欧拉角和四元数的相互转换关系.

参考 

Quaterniond toQuaternion( double yaw, double pitch, double roll) // yaw (Z), pitch (Y), roll (X)
{
    // Abbreviations for the various angular functions
    double cy = cos(yaw * 0.5);
    double sy = sin(yaw * 0.5);
    double cp = cos(pitch * 0.5);
    double sp = sin(pitch * 0.5);
    double cr = cos(roll * 0.5);
    double sr = sin(roll * 0.5);

    Quaterniond q;
    q.w() = cy * cp * cr + sy * sp * sr;
    q.x() = cy * cp * sr - sy * sp * cr;
    q.y() = sy * cp * sr + cy * sp * cr;
    q.z() = sy * cp * cr - cy * sp * sr;
    return q;
}

static void toEulerAngle(const Quaterniond& q, double& roll, double& pitch, double& yaw)
{
    // roll (x-axis rotation)
    double sinr_cosp = +2.0 * (q.w() * q.x() + q.y() * q.z());
    double cosr_cosp = +1.0 - 2.0 * (q.x() * q.x() + q.y() * q.y());
    roll = atan2(sinr_cosp, cosr_cosp);

    // pitch (y-axis rotation)
    double sinp = +2.0 * (q.w() * q.y() - q.z() * q.x());
    if (fabs(sinp) >= 1)
        pitch = copysign(M_PI / 2, sinp); // use 90 degrees if out of range
    else
        pitch = asin(sinp);

    // yaw (z-axis rotation)
    double siny_cosp = +2.0 * (q.w() * q.z() + q.x() * q.y());
    double cosy_cosp = +1.0 - 2.0 * (q.y() * q.y() + q.z() * q.z());
    yaw = atan2(siny_cosp, cosy_cosp);
}