Geoscience Reference
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whereby:
R
i
= 1 / A
i
(absolute local density of the i-th point)
R
k
=
1 / A
k
(absolute local density of the k-th point)
A
i
=
the area of the Voronoi polygon containing the i-th point
A
k
=
the area of the Voronoi polygon containing the k-th point
n
= the number of the points
We assume that
R_1
is an array to capture all values of the relative density
on the initial map. The i-th element of
R_1
is
r
i
_1
.
R_2
is an array to cap-
ture all values of the relative density on the reduced map. The i-th element
of
R_2
is
r
i
_2
. The goal is to compare the change of relative local density
between the initial map and the reduced map point by point. Therefore the
following steps are applied:
1.
Test
R_1
, and eliminate
r
i
_1
if the i-th point on the initial map had
been eliminated.
2.
Sort
R_1
in increasing order and organize the elements in
R_2
accord-
ing to the sequences of the values of the corresponding points in
R_1
.
parison of the relative local density change.
With a plot of point numbers (x) and relative local density (y) of both, the
points of the initial as well as of the reduced map, the similarity can be
compared visually. As more the both curves increase in roughly the same
way, as more similarly the relative local densities are.
The relative local density is based on Voronoi areas. For our 3D-point data
we extended the method and used Voronoi volumes instead of Voronoi
areas in Formula (7) and computed the relative local densities based on
Voronoi volumes.
3- Results
3.1 Applying the enhanced PT to a test data set
We used as an original dataset airplane data containing the coordinates
(x,y,z) of 405 airplanes. Our sample dataset have been provided by the
