C++ OpenGL/GLFW：在投影、平移和旋转四边形后，查找鼠标单击的四边形坐标

我在OpenGL中有一个四边形（在两个方向上都在[-1]之间延伸）。我在其顶点上执行正交投影，然后像这样旋转和平移它：

glm::Mat4 map_mvp;
glm::quat rotation = glm::quat(glm::vec3(0,0,-yaw));
map_mvp = glm::toMat4(rotation) * map_mvp;
map_mvp = glm::translate(map_mvp,glm::vec3(-translate_x,translate_y,0));
map_mvp = glm::ortho(-width/map_zoom,width/map_zoom,-height/map_zoom,height/map_zoom ) * map_mvp;

glUseProgram(map_program);
glUniformMatrix4fv(glGetUniformLocation(map_program, "mvp"), 1, GL_FALSE, glm::value_ptr(map_mvp));

根据代码的其他部分，上述代码中的各种变量（偏航、平移x等）随时间而变化。我的目标是知道GLFW窗口的任何区域的四坐标，我用它来显示我点击的窗口。我假设我可以反转投影，但是当我这样做的时候，我得到的坐标看起来完全是随机的，而且是不正确的。我使用的代码是（在鼠标单击的回调中）：

有人能看出我哪里出了问题吗

    double xpos, ypos;
    glfwGetCursorPos(window, &xpos, &ypos);
    //Find click position in the same coord system as the vertices
    int pixel_width, pixel_height, virtual_width, virtual_height;
    glfwGetFramebufferSize(window, &pixel_width, &pixel_height);
    glfwGetWindowSize(window, &virtual_width, &virtual_height);
    double x_world_pos, y_world_pos, x_virt_to_pix, y_virt_to_pix;
    x_world_pos =  (2 * xpos / virtual_width - 1);
    y_world_pos = - (1 - 2 * ypos / virtual_height);

        //Inverse rotation to find map position
    glm::mat4 mvp_rev_map;
    glm::quat rotation = glm::quat(glm::vec3(0,0,yaw));
    mvp_rev_map = glm::inverse(glm::ortho(-v->width/v->map_zoom,v->width/v->map_zoom,-v->height/v->map_zoom,v->height/v->map_zoom)) * mvp_rev_map;
    mvp_rev_map = glm::translate(mvp_rev_map,glm::vec3(translate_x,-translate_y,0));
    mvp_rev_map = glm::toMat4(rotation) * mvp_rev_map;

    // Find z pixel depth
    GLfloat zpixel ;
    glm::vec2 screen_pos=glm::vec2(xpos, ypos);
    glm::vec2 pixel_pos=screen_pos * glm::vec2(pixel_width, pixel_height) / glm::vec2(virtual_width, virtual_height); // note: not necessarily integer
    pixel_pos = pixel_pos + glm::vec2(0.5f, 0.5f); // shift to GL's center convention
    glReadPixels((GLint)pixel_pos.x,(GLint)pixel_height-1-pixel_pos.y,1,1,GL_DEPTH_COMPONENT,GL_FLOAT, &zpixel);

    glm::vec4 quad_pos = mvp_rev_map * glm::vec4(x_world_pos, y_world_pos, (float)zpixel, 1.0);