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#include "qquaternion.h"

#include <QtCore/qmath.h>

#include <QtCore/qvariant.h>

#include <QtCore/qdebug.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

    \ingroup painting-3D

    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.

*/

/*!

    \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.

*/

#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 qSqrt(xp * xp + yp * yp + zp * zp + wp * wp);

}

/*!

    Returns the squared length of the quaternion.

    \sa length()

*/

qreal QQuaternion::lengthSquared() const

{

    return xp * xp + yp * yp + zp * zp + wp * wp;

}

/*!

    Returns the normalized unit form of this quaternion.

    If this quaternion is null, then a null quaternion is returned.

    If the length of the quaternion is very close to 1, then the quaternion

    will be returned as-is.  Otherwise the normalized form of the

    quaternion of length 1 will be returned.

    \sa length(), normalize()

*/

QQuaternion QQuaternion::normalized() const

{

    // Need some extra precision if the length is very small.

    double len = double(xp) * double(xp) +

                 double(yp) * double(yp) +

                 double(zp) * double(zp) +

                 double(wp) * double(wp);

    if (qFuzzyIsNull(len - 1.0f))

        return *this;

    else if (!qFuzzyIsNull(len))

        return *this / qSqrt(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 or the length of the quaternion is very close to 1.

    \sa length(), normalized()

*/

void QQuaternion::normalize()

{

    // Need some extra precision if the length is very small.

    double len = double(xp) * double(xp) +

                 double(yp) * double(yp) +

                 double(zp) * double(zp) +

                 double(wp) * double(wp);

    if (qFuzzyIsNull(len - 1.0f) || qFuzzyIsNull(len))

        return;

    len = qSqrt(len);

    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.rotatedVector(vector);

    \endcode

    is equivalent to the following:

    \code

    QVector3D result = (q * QQuaternion(0, vector) * q.conjugate()).vector();

    \endcode

*/

QVector3D QQuaternion::rotatedVector(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.

    qreal a = (angle / 2.0f) * M_PI / 180.0f;

    qreal s = qSin(a);

    qreal c = qCos(a);

    QVector3D ax = axis.normalized();

    return QQuaternion(c, ax.x() * s, ax.y() * s, ax.z() * s).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)

{

    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, x * s, y * s, z * s).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.

    \sa nlerp()

*/

QQuaternion QQuaternion::slerp

    (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 = q1.xp * q2.xp + q1.yp * q2.yp + q1.zp * q2.zp + 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;