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Diffstat (limited to 'src/gui/math3d/qquaternion.cpp')
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diff --git a/src/gui/math3d/qquaternion.cpp b/src/gui/math3d/qquaternion.cpp new file mode 100644 index 0000000..ece4482 --- /dev/null +++ b/src/gui/math3d/qquaternion.cpp @@ -0,0 +1,631 @@ +/**************************************************************************** +** +** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies). +** Contact: Nokia Corporation (qt-info@nokia.com) +** +** This file is part of the QtGui module of the Qt Toolkit. +** +** $QT_BEGIN_LICENSE:LGPL$ +** No Commercial Usage +** This file contains pre-release code and may not be distributed. +** You may use this file in accordance with the terms and conditions +** contained in the Technology Preview License Agreement accompanying +** this package. +** +** GNU Lesser General Public License Usage +** Alternatively, this file may be used under the terms of the GNU Lesser +** General Public License version 2.1 as published by the Free Software +** Foundation and appearing in the file LICENSE.LGPL included in the +** packaging of this file. Please review the following information to +** ensure the GNU Lesser General Public License version 2.1 requirements +** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html. +** +** In addition, as a special exception, Nokia gives you certain +** additional rights. These rights are described in the Nokia Qt LGPL +** Exception version 1.1, included in the file LGPL_EXCEPTION.txt in this +** package. +** +** If you have questions regarding the use of this file, please contact +** Nokia at qt-info@nokia.com. +** +** +** +** +** +** +** +** +** $QT_END_LICENSE$ +** +****************************************************************************/ + +#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 +{ + qreal len = lengthSquared(); + 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() +{ + qreal len = lengthSquared(); + 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.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. + 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.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) +{ + float xp = x; + float yp = y; + float zp = z; + qreal length = qSqrt(xp * xp + yp * yp + zp * zp); + if (!qIsNull(length)) { + xp /= length; + yp /= length; + zp /= length; + } + qreal a = (angle / 2.0f) * M_PI / 180.0f; + qreal s = qSin(a); + qreal c = qCos(a); + return QQuaternion(c, xp * s, yp * s, zp * s, 1).normalized(); +} + +/*! + \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; +} + +/*! + Interpolates along the shortest linear path between the rotational + positions \a q1 and \a q2. The value \a t should be between 0 and 1, + indicating the distance to travel between \a q1 and \a q2. + The result will be normalized(). + + 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. + + The nlerp() function is typically faster than slerp() and will + give approximate results to spherical interpolation that are + good enough for some applications. + + \sa slerp() +*/ +QQuaternion QQuaternion::nlerp + (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; + + // Perform the linear interpolation. + return (q1 * (1.0f - t) + q2b * t).normalized(); +} + +/*! + Returns the quaternion as a QVariant. +*/ +QQuaternion::operator QVariant() const +{ + return QVariant(QVariant::Quaternion, this); +} + +#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 + +#ifndef QT_NO_DATASTREAM + +/*! + \fn QDataStream &operator<<(QDataStream &stream, const QQuaternion &quaternion) + \relates QQuaternion + + Writes the given \a quaternion to the given \a stream and returns a + reference to the stream. + + \sa {Format of the QDataStream Operators} +*/ + +QDataStream &operator<<(QDataStream &stream, const QQuaternion &quaternion) +{ + stream << double(quaternion.scalar()) << double(quaternion.x()) + << double(quaternion.y()) << double(quaternion.z()); + return stream; +} + +/*! + \fn QDataStream &operator>>(QDataStream &stream, QQuaternion &quaternion) + \relates QQuaternion + + Reads a quaternion from the given \a stream into the given \a quaternion + and returns a reference to the stream. + + \sa {Format of the QDataStream Operators} +*/ + +QDataStream &operator>>(QDataStream &stream, QQuaternion &quaternion) +{ + double scalar, x, y, z; + stream >> scalar; + stream >> x; + stream >> y; + stream >> z; + quaternion.setScalar(qreal(scalar)); + quaternion.setX(qreal(x)); + quaternion.setY(qreal(y)); + quaternion.setZ(qreal(z)); + return stream; +} + +#endif // QT_NO_DATASTREAM + +#endif + +QT_END_NAMESPACE |