path: root/src/gui/math3d/qquaternion.cpp

/****************************************************************************
**
** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies).
** Contact: Qt Software Information (qt-info@nokia.com)
**
** This file is part of the $MODULE$ of the Qt Toolkit.
**
** $TROLLTECH_DUAL_LICENSE$
**
****************************************************************************/

#include "qquaternion.h"
#include "qmath3dutil_p.h"
#include <QtCore/qmath.h>

QT_BEGIN_NAMESPACE

#ifndef QT_NO_QUATERNION

/*!
    \class QQuaternion
    \brief The QQuaternion class represents a quaternion consisting of a vector and scalar.
    \since 4.6

    Quaternions are used to represent rotations in 3D space, and
    consist of a 3D rotation axis specified by the x, y, and z
    coordinates, and a scalar representing the rotation angle.

    The components of a quaternion are stored internally using the most
    efficient representation for the GL rendering engine, which will be
    either floating-point or fixed-point.
*/

/*!
    \fn QQuaternion::QQuaternion()

    Constructs an identity quaternion, i.e. with coordinates (1, 0, 0, 0).
*/

/*!
    \fn QQuaternion::QQuaternion(qreal scalar, qreal xpos, qreal ypos, qreal zpos)

    Constructs a quaternion with the vector (\a xpos, \a ypos, \a zpos)
    and \a scalar.
*/

/*!
    \fn QQuaternion::QQuaternion(int scalar, int xpos, int ypos, int zpos)

    Constructs a quaternion with the vector (\a xpos, \a ypos, \a zpos)
    and \a scalar.
*/

#ifndef QT_NO_VECTOR3D

/*!
    \fn QQuaternion::QQuaternion(qreal scalar, const QVector3D& vector)

    Constructs a quaternion vector from the specified \a vector and
    \a scalar.

    \sa vector(), scalar()
*/

/*!
    \fn QVector3D QQuaternion::vector() const

    Returns the vector component of this quaternion.

    \sa setVector(), scalar()
*/

/*!
    \fn void QQuaternion::setVector(const QVector3D& vector)

    Sets the vector component of this quaternion to \a vector.

    \sa vector(), setScalar()
*/

#endif

/*!
    \fn void QQuaternion::setVector(qreal x, qreal y, qreal z)

    Sets the vector component of this quaternion to (\a x, \a y, \a z).

    \sa vector(), setScalar()
*/

#ifndef QT_NO_VECTOR4D

/*!
    \fn QQuaternion::QQuaternion(const QVector4D& vector)

    Constructs a quaternion from the components of \a vector.
*/

/*!
    \fn QVector4D QQuaternion::toVector4D() const

    Returns this quaternion as a 4D vector.
*/

#endif

/*!
    \fn bool QQuaternion::isNull() const

    Returns true if the x, y, z, and scalar components of this
    quaternion are set to 0.0; otherwise returns false.
*/

/*!
    \fn bool QQuaternion::isIdentity() const

    Returns true if the x, y, and z components of this
    quaternion are set to 0.0, and the scalar component is set
    to 1.0; otherwise returns false.
*/

/*!
    \fn qreal QQuaternion::x() const

    Returns the x coordinate of this quaternion's vector.

    \sa setX(), y(), z(), scalar()
*/

/*!
    \fn qreal QQuaternion::y() const

    Returns the y coordinate of this quaternion's vector.

    \sa setY(), x(), z(), scalar()
*/

/*!
    \fn qreal QQuaternion::z() const

    Returns the z coordinate of this quaternion's vector.

    \sa setZ(), x(), y(), scalar()
*/

/*!
    \fn qreal QQuaternion::scalar() const

    Returns the scalar component of this quaternion.

    \sa setScalar(), x(), y(), z()
*/

/*!
    \fn void QQuaternion::setX(qreal x)

    Sets the x coordinate of this quaternion's vector to the given
    \a x coordinate.

    \sa x(), setY(), setZ(), setScalar()
*/

/*!
    \fn void QQuaternion::setY(qreal y)

    Sets the y coordinate of this quaternion's vector to the given
    \a y coordinate.

    \sa y(), setX(), setZ(), setScalar()
*/

/*!
    \fn void QQuaternion::setZ(qreal z)

    Sets the z coordinate of this quaternion's vector to the given
    \a z coordinate.

    \sa z(), setX(), setY(), setScalar()
*/

/*!
    \fn void QQuaternion::setScalar(qreal scalar)

    Sets the scalar component of this quaternion to \a scalar.

    \sa scalar(), setX(), setY(), setZ()
*/

/*!
    Returns the length of the quaternion.  This is also called the "norm".

    \sa lengthSquared(), normalized()
*/
qreal QQuaternion::length() const
{
    return qvtsqrt64(qvtmul64(xp, xp) + qvtmul64(yp, yp) +
                     qvtmul64(zp, zp) + qvtmul64(wp, wp));
}

/*!
    Returns the squared length of the quaternion.

    \sa length()
*/
qreal QQuaternion::lengthSquared() const
{
    return qvtdot64(qvtmul64(xp, xp) + qvtmul64(yp, yp) +
                    qvtmul64(zp, zp) + qvtmul64(wp, wp));
}

/*!
    Returns the normalized unit form of this quaternion.  If this quaternion
    is not null, the returned quaternion is guaranteed to be 1.0 in length.
    If this quaternion is null, then a null quaternion is returned.

    \sa length(), normalize()
*/
QQuaternion QQuaternion::normalized() const
{
    qreal len = length();
    if (!qIsNull(len))
        return *this / len;
    else
        return QQuaternion(0.0f, 0.0f, 0.0f, 0.0f);
}

/*!
    Normalizes the currect quaternion in place.  Nothing happens if this
    is a null quaternion.

    \sa length(), normalized()
*/
void QQuaternion::normalize()
{
    qreal len = length();
    if (qIsNull(len))
        return;

    xp /= len;
    yp /= len;
    zp /= len;
    wp /= len;
}


/*!
    \fn QQuaternion QQuaternion::conjugate() const

    Returns the conjugate of this quaternion, which is
    (-x, -y, -z, scalar).
*/

/*!
    Rotates \a vector with this quaternion to produce a new vector
    in 3D space.  The following code:

    \code
    QVector3D result = q.rotateVector(vector);
    \endcode

    is equivalent to the following:

    \code
    QVector3D result = (q * QQuaternion(0, vector) * q.conjugate()).vector();
    \endcode
*/
QVector3D QQuaternion::rotateVector(const QVector3D& vector) const
{
    return (*this * QQuaternion(0, vector) * conjugate()).vector();
}

/*!
    \fn QQuaternion &QQuaternion::operator+=(const QQuaternion &quaternion)

    Adds the given \a quaternion to this quaternion and returns a reference to
    this quaternion.

    \sa operator-=()
*/

/*!
    \fn QQuaternion &QQuaternion::operator-=(const QQuaternion &quaternion)

    Subtracts the given \a quaternion from this quaternion and returns a
    reference to this quaternion.

    \sa operator+=()
*/

/*!
    \fn QQuaternion &QQuaternion::operator*=(qreal factor)

    Multiplies this quaternion's components by the given \a factor, and
    returns a reference to this quaternion.

    \sa operator/=()
*/

/*!
    \fn QQuaternion &QQuaternion::operator*=(const QQuaternion &quaternion)

    Multiplies this quaternion by \a quaternion and returns a reference
    to this quaternion.
*/

/*!
    \fn QQuaternion &QQuaternion::operator/=(qreal divisor)

    Divides this quaternion's components by the given \a divisor, and
    returns a reference to this quaternion.

    \sa operator*=()
*/

#ifndef QT_NO_VECTOR3D

/*!
    Creates a normalized quaternion that corresponds to rotating through
    \a angle degrees about the specified 3D \a axis.
*/
QQuaternion QQuaternion::fromAxisAndAngle(const QVector3D& axis, qreal angle)
{
    // Algorithm from:
    // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56
    // We normalize the result just in case the values are close
    // to zero, as suggested in the above FAQ.
    qrealinner s, c;
    QVector3D ax = axis.normalized();
    qt_math3d_sincos(angle / 2.0f, &s, &c);
    return QQuaternion(c, ax.xp * s, ax.yp * s, ax.zp * s, 1).normalized();
}

#endif

/*!
    Creates a normalized quaternion that corresponds to rotating through
    \a angle degrees about the 3D axis (\a x, \a y, \a z).
*/
QQuaternion QQuaternion::fromAxisAndAngle
        (qreal x, qreal y, qreal z, qreal angle)
{
    qrealinner xp = x;
    qrealinner yp = y;
    qrealinner zp = z;
    qrealinner s, c;
    qreal length = qvtsqrt(xp * xp + yp * yp + zp * zp);
    if (!qIsNull(length)) {
        xp /= length;
        yp /= length;
        zp /= length;
    }
    qt_math3d_sincos(angle / 2.0f, &s, &c);
    return QQuaternion(c, xp * s, yp * s, zp * s, 1).normalized();
}

/*!
    \fn bool operator==(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns true if \a q1 is equal to \a q2; otherwise returns false.
    This operator uses an exact floating-point comparison.
*/

/*!
    \fn bool operator!=(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns true if \a q1 is not equal to \a q2; otherwise returns false.
    This operator uses an exact floating-point comparison.
*/

/*!
    \fn const QQuaternion operator+(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns a QQuaternion object that is the sum of the given quaternions,
    \a q1 and \a q2; each component is added separately.

