ABSTRACT
In the algorithms to be presented in the later chapters, mathematical tools at various levels are involved. To facilitate those discussions, this chapter provides some basic mathematical background.
To make a spatial representation possess a certain level of metric quality, a
coordinate system
needs to be employed. The
Cartesian coordinate system
is the basic system in Euclidean space and is most familiar to us. It could be threedimensional (3-D) or 2-D. The latter is a result of the orthogonal projection of the former. A
geographical coordinate system
is also a fundamental system for spatial representation, consisting of longitude and latitude. A geographical coordinate system can be defined on a sphere (or spheroid) or on a 2-D plane. The latter is a result of a projection of the former. Such a projection is called a
map projection
.
