I've just finished the LFS book and my Linux system is working right now. I want to use OpenGL to display graphics on the screen, while the only installed package right now are those described on http://www.linuxfromscratch.org/lfs/view/stable/chapter03/packages.html.
I don't want to install something like Gnome, KDE or X.org. Instead, I want to use OpenGL directly from my software. Is this possible, and how can I do this? Or is it just as easy (I don't think so :'p) as writing an OpenGL application which runs full screen?
You don't have to install Gnome or KDE. These are used to managed windows, and you can launch graphical applications without having a window manager.
Therefore, you'll have to install a X server. The X server is responsible of drawing things on your screen. Without X server, you can't launch graphical applications.
Once X has been installed, launch it, export your DISPLAY environment variable, and the rest is like writing an OpenGL application which runs full screen :-)