C++ ChQuaternion::e0方法代码示例

// Get the X axis of a coordsystem, given the quaternion which
// represents the alignment of the coordsystem.
ChVector<double> VaxisXfromQuat(const ChQuaternion<double>& quat) {
    ChVector<double> res;
    res.x() = (pow(quat.e0(), 2) + pow(quat.e1(), 2)) * 2 - 1;
    res.y() = ((quat.e1() * quat.e2()) + (quat.e0() * quat.e3())) * 2;
    res.z() = ((quat.e1() * quat.e3()) - (quat.e0() * quat.e2())) * 2;
    return res;
}

// Return the conjugate of the quaternion [s,v1,v2,v3] is [s,-v1,-v2,-v3]
ChQuaternion<double> Qconjugate(const ChQuaternion<double>& q) {
    ChQuaternion<double> res;
    res.e0() = q.e0();
    res.e1() = -q.e1();
    res.e2() = -q.e2();
    res.e3() = -q.e3();
    return (res);
}

ChQuaternion<double> Qsub(const ChQuaternion<double>& qa, const ChQuaternion<double>& qb) {
    ChQuaternion<double> result;
    result.e0() = qa.e0() - qb.e0();
    result.e1() = qa.e1() - qb.e1();
    result.e2() = qa.e2() - qb.e2();
    result.e3() = qa.e3() - qb.e3();
    return result;
}

ChQuaternion<double> Qscale(const ChQuaternion<double>& q, double fact) {
    ChQuaternion<double> result;
    result.e0() = q.e0() * fact;
    result.e1() = q.e1() * fact;
    result.e2() = q.e2() * fact;
    result.e3() = q.e3() * fact;
    return result;
}

// Given the imaginary (vectorial) {e1 e2 e3} part of a quaternion time derivative,
// find the entire quaternion q = {e0, e1, e2, e3}.
// Note: singularities are possible.
ChQuaternion<double> ImmQ_dt_complete(const ChQuaternion<double>& mq, const ChVector<double>& qimm_dt) {
    ChQuaternion<double> mqdt;
    mqdt.e1() = qimm_dt.x();
    mqdt.e2() = qimm_dt.y();
    mqdt.e3() = qimm_dt.z();
    mqdt.e0() = (-mq.e1() * mqdt.e1() - mq.e2() * mqdt.e2() - mq.e3() * mqdt.e3()) / mq.e0();
    return mqdt;
}

ChVector<double> Q_to_NasaAngles(const ChQuaternion<double>& q1) {
    ChVector<double> mnasa;
    double sqw = q1.e0() * q1.e0();
    double sqx = q1.e1() * q1.e1();
    double sqy = q1.e2() * q1.e2();
    double sqz = q1.e3() * q1.e3();
    // heading
    mnasa.z() = atan2(2.0 * (q1.e1() * q1.e2() + q1.e3() * q1.e0()), (sqx - sqy - sqz + sqw));
    // bank
    mnasa.y() = atan2(2.0 * (q1.e2() * q1.e3() + q1.e1() * q1.e0()), (-sqx - sqy + sqz + sqw));
    // attitude
    mnasa.x() = asin(-2.0 * (q1.e1() * q1.e3() - q1.e2() * q1.e0()));
    return mnasa;
}

// Given the imaginary (vectorial) {e1 e2 e3} part of a quaternion,
// find the entire quaternion q = {e0, e1, e2, e3}.
// Note: singularities are possible.
ChQuaternion<double> ImmQ_complete(const ChVector<double>& qimm) {
    ChQuaternion<double> mq;
    mq.e1() = qimm.x();
    mq.e2() = qimm.y();
    mq.e3() = qimm.z();
    mq.e0() = sqrt(1 - mq.e1() * mq.e1() - mq.e2() * mq.e2() - mq.e3() * mq.e3());
    return mq;
}

void Q_to_AngAxis(const ChQuaternion<double>& quat, double& angle, ChVector<double>& axis) {
    if (fabs(quat.e0()) < 0.99999999) {
        double arg = acos(quat.e0());
        double invsine = 1 / sin(arg);
        ChVector<double> vtemp;
        vtemp.x() = invsine * quat.e1();
        vtemp.y() = invsine * quat.e2();
        vtemp.z() = invsine * quat.e3();
        angle = 2 * arg;
        axis = Vnorm(vtemp);
    } else {
        axis.x() = 1;
        axis.y() = 0;
        axis.z() = 0;
        angle = 0;
    }
}

