I'm writing a Minecraft like static 3d block world in C++ / openGL. I'm working at improving framerates, and so far I've implemented frustum culling using an octree. This helps, but I'm still seeing moderate to bad frame rates. The next step would be to cull cubes that are hidden from the viewpoint by closer cubes. However I haven't been able to find many resources on how to accomplish this.
If you have surfaces close to the camera, you can create a frustum which represents an area that is not visible, and cull objects that are entirely contained in that frustum. In the diagram below, C is the camera, | is a flat surface near the camera, and the frustum-shaped region composed of . represents the occluded area. The surface is called an antiportal.
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(You should of course also turn on depth testing and depth writing as mentioned in other answer and comments -- it's very simple to do in OpenGL.)