A THEORY OF THE CARTOGRAPHIC LINE

The presented theory can be associated with an alternative explanation. A � line is a combination of a number of frequencies, each of which can be represented � by certain band-widths. The break-up of a line into series of bands, therefore, � could be equated with the stepwise removal of the high frequencies from the line. � Before going on, however, a few terms should be explained in detail. A line is � here defined as a sequence of connected points. A connection between two points in � a sequence of points is called a segment. The extent of a line is its number of � segments. We thus exclude from this discussion those lines which are defined by one � or several mathematical functions since their characteristics and problems are quite � different from the discretely identified lines. �