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Types Rf iQfRrPatiRQ
0easures
StatisticaO
1uPber Rf pRiQts
ThePatic
IPpRrtaQce vaOue
TRpRORgicaO
1eighbRriQg pRiQts
(e.g. Voronoi neighbors, fixed radius
neighbors, k-nearest neighbors, etc.)
0etric
AbsROute ORcaO deQsity
ReOative ORcaO deQsity
DistributiRQ raQge
Table 1: Relations between measures and types of information (Yan and Weibel 2008 )
Within cartographic generalization a number of point selection algorithms
can be found in literature, among others the Settlement-Spacing Ratio
Algorithm, the Gravity-modeling algorithm, the Distribution-coefficient con-
trol algorithm, the Set-segmentation algorithm and the Quadrat-reduction
algorithm, which all are proposed in Langran and Poicker (1986). Further
algorithms are the Circle-growth algorithm by Van Kreveld et al. (1997),
the Quadtree-based algorithm by Burghardt et al. (2004) and a Simplifica-
tion algorithm by De Berg et al. (2004). The Settlement-Spacing Ratio
Algorithm and the Circle-Growth Algorithm are also described and evaluated
in Li (2007). Yan and Weibel (2008) summarized, evaluated and compared
these algorithms and introduced a new algorithm based on the Voronoi
diagram where all four types of information (statistical, thematic, topologi-
cal, and metric) are transmitted in a point generalization process.
The Polarization approach, proposed by Qian (2006), is a further algorithm
for point generalization and it is the basis of this approach and described in
more details in the next chapter. Table 2 gives an overview about the
transmitted information of each point-generalization method.
The Set-segmentation algorithm and the Quadrat-reduction algorithm re-
quire a high level of human intervention. As shown in Table 2 all algo-
rithms which consider the transmission of thematic information use an
importance value for each point of the original data set. What if there is no
importance value, if all points have the same value or if just very few of
the points have a different importance value? Thus the Circle-growth algo-
rithm, the Settlement-Spacing Ratio Algorithm, the Voronoi-based algo-
rithm, the Gravity-modeling algorithm and the Distribution-coefficient
control algorithm do not work at all. In these cases the importance value of
 
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