qt-everywhere-src-5.15.1/qt3d/src/core/transforms/qmath3d_p.h

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#ifndef QT3DCORE_QMATH3D_P_H
#define QT3DCORE_QMATH3D_P_H

//
//  W A R N I N G
//  -------------
//
// This file is not part of the Qt3D API.  It exists purely as an
// implementation detail.  This header file may change from version to
// version without notice, or even be removed.
//
// We mean it.
//
#include <QtGui/qmatrix4x4.h>
#include <QtGui/qquaternion.h>
#include <QtGui/qvector3d.h>
#include <Qt3DCore/private/sqt_p.h>

#include <cmath>

QT_BEGIN_NAMESPACE

inline void composeQMatrix4x4(const QVector3D &position, const QQuaternion &orientation, const QVector3D &scale, QMatrix4x4 &m)
{
    const QMatrix3x3 rot3x3(orientation.toRotationMatrix());

    // set up final matrix with scale, rotation and translation
    m(0, 0) = scale.x() * rot3x3(0, 0); m(0, 1) = scale.y() * rot3x3(0, 1); m(0, 2) = scale.z() * rot3x3(0, 2); m(0, 3) = position.x();
    m(1, 0) = scale.x() * rot3x3(1, 0); m(1, 1) = scale.y() * rot3x3(1, 1); m(1, 2) = scale.z() * rot3x3(1, 2); m(1, 3) = position.y();
    m(2, 0) = scale.x() * rot3x3(2, 0); m(2, 1) = scale.y() * rot3x3(2, 1); m(2, 2) = scale.z() * rot3x3(2, 2); m(2, 3) = position.z();
    // no projection term
    m(3, 0) = 0.0f; m(3, 1) = 0.0f; m(3, 2) = 0.0f; m(3, 3) = 1.0f;
}

inline void decomposeQMatrix3x3(const QMatrix3x3 &m, QMatrix3x3 &Q, QVector3D &D, QVector3D &U)
{
    // Factor M = QR = QDU where Q is orthogonal, D is diagonal,
    // and U is upper triangular with ones on its diagonal.
    // Algorithm uses Gram-Schmidt orthogonalization (the QR algorithm).
    //
    // If M = [ m0 | m1 | m2 ] and Q = [ q0 | q1 | q2 ], then
    //   q0 = m0/|m0|
    //   q1 = (m1-(q0*m1)q0)/|m1-(q0*m1)q0|
    //   q2 = (m2-(q0*m2)q0-(q1*m2)q1)/|m2-(q0*m2)q0-(q1*m2)q1|
    //
    // where |V| indicates length of vector V and A*B indicates dot
    // product of vectors A and B.  The matrix R has entries
    //
    //   r00 = q0*m0  r01 = q0*m1  r02 = q0*m2
    //   r10 = 0      r11 = q1*m1  r12 = q1*m2
    //   r20 = 0      r21 = 0      r22 = q2*m2
    //
    // so D = diag(r00,r11,r22) and U has entries u01 = r01/r00,
    // u02 = r02/r00, and u12 = r12/r11.

    // Q = rotation
    // D = scaling
    // U = shear

    // D stores the three diagonal entries r00, r11, r22
    // U stores the entries U[0] = u01, U[1] = u02, U[2] = u12

    // build orthogonal matrix Q
    float invLen = 1.0f / std::sqrt(m(0, 0) * m(0, 0) + m(1, 0) * m(1, 0) + m(2, 0) * m(2, 0));
    Q(0, 0) = m(0, 0) * invLen;
    Q(1, 0) = m(1, 0) * invLen;
    Q(2, 0) = m(2, 0) * invLen;

    float dot = Q(0, 0) * m(0, 1) + Q(1, 0) * m(1, 1) + Q(2, 0) * m(2, 1);
    Q(0, 1) = m(0, 1) - dot * Q(0, 0);
    Q(1, 1) = m(1, 1) - dot * Q(1, 0);
    Q(2, 1) = m(2, 1) - dot * Q(2, 0);
    invLen = 1.0f / std::sqrt(Q(0, 1) * Q(0, 1) + Q(1, 1) * Q(1, 1) + Q(2, 1) * Q(2, 1));
    Q(0, 1) *= invLen;
    Q(1, 1) *= invLen;
    Q(2, 1) *= invLen;

    dot = Q(0, 0) * m(0, 2) + Q(1, 0) * m(1, 2) + Q(2, 0) * m(2, 2);
    Q(0, 2) = m(0, 2) - dot * Q(0, 0);
    Q(1, 2) = m(1, 2) - dot * Q(1, 0);
    Q(2, 2) = m(2, 2) - dot * Q(2, 0);
    dot = Q(0, 1) * m(0, 2) + Q(1, 1) * m(1, 2) + Q(2, 1) * m(2, 2);
    Q(0, 2) -= dot * Q(0, 1);
    Q(1, 2) -= dot * Q(1, 1);
    Q(2, 2) -= dot * Q(2, 1);
    invLen = 1.0f / std::sqrt(Q(0, 2) * Q(0, 2) + Q(1, 2) * Q(1, 2) + Q(2, 2) * Q(2, 2));
    Q(0, 2) *= invLen;
    Q(1, 2) *= invLen;
    Q(2, 2) *= invLen;

