How to check whether mouse clicked over a polygon in OpenGL?

Question

I'm trying to make a color picker tool in OpenGL. It works you can use the code below. However there is one glaring issue, if you test the program you will find that if you click the black background, the color selected will become black. So my question is how do I change the code such that it recognizes which polygon I clicked or recognizes that I clicked on something or a polygon.

#include <GL/glew.h>
#include <GLFW/glfw3.h>
#include <iostream>
#include <cmath>
#include <iterator>

//static void mouseButtonCallback(GLFWwindow* window, int button, int action, int mod);
static void mouse_cursor_callback(GLFWwindow* window, double xpos, double ypos);
float randfloat(){
  float r = ((float)(rand() % 10))/10;
  return r;
}
class RGB{
  public:
    float r;
    float g;
    float b;
    void setColor(float _r, float _g, float _b){
      r = _r;
      g = _g;
      b = _b;
    }
};
RGB selected_col;
RGB mixColor(RGB color1, RGB color2){
  float r = 0;
  float g = 0;
  float b = 0;
  r = sqrt((pow(color1.r,2)+pow(color2.r,2))/2);
  g = sqrt((pow(color1.g,2)+pow(color2.g,2))/2);
  b = sqrt((pow(color1.b,2)+pow(color2.b,2))/2);
  RGB a;
  a.setColor(r,g,b);
  return a;
}


int main() {
  int side_count;
  std::cout<<"Type the no. of sides: "<<std::endl;
  std::cin>>side_count;
  if(side_count < 3){
    return 1;
  }
  srand((unsigned)time(0));
  float rs[side_count];
  float gs[side_count];
  float bs[side_count];
  RGB colors[side_count];
  for (int i=0;i<side_count;i++)
  {
    rs[i] = randfloat();
    gs[i] = randfloat();
    bs[i] = randfloat();
    colors[i].setColor(rs[i],gs[i],bs[i]);
  }

  GLFWwindow* window;
  if (!glfwInit())
    return 1;
  window = glfwCreateWindow(400, 400, "Window", NULL, NULL);

  //glfwSetMouseButtonCallback(window, mouseButtonCallback);
  glfwSetCursorPosCallback(window, mouse_cursor_callback);

  if (!window) {
    glfwTerminate();
    return 1;
  }
  glfwMakeContextCurrent(window);
  if(glewInit()!=GLEW_OK)
    std::cout<<"Error"<<std::endl;
  RGB mcol = colors[1];
  for(int i=0;i<side_count-1;i++)
  {
    mcol = mixColor(mcol, colors[i+1]);
  }
  while(!glfwWindowShouldClose(window)) {
    glClear(GL_COLOR_BUFFER_BIT);
    glBegin(GL_POLYGON);
      glColor3f(mcol.r,mcol.g,mcol.b);glVertex2f(0,0);
      //glColor3f(1.0f,0.0f,0.0f);glVertex3f(-0.5f,0.0f,0.0f);
      for(int i=0; i<=side_count;i++)
      {
        float r = rs[i%side_count];
        float g = gs[i%side_count];
        float b = bs[i%side_count];
        float x = 0.5f * sin(2.0*M_PI*i/side_count);
        float y = 0.5f * cos(2.0*M_PI*i/side_count);
        glColor3f(r,g,b);glVertex2f(x,y);
      }
    glEnd();
    glBegin(GL_QUADS);
    glColor3f(selected_col.r, selected_col.g, selected_col.b);glVertex2f(-1.0f,0.5f);
    glColor3f(selected_col.r, selected_col.g, selected_col.b);glVertex2f(-.5f,0.5f);
    glColor3f(selected_col.r, selected_col.g, selected_col.b);glVertex2f(-.5f,1.5f);
    glColor3f(selected_col.r, selected_col.g, selected_col.b);glVertex2f(-1.0f,1.5f);
    glEnd();
    glfwSwapBuffers(window);
    glfwPollEvents();
  }
  glfwTerminate();
  return 0;
}

/*static void mouseButtonCallback(GLFWwindow* window, int button, int action, int mods){
  if(button == GLFW_MOUSE_BUTTON_LEFT && action == GLFW_PRESS){
    double xPos, yPos;
    glfwGetCursorPos(window, &xPos, &yPos);
    //std::cout<<"X: "<<xPos<<" Y: "<<yPos<<std::endl;
    double x=xPos;
    int height,width;
    glfwGetWindowSize(window, &width, &height);
    double y = height - yPos;
    unsigned char pixel[4];
    glReadPixels(x, y, 1, 1, GL_RGB,GL_UNSIGNED_BYTE, &pixel);
    selected_col.setColor((float)pixel[0]/255,(float)pixel[1]/255,(float)pixel[2]/255);
    //std::cout<<"R: "<<selected_col.r<<" G: "<<selected_col.g<<" B: "<<selected_col.b<<std::endl;
  }
}*/
void mouse_cursor_callback( GLFWwindow * window, double xpos, double ypos)  
{

  if (glfwGetMouseButton(window, GLFW_MOUSE_BUTTON_LEFT) == GLFW_RELEASE) 
  {
     return;
  }

  double xPos, yPos;
  glfwGetCursorPos(window, &xPos, &yPos);
  //std::cout<<"X: "<<xPos<<" Y: "<<yPos<<std::endl;
  double x=xPos;
  int height,width;
  glfwGetWindowSize(window, &width, &height);
  double y = height - yPos;
  unsigned char pixel[4];
  glReadPixels(x, y, 1, 1, GL_RGB,GL_UNSIGNED_BYTE, &pixel);
  selected_col.setColor((float)pixel[0]/255,(float)pixel[1]/255,(float)pixel[2]/255);
  //std::cout<<"R: "<<selected_col.r<<" G: "<<selected_col.g<<" B: "<<selected_col.b<<std::endl;
}