// Get the quaternion from a source vector and a destination vector which specifies
// the rotation from one to the other.  The vectors do not need to be normalized.
ChQuaternion<double> Q_from_Vect_to_Vect(const ChVector<double>& fr_vect, const ChVector<double>& to_vect) {
    const double ANGLE_TOLERANCE = 1e-6;
    ChQuaternion<double> quat;
    double halfang;
    double sinhalf;
    ChVector<double> axis;

    double lenXlen = fr_vect.Length() * to_vect.Length();
    axis = fr_vect % to_vect;
    double sinangle = ChClamp(axis.Length() / lenXlen, -1.0, +1.0);
    double cosangle = ChClamp(fr_vect ^ to_vect / lenXlen, -1.0, +1.0);

    // Consider three cases: Parallel, Opposite, non-collinear
    if (std::abs(sinangle) == 0.0 && cosangle > 0) {
        // fr_vect & to_vect are parallel
        quat.e0() = 1.0;
        quat.e1() = 0.0;
        quat.e2() = 0.0;
        quat.e3() = 0.0;
    } else if (std::abs(sinangle) < ANGLE_TOLERANCE && cosangle < 0) {
        // fr_vect & to_vect are opposite, i.e. ~180 deg apart
        axis = fr_vect.GetOrthogonalVector() + (-to_vect).GetOrthogonalVector();
        axis.Normalize();
        quat.e0() = 0.0;
        quat.e1() = ChClamp(axis.x(), -1.0, +1.0);
        quat.e2() = ChClamp(axis.y(), -1.0, +1.0);
        quat.e3() = ChClamp(axis.z(), -1.0, +1.0);
    } else {
        // fr_vect & to_vect are not co-linear case
        axis.Normalize();
        halfang = 0.5 * ChAtan2(sinangle, cosangle);
        sinhalf = sin(halfang);

        quat.e0() = cos(halfang);
        quat.e1() = ChClamp(axis.x(), -1.0, +1.0);
        quat.e2() = ChClamp(axis.y(), -1.0, +1.0);
        quat.e3() = ChClamp(axis.z(), -1.0, +1.0);
    }
    return (quat);
}

// Return the product of two quaternions. It is non-commutative (like cross product in vectors).
ChQuaternion<double> Qcross(const ChQuaternion<double>& qa, const ChQuaternion<double>& qb) {
    ChQuaternion<double> res;
    res.e0() = qa.e0() * qb.e0() - qa.e1() * qb.e1() - qa.e2() * qb.e2() - qa.e3() * qb.e3();
    res.e1() = qa.e0() * qb.e1() + qa.e1() * qb.e0() - qa.e3() * qb.e2() + qa.e2() * qb.e3();
    res.e2() = qa.e0() * qb.e2() + qa.e2() * qb.e0() + qa.e3() * qb.e1() - qa.e1() * qb.e3();
    res.e3() = qa.e0() * qb.e3() + qa.e3() * qb.e0() - qa.e2() * qb.e1() + qa.e1() * qb.e2();
    return (res);
}

// Get the quaternion from an angle of rotation and an axis, defined in _abs_ coords.
// The axis is supposed to be fixed, i.e. it is constant during rotation.
// The 'axis' vector must be normalized.
ChQuaternion<double> Q_from_AngAxis(double angle, const ChVector<double>& axis) {
    ChQuaternion<double> quat;
    double halfang;
    double sinhalf;

    halfang = (angle * 0.5);
    sinhalf = sin(halfang);

    quat.e0() = cos(halfang);
    quat.e1() = axis.x() * sinhalf;
    quat.e2() = axis.y() * sinhalf;
    quat.e3() = axis.z() * sinhalf;
    return (quat);
}

ChQuaternion<double> Q_from_NasaAngles(const ChVector<double>& mang) {
    ChQuaternion<double> mq;
    double c1 = cos(mang.z() / 2);
    double s1 = sin(mang.z() / 2);
    double c2 = cos(mang.x() / 2);
    double s2 = sin(mang.x() / 2);
    double c3 = cos(mang.y() / 2);
    double s3 = sin(mang.y() / 2);
    double c1c2 = c1 * c2;
    double s1s2 = s1 * s2;
    mq.e0() = c1c2 * c3 + s1s2 * s3;
    mq.e1() = c1c2 * s3 - s1s2 * c3;
    mq.e2() = c1 * s2 * c3 + s1 * c2 * s3;
    mq.e3() = s1 * c2 * c3 - c1 * s2 * s3;
    return mq;
}

// Check if quaternion is not null
bool Qnotnull(const ChQuaternion<double>& qa) {
    return (qa.e0() != 0) || (qa.e1() != 0) || (qa.e2() != 0) || (qa.e3() != 0);
}

double Qlength(const ChQuaternion<double>& q) {
    return (sqrt(pow(q.e0(), 2) + pow(q.e1(), 2) + pow(q.e2(), 2) + pow(q.e3(), 2)));
}