Question

我正在尝试在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度旋转。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正常，直到相机从+ z旋转约45度此时向上或向下倾斜相机似乎会使相机绕目标轴倾斜，从而转动向上矢量。

当相机朝向-z向上或向下倾斜时，会产生相反的错觉，向上和向下倾斜向上倾斜。

我已经看到其他实现建议使用非uvn系统，其中四元数被累积为一个，其将当前方向描述为从任意任意起始角度的增量。这听起来不错，但我似乎无法确切地知道如何实现这一点，特别是从此转换为视图矩阵。

在其他地方，我读到了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，请纠正我但是我的理解是你应用两次旋转的顺序并不重要。

相关的源代码片段：

Quarternion Operations

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;
}

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();
}

};

我猜测问题出现在我的四元数实现或我使用它的方式上，但由于系统的复杂性，我似乎无法再解决这个问题了。由于遇到了奇怪的错误，我不确定我试图实现相机的方式是否有问题？

教程

四分之一/矢量数学

如何在现代opengl中正确实现四元数相机？

0 个答案: