Sampling theorem In order to accurately reconstruct a signal from a periodically sampled version of it, the sampling frequency must be at least twice the maximum frequency of the signal. (Nyquist’s theorem) Due to limited resolution in the spatial (pixel-size) or colour domain, we are forced to under sample. This results in effects called aliasing.

Anti-aliasing To reduce the effect of aliasing various anti-aliasing techniques can be applied. Some examples are: Low-pass filtering (poor mans anti-aliasing) Area-sampling (colour proportional to area) Super-sampling (more samples than pixels) Dithering (anti-aliasing in the colour domain)

Area-sampling Intensity proportional to the area covered by the object. Simplified version: Intensity proportional to (1-distance to pixel)

Super-sampling Normal rasterisation, in a frame-buffer of higher resolution than the screen. Average the intensity of the covered sub- pixels when setting the real pixel value. 6/9 green + 3/9 white

Anti-aliasing solves the problem of sliver as well as the problem of shared vertices. Sliver