如何在现代opengl中正确实现四元数相机

我试图在opengl中创建一个基于uvn四元数的相机，使用了下面列出的各种教程，并阅读了四元数和轴角旋转。我留下了一个奇怪的错误，我似乎无法修复。

基本上相机似乎工作得很好，直到相机从+z旋转约45度，在这一点上倾斜相机向上或向下似乎倾斜相机围绕其目标轴，转动向上矢量。

当相机沿-z方向向上或向下倾斜时，会产生相反的错觉，向上向下倾斜，向下向上倾斜。

我已经看到其他的实现建议使用非uvn系统，其中四元数累积成一个描述当前方向的delta从一些任意的开始角度。这听起来很棒，但是我似乎不能确切地知道我将如何实现这一点，特别是从这个到视图矩阵的转换。

在SO的其他地方，我读到关于将旋转分成两个四元数分别代表偏航和俯仰，但我不相信这是问题的原因，因为在这种情况下，如果我错了，请纠正我，但我的理解是，你应用这两个旋转的顺序并不重要。

相关源代码片段:

Quarternion操作

Quaternion<TValue> conjugate() const{
            return Quaternion({ { -m_values[X], -m_values[Y], -m_values[Z], m_values[W] } });
};
Quaternion<TValue>& operator*=(const Quaternion<TValue>& rhs) {
        TValue x, y, z, w;
            w = rhs[W] * m_values[W] - rhs[X] * m_values[X] - rhs[Y] * m_values[Y] - rhs[Z] * m_values[Z];
            x = rhs[W] * m_values[X] + rhs[X] * m_values[W] - rhs[Y] * m_values[Z] + rhs[Z] * m_values[Y];
            y = rhs[W] * m_values[Y] + rhs[X] * m_values[Z] + rhs[Y] * m_values[W] - rhs[Z] * m_values[X];
            z = rhs[W] * m_values[Z] - rhs[X] * m_values[Y] + rhs[Y] * m_values[X] + rhs[Z] * m_values[W];          
            m_values[X] = x;
            m_values[Y] = y;
            m_values[Z] = z;
            m_values[W] = w;
            return *this;
};
static Quaternion<TValue> rotation(Vector<3, TValue> axis, TValue angle){
        float x, y, z, w;
        TValue halfTheta = angle / 2.0f;
        TValue sinHalfTheta = sin(halfTheta);
        return Quaternion<TValue>({ { axis[X] * sinHalfTheta, axis[Y] * sinHalfTheta, axis[Z] * sinHalfTheta, cos(halfTheta) } });
};

矢量旋转操作

Vector<dimensions, TValue> rotate(const Vector<3, TValue> axis, float angle){
        Quaternion<TValue> R = Quaternion<TValue>::rotation(axis, angle);
        Quaternion<TValue> V = (*this);
        Vector<dimensions, TValue> result = R * V * R.conjugate();
        return result;
}

照相机方法

Camera::Camera(Vector<2, int> windowSize, float fov, float near, float far):
m_uvn(Matrix<4, float>::identity()),
m_translation(Matrix<4, float>::identity()),
m_ar(windowSize[Dimensions::X] / (float)windowSize[Dimensions::Y]),
m_fov(fov),
m_near(near),
m_far(far),
m_position(),
m_forward({ { 0, 0, 1 } }),
m_up({ { 0, 1, 0 } })
{
    setViewMatrix(Matrix<4, float>::identity());
    setProjectionMatrix(Matrix<4, float>::perspective(m_ar, m_near, m_far, m_fov));
};
Matrix<4, float> Camera::getVPMatrix() const{
    return m_vp;
};
const Vector<3, float> Camera::globalY = Vector<3, float>({ { 0, 1, 0 } });
void Camera::setProjectionMatrix(const Matrix<4, float> p){
    m_projection = p;
    m_vp = m_projection * m_view;
};
void Camera::setViewMatrix(const Matrix<4, float> v){
    m_view = v;
    m_vp = m_projection * m_view;
};
void Camera::setTranslationMatrix(const Matrix<4, float> t){
    m_translation = t;
    setViewMatrix(m_uvn * m_translation);
}
void Camera::setPosition(Vector<3, float> position){
    if (position != m_position){
        m_position = position;
        setTranslationMatrix(Matrix<4, float>::translation(-position));
    }
};
void Camera::moveForward(float ammount){
    setPosition(m_position + (m_forward * ammount));
}
void Camera::moveRight(float ammount){
    setPosition(m_position + (getRight() * ammount));
}
void Camera::moveUp(float ammount){
    setPosition(m_position + (m_up * ammount));
}
void Camera::setLookAt(Vector<3, float> target, Vector<3, float> up){
    Vector<3, float> newUp = up.normalize();
    Vector<3, float> newForward = target.normalize();
    if (newUp != m_up || newForward != m_forward){
        m_up = newUp;
        m_forward = newForward;
        Vector<3, float> newLeft = getLeft();
        m_up = newLeft * m_forward;
        m_uvn = generateUVN();
        setViewMatrix(m_uvn * m_translation);
    }
};
void Camera::rotateX(float angle){
    Vector<3, float> hAxis = (globalY * m_forward).normalize();
    m_forward = m_forward.rotate(hAxis, angle).normalize();
    m_up = (m_forward * hAxis).normalize();
    m_uvn = generateUVN();
    setViewMatrix(m_translation * m_uvn);
}
void Camera::rotateY(float angle){
    Vector<3, float> hAxis = (globalY * m_forward).normalize();
    m_forward = m_forward.rotate(globalY, angle).normalize();
    m_up = (m_forward * hAxis).normalize();
    m_uvn = generateUVN();
    setViewMatrix(m_translation * m_uvn);
}
Vector<3, float> Camera::getRight(){
    return (m_forward * m_up).normalize();
}
Vector <3, float> Camera::getLeft(){
    return (m_up * m_forward).normalize();
}

};

我猜问题在于我的四元数的实现或我使用它的方式，但由于系统的复杂性，我似乎无法进一步确定问题。由于遇到了奇怪的bug，我不确定是否只是我试图实现相机的方式有问题?

教程

• https://www.youtube.com/watch?v=1Aw1PDu33PI
• http://www.gamedev.net/page/resources/_/technical/math-and-physics/a-simple-quaternion-based-camera-r1997

Quarternion/矢量数学

• http://mathworld.wolfram.com/Quaternion.html
• https://en.wikipedia.org/wiki/Cross_product
• http://ogldev.atspace.co.uk/www/tutorial13/tutorial13.html
• http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/index.htm