt-info@nokia.com.+
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**+
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**+
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** $QT_END_LICENSE$+
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**+
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****************************************************************************/+
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+
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#include "qvector3d.h"+
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#include "qvector2d.h"+
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#include "qvector4d.h"+
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#include <QtCore/qmath.h>+
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#include <QtCore/qvariant.h>+
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#include <QtCore/qdebug.h>+
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+
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QT_BEGIN_NAMESPACE+
−
+
−
#ifndef QT_NO_VECTOR3D+
−
+
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/*!+
−
    \class QVector3D+
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    \brief The QVector3D class represents a vector or vertex in 3D space.+
−
    \since 4.6+
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    \ingroup painting-3D+
−
+
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    Vectors are one of the main building blocks of 3D representation and+
−
    drawing.  They consist of three coordinates, traditionally called+
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    x, y, and z.+
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+
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    The QVector3D class can also be used to represent vertices in 3D space.+
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    We therefore do not need to provide a separate vertex class.+
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+
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    \sa QVector2D, QVector4D, QQuaternion+
−
*/+
−
+
−
/*!+
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    \fn QVector3D::QVector3D()+
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+
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    Constructs a null vector, i.e. with coordinates (0, 0, 0).+
−
*/+
−
+
−
/*!+
−
    \fn QVector3D::QVector3D(qreal xpos, qreal ypos, qreal zpos)+
−
+
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    Constructs a vector with coordinates (\a xpos, \a ypos, \a zpos).+
−
*/+
−
+
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/*!+
−
    \fn QVector3D::QVector3D(const QPoint& point)+
−
+
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    Constructs a vector with x and y coordinates from a 2D \a point, and a+
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    z coordinate of 0.+
−
*/+
−
+
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/*!+
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    \fn QVector3D::QVector3D(const QPointF& point)+
−
+
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    Constructs a vector with x and y coordinates from a 2D \a point, and a+
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    z coordinate of 0.+
−
*/+
−
+
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#ifndef QT_NO_VECTOR2D+
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+
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/*!+
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    Constructs a 3D vector from the specified 2D \a vector.  The z+
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    coordinate is set to zero.+
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+
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    \sa toVector2D()+
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*/+
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QVector3D::QVector3D(const QVector2D& vector)+
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{+
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    xp = vector.xp;+
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    yp = vector.yp;+
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    zp = 0.0f;+
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}+
−
+
−
/*!+
−
    Constructs a 3D vector from the specified 2D \a vector.  The z+
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    coordinate is set to \a zpos.+
−
+
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    \sa toVector2D()+
−
*/+
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QVector3D::QVector3D(const QVector2D& vector, qreal zpos)+
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{+
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    xp = vector.xp;+
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    yp = vector.yp;+
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    zp = zpos;+
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}+
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+
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#endif+
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+
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#ifndef QT_NO_VECTOR4D+
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+
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/*!+
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    Constructs a 3D vector from the specified 4D \a vector.  The w+
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    coordinate is dropped.+
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+
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    \sa toVector4D()+
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*/+
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QVector3D::QVector3D(const QVector4D& vector)+
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{+
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    xp = vector.xp;+
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    yp = vector.yp;+
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    zp = vector.zp;+
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}+
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+
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#endif+
−
+
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/*!+
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    \fn bool QVector3D::isNull() const+
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+
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    Returns true if the x, y, and z coordinates are set to 0.0,+
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    otherwise returns false.+
−
*/+
−
+
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/*!+
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    \fn qreal QVector3D::x() const+
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+
