Editing Rendering (computer graphics) (section)

=== Sampling and filtering ===
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–Shannon sampling theorem]] (or Kotelnikov theorem), any spatial waveform that can be displayed must consist of at least two pixels, which is proportional to [[image resolution]].  In simpler terms, this expresses the idea that an image cannot display details, peaks or troughs in color or intensity, that are smaller than one pixel.

If a naive rendering algorithm is used without any filtering, 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 use some kind of [[low-pass filter]] on the image function to remove high frequencies, a process called [[Spatial anti-aliasing|antialiasing]].