Geoscience Reference
In-Depth Information
and allows an interpolation between two source scales as given in a
Multirepresentation Database. With Töpfer's radical law the number of
kept points ( N T ) of the original points ( N S ) is calculated by a given map
scale ( S S ) and a given reduced scale ( S T ) as followed:
Formula (1):
S
N
=
N
S
T
S
S
T
Töpfer called the equation also “law of natural dimension”
N T = number ( N ) of cartographic features represented on a map
N S = original number of points
S S = initial scale (scale1)
S T = reduced scale (scale2)
We used Töpfer's radical law to calculate the number of the points which
have to be kept for any user-defined reduced scale (scale 2).
2.1 Detailed description of the enhanced PT:
In our interactive tool first the point data set can be read in. In the case that
several points have exactly the same coordinates the data set will be
changed to containing just unique points. The user can define the desired
output dimension, 2D or 3D. In case of different time series the user also
can use an interactive slider (see Fig. 4 ) to define the moment of time so
that the corresponding coordinates will be read in. Then the user has to de-
fine the initial scale. Furthermore a maximal possible reduction scale
( S Tmax ) was calculated using Töpfer's radical law while keeping a mini-
mum of 4 points:
Formula (2): Töpfers law
2
N
S
=
S
S
T
max
S
16
Now the reduced scale or the number of points to be eliminated will be de-
fined by the user. In case of a defined reduced scale (whereby the scale
value has to be smaller than S Tmax ), the number of points which have to be
Search WWH ::




Custom Search