OpenGL: Quads seemingly not culled properly - c++

Question

I have built a simple scene like the following:
The problem is, the blue shape is lower than the red one but somehow bleeds through. It looks proper when I rotate it like the following:
From what I searched this could be related to the order of vertices being sent, and here is my definition for those:
Shape* Obj1 = new Quad(Vec3(-5.0, 5.0, 0.0), Vec3(5.0, 5.0, 0.0), Vec3(5.0, 5.0, -10.0), Vec3(-5.0, 5.0, -10.0));
Shape* Obj2 = new Quad(Vec3(-5.0, 3.0, 0.0), Vec3(5.0, 3.0, 0.0), Vec3(5.0, 3.0, -10.0), Vec3(-5.0, 3.0, -10.0));
The Vec3 class just holds 3 doubles for x,y,z coordinates. I add these Vec3 classes to a vector, and iterate through them when I want to draw, as such:
glBegin(GL_QUADS);
for (auto it = vertex_list.begin(); it != vertex_list.end(); ++it)
glVertex3d(it->get_x(), it->get_y(), it->get_z());
glEnd();
Finally, my settings:
glEnable(GL_ALPHA_TEST | GL_DEPTH_TEST | GL_CULL_FACE);
glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST);
glAlphaFunc(GL_GREATER, 0.0f);
glViewport(0, 0, WINDOW_X, WINDOW_Y);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glFrustum(-1.0, 1.0, -1.0, 1.0, 1.0f, 300.0);
// camera origin xyz, point to look at xyz, camera rot xyz
gluLookAt(10, 10, -20, 2.5, 2.5, -10, 0, 1, 0);

Answer 1

You should enable depth test, face culling and alpha testing separately.
glEnable(GL_DEPTH_TEST);
glEnable(GL_CULL_FACE);
They are not flags. You cannot use them in that way.

Answer 2

See glEnable:
glEnable — enable or disable server-side GL capabilities
void glEnable(GLenum cap);
cap Specifies a symbolic constant indicating a GL capability.
This means the paramter of glEnable is a constant and not a set of bits and GL_ALPHA_TEST, GL_DEPTH_TEST, GL_CULL_FACE are symbolic constats and not bits of a bit set.
Change your code like this:
glEnable(GL_ALPHA_TEST);
glEnable(GL_DEPTH_TEST);
glEnable(GL_CULL_FACE);
See OpenGL Specifiction - 17.3.4 Depth Buffer Test, p. 500:
17.3.4 Depth Buffer Test
The depth buffer test discards the incoming fragment if a depth comparison fails. The comparison is enabled or disabled with the generic Enable and Disable commands using target DEPTH_TEST.
See OpenGL Specifiction - 14.6.1 Basic Polygon Rasterization, p. 473:
Culling is enabled or disabled by calling Enable or Disable with target CULL_FACE.