The following stage is "lighting" or "illumination". A scene would be awfully boring if it was completely dark and you couldn't see anything. This is a fairly complicated stage, as not only do all the light sources have to be accounted for, but depending on how that lighting affects the models, changes their colour and how they look. In normal 3D modeling, perfect lighting (or as close as possible) is expected. This often involves a lot of waiting, as anyone who's taken a course in OpenGL can tell you. Even with a powerful system, allowing POV-Ray or the equivalent program to execute ray tracing with many lights and reflective surfaces will leave you with time to go catch a nap, grab a coffee, shop for groceries, and flip through some TV.
Of course, the results are often outstanding. But if you had to wait two to 48 hours for each frame to render in your game, I think you'd find something else to do. As a result, lighting in games is more of a compromise between speed and eye candy. Usually a smaller number of lights are involved, and reflected lighting doesn't find itself involved too often. Instead only lighting from discreet sources are calculated, be they global (sky out in the open), or local (a light bulb or flashlight).
So now our scene is turned to how the camera would see it, we've ditched models and triangles we can't see from this point of view, as well as lit our scene and given our models their colour (but no texture or shading, that comes later). This is the point where we cut down on what's being computed again. While the whole scene is from our point of view, we can't possibly take in all that information on the screen. A "view frustum" is created, which ends up looking like a widening tunnel.
All the models outside of that frustum are discarded. That's the easy part mathematically. The hard part is where you have parts of triangles that are on the border, part in the view and part outside of it. These need to be "clipped".
After determining which triangles need to fall under the knife, the part that remains in view is broken up into smaller triangles that do fit. This leaves more vertices and triangles for rasterization later in the pipeline, so the idea is to attempt to clip as few triangles as possible, and arrange the ones that are clipped as efficiently as possible. Different architectures use different methods for this, and hence different speed and quality come as a result. After this stage is completed, we're left with all the triangles we're going to use.
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