    // guarantee that orthogonal matrix has determinant 1 (no reflections)
    const float det = Q(0, 0) * Q(1, 1) * Q(2, 2) + Q(0, 1) * Q(1, 2) * Q(2, 0) +
                      Q(0, 2) * Q(1, 0) * Q(2, 1) - Q(0, 2) * Q(1, 1) * Q(2, 0) -
                      Q(0, 1) * Q(1, 0) * Q(2, 2) - Q(0, 0) * Q(1, 2) * Q(2, 1);
    if (det < 0.0f)
        Q *= -1.0f;

    // build "right" matrix R
    QMatrix3x3 R(Qt::Uninitialized);
    R(0, 0) = Q(0, 0) * m(0, 0) + Q(1, 0) * m(1, 0) + Q(2, 0) * m(2, 0);
    R(0, 1) = Q(0, 0) * m(0, 1) + Q(1, 0) * m(1, 1) + Q(2, 0) * m(2, 1);
    R(1, 1) = Q(0, 1) * m(0, 1) + Q(1, 1) * m(1, 1) + Q(2, 1) * m(2, 1);
    R(0, 2) = Q(0, 0) * m(0, 2) + Q(1, 0) * m(1, 2) + Q(2, 0) * m(2, 2);
    R(1, 2) = Q(0, 1) * m(0, 2) + Q(1, 1) * m(1, 2) + Q(2, 1) * m(2, 2);
    R(2, 2) = Q(0, 2) * m(0, 2) + Q(1, 2) * m(1, 2) + Q(2, 2) * m(2, 2);

    // the scaling component
    D[0] = R(0, 0);
    D[1] = R(1, 1);
    D[2] = R(2, 2);

    // the shear component
    U[0] = R(0, 1) / D[0];
    U[1] = R(0, 2) / D[0];
    U[2] = R(1, 2) / D[1];
}

inline bool hasScale(const QMatrix4x4 &m)
{
    // If the columns are orthonormal and form a right-handed system, then there is no scale
    float t(m.determinant());
    if (!qFuzzyIsNull(t - 1.0f))
        return true;
    t = m(0, 0) * m(0, 0) + m(1, 0) * m(1, 0) + m(2, 0) * m(2, 0);
    if (!qFuzzyIsNull(t - 1.0f))
        return true;
    t = m(0, 1) * m(0, 1) + m(1, 1) * m(1, 1) + m(2, 1) * m(2, 1);
    if (!qFuzzyIsNull(t - 1.0f))
        return true;
    t = m(0, 2) * m(0, 2) + m(1, 2) * m(1, 2) + m(2, 2) * m(2, 2);
    if (!qFuzzyIsNull(t - 1.0f))
        return true;
    return false;
}

inline void decomposeQMatrix4x4(const QMatrix4x4 &m, QVector3D &position, QQuaternion &orientation, QVector3D &scale)
{
    Q_ASSERT(m.isAffine());

    const QMatrix3x3 m3x3(m.toGenericMatrix<3, 3>());

    QMatrix3x3 rot3x3(Qt::Uninitialized);
    if (hasScale(m)) {
        decomposeQMatrix3x3(m3x3, rot3x3, scale, position);
    } else {
        // we know there is no scaling part; no need for QDU decomposition
        scale = QVector3D(1.0f, 1.0f, 1.0f);
        rot3x3 = m3x3;
    }
    orientation = QQuaternion::fromRotationMatrix(rot3x3);
    position = QVector3D(m(0, 3), m(1, 3), m(2, 3));
}

inline void decomposeQMatrix4x4(const QMatrix4x4 &m, Qt3DCore::Sqt &sqt)
{
    Q_ASSERT(m.isAffine());

    const QMatrix3x3 m3x3(m.toGenericMatrix<3, 3>());

    QMatrix3x3 rot3x3(Qt::Uninitialized);
    if (hasScale(m)) {
        decomposeQMatrix3x3(m3x3, rot3x3, sqt.scale, sqt.translation);
    } else {
        // we know there is no scaling part; no need for QDU decomposition
        sqt.scale = QVector3D(1.0f, 1.0f, 1.0f);
        rot3x3 = m3x3;
    }
    sqt.rotation = QQuaternion::fromRotationMatrix(rot3x3);
    sqt.translation = QVector3D(m(0, 3), m(1, 3), m(2, 3));
}

QT_END_NAMESPACE

#endif // QT3DCORE_QMATH3D_P_H