OpenGL is not displaying anything when looking along the y axis - opengl

Question

I am currently trying to display a red grid viewed from the top using SFML and OpenGL.
The grid plan is normal to the y axis (y axis is the vector looking to the top).
This is called before my rendering loop:
glEnable(GL_DEPTH_TEST);
gluPerspective(90.0f, (GLfloat)640/(GLfloat)480, 1.0f, 1000.0f);
Inside my rendering loop:
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
gluLookAt(0.0, -3.0, 0.0,
0.0, -0.8, 0.0,
0.0, 1.0, 0.0);
for (float x = -10.0f, x < 10.0f, x += 1.0f) {
glColor3f(1.0f, 0.0f, 0.0f);
glBegin(GL_LINES);
glVertex3f(x, -0.5f, -10.0f);
glVertex3f(x, -0.5f, 10.0f);
glVertex3f(-10.0f, -0.5f, x);
glVertex3f(10.0f, -0.5f, x);
glEnd();
}
window.display(); // swap buffers in SFML
I stripped the SFML part.
When I replace the gluLookAt(); part by this one (slight tilt of the camera):
gluLookAt(0.0, -3.0, 0.0,
0.0, -0.8, 0.01,
0.0, 1.0, 0.0);
or this one:
gluLookAt(0.0, -3.0, 0.0,
0.0, -0.8, 0.0,
0.0, 0.0, 1.0);
Everything is displayed fine.
I concluded that when I look exactly in the -y direction (90°), nothing is drawn. But why? Did I miss something?
My OpenGL supported version is 2.1 Mesa 10.2.4
Many thanks in advance!

Answer 1

The problem is, that you up-axis also points towards the y-axis. It is not necessary that the up-vector points exactly upwards, but it has to be different from your viewing-direction. For more details have a look at this answer
Edit: Since requested, here is the mathematical explaination:
gluLookAt generates a 3d coordinate frame, that consists of three perpendicular vectors.
Assuming the input to gluLookAt is a camera position (C), a eye-position (E), and a up-vector (U), than the matrix is constructed using the following equations:
F = C - E
f = F / |F|
U' = U / |U|
this results in two vectors that span a plane. We already know, that f (the view-vector) will be the -z axis of our final coordinate frame (opengl looks always along the negative z-axis). The x-axis can be calculated by finding the normal vector of the plane spanned by f and u and can thus be calculated via
S = f x U' (x is the cross product)
s = S / |S|
Note that the normalization would not be required if u and f are already perpendicular, but since gluLookAt does not require the real up vector this is not necessarily given. Out of the same reason we cannot use u directly as y-axis. What we are looking for is a y-vector that is perpendicular to both, f and s, which is given as:
u = s x f
The final matrix is than constructed by
| s 0 |
M = | u 0 |
| -f 0 |
| 0 0 0 1 |
Now consider your case where f = U':
When calculating S we get
S = f x U' = U' x U' = [0, 0, 0]
Since this gives a null-vector, u will also be a null-vector. In total this results in a matrix where the first two rows are all zero, and thus each vector multiplied with this matrix will end up with x and y beeing 0.
Hope this helps you. The formulas for gluLookAt are taken from here