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    Returns the x coordinate of this point.+
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+
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    \sa setX(), y(), z()+
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*/+
−
+
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/*!+
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    \fn qreal QVector3D::y() const+
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+
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    Returns the y coordinate of this point.+
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+
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    \sa setY(), x(), z()+
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*/+
−
+
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/*!+
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    \fn qreal QVector3D::z() const+
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+
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    Returns the z coordinate of this point.+
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+
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    \sa setZ(), x(), y()+
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*/+
−
+
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/*!+
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    \fn void QVector3D::setX(qreal x)+
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+
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    Sets the x coordinate of this point to the given \a x coordinate.+
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+
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    \sa x(), setY(), setZ()+
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*/+
−
+
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/*!+
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    \fn void QVector3D::setY(qreal y)+
−
+
−
    Sets the y coordinate of this point to the given \a y coordinate.+
−
+
−
    \sa y(), setX(), setZ()+
−
*/+
−
+
−
/*!+
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    \fn void QVector3D::setZ(qreal z)+
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+
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    Sets the z coordinate of this point to the given \a z coordinate.+
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+
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    \sa z(), setX(), setY()+
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*/+
−
+
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/*!+
−
    Returns the normalized unit vector form of this vector.+
−
+
−
    If this vector is null, then a null vector is returned.  If the length+
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    of the vector is very close to 1, then the vector will be returned as-is.+
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    Otherwise the normalized form of the vector of length 1 will be returned.+
−
+
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    \sa length(), normalize()+
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*/+
−
QVector3D QVector3D::normalized() const+
−
{+
−
    // Need some extra precision if the length is very small.+
−
    double len = double(xp) * double(xp) ++
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                 double(yp) * double(yp) ++
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                 double(zp) * double(zp);+
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    if (qFuzzyIsNull(len - 1.0f))+
−
        return *this;+
−
    else if (!qFuzzyIsNull(len))+
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        return *this / qSqrt(len);+
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    else+
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        return QVector3D();+
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}+
−
+
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/*!+
−
    Normalizes the currect vector in place.  Nothing happens if this+
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    vector is a null vector or the length of the vector is very close to 1.+
−
+
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    \sa length(), normalized()+
−
*/+
−
void QVector3D::normalize()+
−
{+
−
    // Need some extra precision if the length is very small.+
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    double len = double(xp) * double(xp) ++
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                 double(yp) * double(yp) ++
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                 double(zp) * double(zp);+
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    if (qFuzzyIsNull(len - 1.0f) || qFuzzyIsNull(len))+
−
        return;+
−
+
−
    len = qSqrt(len);+
−
+
−
    xp /= len;+
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    yp /= len;+
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    zp /= len;+
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}+
−
+
−
/*!+
−
    \fn QVector3D &QVector3D::operator+=(const QVector3D &vector)+
−
+
−
    Adds the given \a vector to this vector and returns a reference to+
−
    this vector.+
−
+
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    \sa operator-=()+
−
*/+
−
+
−
/*!+
−
    \fn QVector3D &QVector3D::operator-=(const QVector3D &vector)+
−
+
−
    Subtracts the given \a vector from this vector and returns a reference to+
−
    this vector.+
−
+
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    \sa operator+=()+
−
*/+
−
+
−
/*!+
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    \fn QVector3D &QVector3D::operator*=(qreal factor)+
−
+
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    Multiplies this vector's coordinates by the given \a factor, and+
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    returns a reference to this vector.+
−
+
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    \sa operator/=()+
−
*/+
−
+
−
/*!+
−
    \fn QVector3D &QVector3D::operator*=(const QVector3D& vector)+
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    \overload+
−
+
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    Multiplies the components of this vector by the corresponding+
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    components in \a vector.+
−
+
−
    Note: this is not the same as the crossProduct() of this+
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    vector and \a vector.+
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+
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    \sa crossProduct()+
−
*/+
−
+
−
/*!+
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    \fn QVector3D &QVector3D::operator/=(qreal divisor)+
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+
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    Divides this vector's coordinates by the given \a divisor, and+
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    returns a reference to this vector.+
