the skeletal representation of cartographic lines, areas, polygons, 
cartographic elements, and so forth. It carries positional and 
representational information. The alphabetic sign curve has a 
nonlinear functional representation, has length, and occupies no 
area. It joins at least three points on the plane or the space. It is 
part of the skeletal representation of areas, cartographic 
elements, and so forth. It carries positional and representational 
information. The alphabetic sign blank space carries only 
positional information and has no visible representation. 
There are four cartographic operations: (1) concatenation, (2) 
image construction, (3) coordinate transformation, and (4) 
addition. Concatenation is the operation which allows the 
connection of two alphabetic signs to create a more complex 
sign, two complex signs, or a complex sign and an alphabetic 
sign to create even more complex signs. 
Image construction is the operation that adds to the skeletal 
representation some or all of the Bertin (1983) visual variables: 
size, value, pattern, color, orientation, and shape, to create a 
cartographic element at the original scale. 
Coordinate transformation is the operation that takes the 
cartographic element (at the original size) and modifies it to 
reduce it to the map size, location, and orientation. 
Addition is the algebraic operation which allows insertion/ 
removal of cartographic elements (or a portion of them) to/from 
a spatial database or a map. In this operation, the graphic 
representation of a spatial database or a map are considered, at 
the beginning, as a blank space (SP) filled only with positional 
information. Then, Sp, is modified by the addition operation by 
adding (or removing) cartographic elements carrying locational 
information, resulting in a new version of the space (SP,,,). 
Cartographic rules are the regulations for constructing 
cartographic elements. There are three different sources of 
cartographic rules: (1) product planning and design, (2) element 
priority, and (3) element representation. 
Product planning and design is the process of selecting all of the 
general and particular characteristics of spatial data (for 
example, an individual map or map series). Characteristics such 
as components, scale, projection, surface of reference, units, 
specific graphic symbols to be used, and characteristics of those 
symbols are set during this process. 
Element priority is the order of placement of cartographic 
elements on the graphic representation of the terrain. Features 
with higher priority are placed before features with lower 
priority. This priority is related to each particular application 
and is generally related to the level of importance and 
permanency of terrain features. 
Element representation is how terrain features are represented 
graphically, and the interrelation of these representations. For 
example, on most topographic maps, relief is represented by 
contour lines. 
Cartographic rules can be grouped as general, layer-related, and 
priority rules. General rules apply to complete spatial data bases 
(topographic map series) as a whole. For example, the following 
rule applies to the 7.5-minute series (1:24,000 scale) of the 
USGS: 
Every 7.5-minute map should have a legend and a title block as 
part of the map heading. The title block must include the 
following information: Quadrangle and state or states’ names, 
county name, map series ID, and agency. The legend must show 
the road classification and route signs and must be placed on the 
lower-right margin of the map. 
Layer-related rules apply to each coverage of cartographic 
elements, in particular, and to intercoverage relations. There are 
rules for each one of these coverages. For example, the following 
rule applies to hydrography and hypsography, respectively: 
Two natural flowing water features cannot cross each other. 
Contour lines of the same type should not cross each other. 
The following interfamily rule applies to hydrography and 
hypsography: 
A standing water body cannot be crossed by contours. 
There are more than seventy general, coverage-related, and 
interfamily cartographic rules at this time (Ramirez, 1988), and 
as the analytical study of maps progresses, more rules are 
expected to be found. 
Priority rules are purpose dependent. Two major criteria are used 
in their establishment: importance and permanency. The most 
important cartographic features are those that will remain 
unchanged on a graphic representation (such as a map) in those 
situations where some features must be altered (for example, in 
overcrowded areas). If two features are of equal importance, then 
the most permanent is the one that will remain unchanged. 
Permanency is related to the longevity of terrain features. The 
longer a terrain feature stays without undergoing any change, the 
more permanent its cartographic representation. 
The writing mechanism of the cartographic language is the 
Universal Mapping Command (UMC) (Ramirez, 1991). The 
general expression of a UMC is: 
UMCz-«(QG(K(((cA^)^[(ciB)]^-)(«U»«V»« 
U5«Vi»)))). (1) 
A UMC is a formula-like expression that allows analytical 
representation of any graphic element of a spatial product (such 
as a topographic map). UMCs make use of the cartographic 
alphabet and cartographic operations, plus some additional 
operators (K, c, c1) to express cartographic elements. 
K is the cartographic element restriction which is one or more 
constraints imposed over the whole cartographic element. 
Topology and layer and feature constraints can be defined 
680 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996 
  
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