Geography Reference
In-Depth Information
polygon with the shortest possible perimeter that fully encompasses it (Parent
2014
). In other words, the index refers about the shape compactness. The more
extremities (e.g. spikes) the shape has, the lower the index value. Ideally, in the case
of a circle, the index value is equal to 1. Output values of Normalized Detour index
(Fig.
2d
) are relatively high with no major extremes, in this case. However,
interesting trapezoidal graph has St. Maurice church. This is because the general-
ization algorithm preserves only a few big spikes at simplification tolerance ranging
from 20 m to 300 m. This is desirable to keep typical features of the shape on one
hand, but on the other, these sudden changes may confuse the cartographer.
Whenever big spikes are eliminated, the shape becomes more compact and Nor-
malized Detour index arise. Similar interpretation could be done with the other
building ground plans. In general, the higher level of generalization, the higher
Normalized Detour index value.
Normalized Perimeter index transforms shape perimeter value into relative
number using Equal Area Circle. It is the ratio of shape perimeter to perimeter of
Equal Area Circle. This index indicates how much the shape differs from the ideal
circular shape. Lower the value, the less compact the shape. In the generalization
process, this index should gradually increase. This presumption is proven in Fig.
2e
.
Also in this case, there are some exceptions, especially in the case of Houses of
Parliament and St. Maurice church at the tail of the graph. Level of generalization at
simplification tolerance values of 200 m, 300 m (Houses of Parliament) and 320 m
(St. Maurice) affects the shape and preserves higher complexity of the shape
(Fig.
2i
), instead of simplifying the shape. This should be stressed, because geo-
metric generalization procedures should preserve core geometry characteristics.
This requirement was violated in this particular case.
Normalized Spin index is appropriate for measuring compactness when focus is
on shape extremities (Parent
2014
). Again, the higher the index value the more
compact the shape (close to the circularity). Abrupt and steep increase of Normal-
ized Spin index values of Petronas Towers (Fig.
2f
) underlined the specific char-
acter of its ground plan. In most cases, Petronas Towers holds its shape metrics
values constant until the level of generalization at simplification tolerance value of
200 m is reached. At this level, the shape is suddenly transformed into the rectangle
with no intermediate stage (see Fig.
1b
). Looking at the Lund University graph, for
example, it is possible to see that it loses extremities of its shape more or less
constantly. In this case, geometry generalization is the most effective between
10 and 80 m simplification tolerance values. Shape metrics values fluctuate the
most in case of Houses of Parliament ground plan generalization. Unexpected
increase of its shape extremities can be best identified at simplification tolerance
values ranging 60 to 200 m. Generalization algorithm simplified the shape at values
80 and 100 m, but afterwards it resulted into more complicated shape (Fig.
2h
).
Rest of the calculated shape metrics shows analogous findings. Their graphs are
depicting shape metrics values progress at various generalization levels revealing
other nuances but not so significantly as presented ones. Moreover, according to
Parent (
2014
), normalized metrics tend to be correlated with each other, therefore it
is redundant to present all shape metrics graphs in this article.
