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One problem that any rendering system must deal with, no matter which approach it takes, is the sampling problem. Essentially, the rendering process tries to depict a continuous function from image space to colors by using a finite number of pixels. As a consequence of the Nyquist theorem, the scanning frequency must be twice the dot rate, which is proportional to image resolution. In simpler terms, this expresses the idea that an image cannot display details smaller than one pixel.
If a naive rendering algorithm is used, high frequencies in the image function will cause ugly aliasing to be present in the final image. Aliasing typically manifests itself as jaggies, or jagged edges on objects where the pixel grid is visible. In order to remove aliasing, all rendering algorithms (if they are to produce good-looking images) must filter the image function to remove high frequencies, a process called antialiasing.
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