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+
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    \sa operator*=()+
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*/+
−
+
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/*!+
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    Returns the dot product of \a v1 and \a v2.+
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*/+
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qreal QVector3D::dotProduct(const QVector3D& v1, const QVector3D& v2)+
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{+
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    return v1.xp * v2.xp + v1.yp * v2.yp + v1.zp * v2.zp;+
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}+
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+
−
/*!+
−
    Returns the cross-product of vectors \a v1 and \a v2, which corresponds+
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    to the normal vector of a plane defined by \a v1 and \a v2.+
−
+
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    \sa normal()+
−
*/+
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QVector3D QVector3D::crossProduct(const QVector3D& v1, const QVector3D& v2)+
−
{+
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    return QVector3D(v1.yp * v2.zp - v1.zp * v2.yp,+
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                    v1.zp * v2.xp - v1.xp * v2.zp,+
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                    v1.xp * v2.yp - v1.yp * v2.xp, 1);+
−
}+
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+
−
/*!+
−
    Returns the normal vector of a plane defined by vectors \a v1 and \a v2,+
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    normalized to be a unit vector.+
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+
−
    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()+
−
*/+
−
QVector3D QVector3D::normal(const QVector3D& v1, const QVector3D& v2)+
−
{+
−
    return crossProduct(v1, v2).normalized();+
−
}+
−
+
−
/*!+
−
    \overload+
−
+
−
    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()+
−
*/+
−
QVector3D QVector3D::normal+
−
        (const QVector3D& v1, const QVector3D& v2, const QVector3D& v3)+
−
{+
−
    return crossProduct((v2 - v1), (v3 - v1)).normalized();+
−
}+
−
+
−
/*!+
−
    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()+
−
*/+
−
qreal QVector3D::distanceToPlane+
−
        (const QVector3D& plane, const QVector3D& normal) const+
−
{+
−
    return dotProduct(*this - plane, normal);+
−
}+
−
+
−
/*!+
−
    \overload+
−
+
−
    Returns the distance from this vertex 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()+
−
*/+
−
qreal QVector3D::distanceToPlane+
−
    (const QVector3D& plane1, const QVector3D& plane2, const QVector3D& plane3) const+
−
{+
−
    QVector3D n = normal(plane2 - plane1, plane3 - plane1);+
−
    return dotProduct(*this - plane1, n);+
−
}+
−
+
−
/*!+
−
    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()+
−
*/+
−
qreal QVector3D::distanceToLine+
−
        (const QVector3D& point, const QVector3D& direction) const+
−
{+
−
    if (direction.isNull())+
−
        return (*this - point).length();+
−
    QVector3D p = point + dotProduct(*this - point, direction) * direction;+
−
    return (*this - p).length();+
−
}+
−
+
−
/*!+
−
    \fn bool operator==(const QVector3D &v1, const QVector3D &v2)+
−
    \relates QVector3D+
−
+
−
    Returns true if \a v1 is equal to \a v2; otherwise returns false.+
−
    This operator uses an exact floating-point comparison.+
−
*/+
−
+
−
/*!+
−
    \fn bool operator!=(const QVector3D &v1, const QVector3D &v2)+
−
    \relates QVector3D+
−
+
−
    Returns true if \a v1 is not equal to \a v2; otherwise returns false.+
−
    This operator uses an exact floating-point comparison.+
−
*/+
−
+
−
/*!+
−
    \fn const QVector3D operator+(const QVector3D &v1, const 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-(const QVector3D &v1, const 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*(qreal factor, const 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*(const QVector3D &vector, qreal factor)+
−
    \relates QVector3D+
−
+
−
    Returns a copy of the given \a vector,  multiplied by the given \a factor.+
−
+
−
    \sa QVector3D::operator*=()+
−
*/+
−
+
−
/*!+
−
    \fn const QVector3D operator*(const QVector3D &v1, const 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-(const 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/(const QVector3D &vector, qreal 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 bool qFuzzyCompare(const QVector3D& v1, const QVector3D& v2)+
−
    \relates QVector3D+
−
+
−
    Returns 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+
−
+
−
/*!+
−
    Returns the 2D vector form of this 3D vector, dropping the z coordinate.+
−
+
−
    \sa toVector4D(), toPoint()+
−
*/+
−
QVector2D QVector3D::toVector2D() const+
−
{+
−
    return QVector2D(xp, yp, 1);+
−
}+
−
+
−
#endif+
−
+
−
#ifndef QT_NO_VECTOR4D+
−
+
−
/*!+
−
    Returns the 4D form of this 3D vector, with the w coordinate set to zero.+
−
+
−
    \sa toVector2D(), toPoint()+
−
*/+
−
QVector4D QVector3D::toVector4D() const+
−
{+
−
    return QVector4D(xp, yp, zp, 0.0f, 1);+
−
}+
−
+
−
#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(QVariant::Vector3D, this);+
−
}+
−
+
−
/*!+
−
    Returns the length of the vector from the origin.+
−
+
−
    \sa lengthSquared(), normalized()+
−
*/+
−
qreal QVector3D::length() const+
−
{+
−
    return qSqrt(xp * xp + yp * yp + zp * zp);+
−
}+
−
+
−
/*!+
−
    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()+
−
*/+
−
qreal QVector3D::lengthSquared() const+
−
{+
−
    return xp * xp + yp * yp + zp * zp;+
−
}+
−
+
−
#ifndef QT_NO_DEBUG_STREAM+
−
+
−
QDebug operator<<(QDebug dbg, const QVector3D &vector)+
−
{+
−
    dbg.nospace() << "QVector3D("+
−
        << vector.x() << ", " << vector.y() << ", " << vector.z() << ')';+
−
    return dbg.space();+
−
}+
−
+
−
#endif+
−
+
−
#ifndef QT_NO_DATASTREAM+
−
+
−
/*!+
−
    \fn QDataStream &operator<<(QDataStream &stream, const QVector3D &vector)+
−
    \relates QVector3D+
−
+
−
    Writes the given \a vector to the given \a stream and returns a+
−
    reference to the stream.+
−
+
−
    \sa {Format of the QDataStream Operators}+
−
*/+
−
+
−
QDataStream &operator<<(QDataStream &stream, const QVector3D &vector)+
−
{+
−
    stream << double(vector.x()) << double(vector.y())+
−
           << double(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 {Format of the QDataStream Operators}+
−
*/+
−
+
−
QDataStream &operator>>(QDataStream &stream, QVector3D &vector)+
−
{+
−
    double x, y, z;+
−
    stream >> x;+
−
    stream >> y;+
−
    stream >> z;+
−
    vector.setX(qreal(x));+
−
    vector.setY(qreal(y));+
−
    vector.setZ(qreal(z));+
−
    return stream;+
−
}+
−
+
−
#endif // QT_NO_DATASTREAM+
−
+
−
#endif // QT_NO_VECTOR3D+
−
+
−
QT_END_NAMESPACE+
−