T4(u,x): 
T5(x,c): 
T6(c,g): 
T7(g,s): 
Associates each geographical unit u with an attribute value x. 
For reasons of simplicity we consider only one attribute at a 
time. For the multivariate mapping case it suffices for the 
present discussion to think of the process as being repeated 
for each attribute involved. T4 is obtained by copying the re 
quired information from the attribute data file which is also 
a part of the permanent data base. 
Identifies for each attribute value x a class c (representing a 
range of values on the attribute scale) to which it belongs. T5 
is the result of some classing operation, usually carried out 
by algorithmic means. 
Assigns to each attribute class c a graphic symbol code g (a 
code signifying a gray level, a color tone, a shading pattern 
etc.). T6 is produced by graphic symbol selection algorithms or 
by interactive user-controlled intervention. The latter will be 
discussed in conjunction with a color CRT as output device in 
section 5* 
Associates each graphic symbol code g with an actual analog 
symbol s. T7 is a digitally controlled hardware implementation. 
Clearly, this is a minimal model in that it comprises the most basic 
steps only. However, it is sufficient in the context of the present dis 
cussion. We note also that not all of the relations listed must be phy 
sically present as tables during the mapping process necessarily. Some 
may be expressed compactly in the form of an assignment rule or an equa 
tion (for example, T5 or T6). 
We are now in a position to formulate the complete mapping process as a 
tabular product: 
M(m,s) = Tl(m,p).T2(p,r).T3(r,u),Tl+(u,x).T5(x,c).T6(c,g).T7(g,s) (4) 
where we use M instead of T1.7 for the result, which is a map, a 2-di 
mensional table in analog form, produced by putting some graphic symbols 
s at appropriate locations m by means of some output device. We observe 
that the whole process can be interpreted as a linked sequence of table 
lookups. However, it is clear that an actual realization cannot start 
with T1 and end with T7 or v.v. (working backward) since both T1 and T7 
are hardware-implemented D/A conversions activated at display time only. 
One must start with digital operations somewhere between T1 and T7 and 
work outward in both directions. The order in which tabular products 
are formed leads to different mapping techniques as explained in the 
next section. 
3. ALTERNATIVE MAPPING TECHNIQUES DERIVED FROM THE RELATIONAL MODEL 
We now direct our attention to the purely digital part of the process, 
i.e., the tables involved in the product T2.T3.T4.T5.T6. It is concei 
vable that one overall table T2.6 could be produced before the link with 
the output hardware in the form of T1 and T7 is established. However, we 
will see that it normally makes sense to produce two tables, say TA and 
TB, so that TA can be linked with T1 and TB with T7 and the final map is 
generated in the form 
M = (T1 . TA) . (TB . T7) . (5) 
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