N 
\ 
\ a: Lake Skagern 
\ b: Lake Vànern 
C: Lake Drevviken 
a bic 
  
  
  
  
  
  
  
f 
Figure 9. Relative inclinations of spectra of shorelines of Swedish 
lakes. 
Comparable spectra were obtained for map scales varying from 1:10 000 
to 1:1 000 000, confirming the intuitive ability of the good carto- 
grapher to maintain the appropriate degree of details at the diffe- 
rent map scales. 
Also with automatic generalization, this proper impression of the 
roughness of the terrain should be preserved. Gottschalk observed 
already a decade ago, that good results in generalization are ob- 
tained by simply reducing the contour map to a smaller scale. This 
operation is correct in the light of our theory for dimension of con- 
tours close to 1. 
In general, for arbitrary D values, all features (amplitudes) below 
the desired resolution limit, should be Suppressed. This can be pro- 
perly done by filtering all frequencies higher than that corresponding 
to the resolution limit. Note, that there exists a non-linear relati- 
onship between spectrum and frequency, thus a scale reduction "a" 
leads to a change in the frequency limit Corresponding to "aa/2" (the 
spectrum represents the second power of the amp itudes). 
The following example (Figure 10), illustrates the idea of automatic 
generalization. Let the upper left curve be a part of a contour line, 
at the map scale 1:5 000. The minimum discernible amplitude at that 
scale is, 0.5 meter (S = 0.25 mê) corresponding to a highest frequency 
of 7.7-10-3, as shown on the spectrum. 
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