The goal of this handout is to describe the mathematical foundations of sampling and aliasing.
Aliasing is a potential problem whenever something continuous is represented by a set of discrete samples. In computer graphics, aliasing is most pervasive when displaying idealized objects with sharp lines and edges. The resulting staircase-like artifacts are known as jaggies. Aliasing also occurs when images are scaled, rotated or even translated. Elimination of aliasing is particularly important for computer-generated animations, where it leads to a number of highly objectionable perceptual artefacts.
Aliasing is often confused with quantization error. Since
aliasing is caused by sampling, it is related to resolution,
which for images measured in number of pixels or pixel density.
Quantization is the roudning off of the color of each pixel into a
finite set of values. It is related to the number of bits of
color. Computer video modes are generally specified in terms of
these parameters (e.g.
resolution with 24-bit
color).
In this handout we will not consider quantization error. We will treat computer arithmetic as if it operated with infinite precision. If the techniques described in this handout are implemented using 32-bit floating point calculations on 8-bit-per-channel source images, then roundoff error may be neglected.