capability for the arbitrary selection of color tones. To this end the 
available tones are displayed on the CRT, i.e., the user is effectively 
presented with a copy of relation table T7(g,s). Because the color space 
is 3-dimensional the presentation must be broken down into a sequence of 
2-dimensional intersections (color planes) which provides a 'walk' 
through the color space. The user can then select a desired tone from 
any plane by cursor control and assign it to a particular class. 
Such a walk through the color space could be carried out in a variety of 
ways. However, some experimentation demonstrates that an attractive so 
lution is to proceed along the intensity axis, i.e., the cube diagonal 
from black (0) to white (W), with planes that are orthogonal to this 
axis and will change in form from a point to a triangle to a hexagon and 
back again to a triangle and a point (see Fig.2). This method can be in 
terpreted as being based on an IHS (intensity-hue-saturation) rather 
than an RGB definition of colors. The color tones contained in a given 
plane will all have equal intensity but will differ in hue and satura 
tion. The latter two variables can be thought of as forming a discrete 
polar coordinate system. 
Let us make the following assumptions: 
1. For each primary there are p different intensity levels. They are 
numbered consecutively from 0 to P (= p-l). 
2. Equally, saturation values range from 0 to P, where full saturation 
P is encountered along the spectral periphery of the color cube (see 
Fig.2). 
3. Hues are defined as increasing integers along the same periphery, 
starting with the value 0 for red as an arbitrary reference, and pro 
ceeding over green and blue back to red. 
Then the following set of equations, given without further explanation, 
provides a discrete transformation from RGB to IHS coordinates: 
i = r + g + b 
s = max(r,g,b) - w 
I round((P/s)(s + i - 2r - w)) if g > b (7) 
round((P/s)(5s - i + 2r + w)) if g < b 
undefined (neutral) if s = 0 , 
where w is the white component of the color tone in question, defined by 
w = min(r,g,b). The inverse transformation is also possible but not 
shown here. 
For each cursor position in a color plane the user is provided with the 
associated IHS as well as RGB coordinates. This feature facilitates a 
systematic procedure of color scale composition (WIRTH 1982). Clearly, 
an interactive selection of color tones puts some work load on the user. 
However, it is not necessary to go through this process during each map 
ping session. Once suitable color scales have been found for a given 
number of classes the respective codes can be stored and called up again 
whenever required. 
A final note of this section concerns map readability. In conventional 
cartography the problem is solved by restricting the number of classes 
to a fairly small number (say 5 to 10). However, one may often be more 
interested in a 'true' overall impression, and this requires as many 
classes as possible. In the extreme this leads to the (quasi-) continu 
ous mapping schemes as proposed by TOBLER (1973) and SIBERT (1980). For 
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