    \sa QQuaternion::operator+=()
*/

/*!
    \fn const QQuaternion operator-(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns a QQuaternion object that is formed by subtracting
    \a q2 from \a q1; each component is subtracted separately.

    \sa QQuaternion::operator-=()
*/

/*!
    \fn const QQuaternion operator*(qreal factor, const QQuaternion &quaternion)
    \relates QQuaternion

    Returns a copy of the given \a quaternion,  multiplied by the
    given \a factor.

    \sa QQuaternion::operator*=()
*/

/*!
    \fn const QQuaternion operator*(const QQuaternion &quaternion, qreal factor)
    \relates QQuaternion

    Returns a copy of the given \a quaternion,  multiplied by the
    given \a factor.

    \sa QQuaternion::operator*=()
*/

/*!
    \fn const QQuaternion operator*(const QQuaternion &q1, const QQuaternion& q2)
    \relates QQuaternion

    Multiplies \a q1 and \a q2 using quaternion multiplication.
    The result corresponds to applying both of the rotations specified
    by \a q1 and \a q2.

    \sa QQuaternion::operator*=()
*/

/*!
    \fn const QQuaternion operator-(const QQuaternion &quaternion)
    \relates QQuaternion
    \overload

    Returns a QQuaternion object that is formed by changing the sign of
    all three components of the given \a quaternion.

    Equivalent to \c {QQuaternion(0,0,0,0) - quaternion}.
*/

/*!
    \fn const QQuaternion operator/(const QQuaternion &quaternion, qreal divisor)
    \relates QQuaternion

    Returns the QQuaternion object formed by dividing all components of
    the given \a quaternion by the given \a divisor.

    \sa QQuaternion::operator/=()
*/

/*!
    \fn bool qFuzzyCompare(const QQuaternion& q1, const QQuaternion& q2)
    \relates QQuaternion

    Returns true if \a q1 and \a q2 are equal, allowing for a small
    fuzziness factor for floating-point comparisons; false otherwise.
*/

/*!
    Interpolates along the shortest spherical path between the
    rotational positions \a q1 and \a q2.  The value \a t should
    be between 0 and 1, indicating the spherical distance to travel
    between \a q1 and \a q2.

    If \a t is less than or equal to 0, then \a q1 will be returned.
    If \a t is greater than or equal to 1, then \a q2 will be returned.
*/
QQuaternion QQuaternion::interpolate
    (const QQuaternion& q1, const QQuaternion& q2, qreal t)
{
    // Handle the easy cases first.
    if (t <= 0.0f)
        return q1;
    else if (t >= 1.0f)
        return q2;

    // Determine the angle between the two quaternions.
    QQuaternion q2b;
    qreal dot;
    dot = qvtdot64(qvtmul64(q1.xp, q2.xp) + qvtmul64(q1.yp, q2.yp) +
                   qvtmul64(q1.zp, q2.zp) + qvtmul64(q1.wp, q2.wp));
    if (dot >= 0.0f) {
        q2b = q2;
    } else {
        q2b = -q2;
        dot = -dot;
    }

    // Get the scale factors.  If they are too small,
    // then revert to simple linear interpolation.
    qreal factor1 = 1.0f - t;
    qreal factor2 = t;
    if ((1.0f - dot) > 0.0000001) {
        qreal angle = qreal(qAcos(dot));
        qreal sinOfAngle = qreal(qSin(angle));
        if (sinOfAngle > 0.0000001) {
            factor1 = qreal(qSin((1.0f - t) * angle)) / sinOfAngle;
            factor2 = qreal(qSin(t * angle)) / sinOfAngle;
        }
    }

    // Construct the result quaternion.
    return q1 * factor1 + q2b * factor2;
}

#ifndef QT_NO_DEBUG_STREAM

QDebug operator<<(QDebug dbg, const QQuaternion &q)
{
    dbg.nospace() << "QQuaternion(scalar:" << q.scalar()
        << ", vector:(" << q.x() << ", "
        << q.y() << ", " << q.z() << "))";
    return dbg.space();
}

#endif

#endif

QT_END_NAMESPACE