Database Reference
In-Depth Information
Table 2. SpatialType function
intersection among all features. Figure 8 shows an
example of overlay of two maps whose geometries
are polygons.
Using the definitions previously given, we
formalize the three steps of our algorithm by
defining two functions (
DisjGeoObjects
and
OverlayGeoObjects)
and two constraints (
Vertical
Aggregation Constraint
and
Horizontal Aggrega-
tion Constraint
) for the
Geographic Aggregation
Mode
.
These two constraints allow the Geographic
Aggregation Mode ensuring a correct geographic
aggregation of geographic measures.
In particular, each alphanumeric aggregation
function ϕ of the
Geographic Aggregation Mode
is decomposed in two functions: κ and φ used
to calculate attributes values of the geographic
objects created at Step 2 and 3 respectively.
Then, the two constraints are defined on κ and φ
according to the requirements of the
Vertical
and
the
Horizontal
steps respectively.
The
Vertical Aggregation Constraint
defines
correct functions for κ considering disjoint
geographic measures using the function
Dis-
jGeoObjects
(see Figure 3), and taking into
account semantics and used dimensions (i.e.
Di-
mensionsMeasure
) of the alphanumeric attributes
(e.g. number of trees cannot be summed on the
time dimension).
For example, in order to calculate geographic
objects of Figure 3 resulting from an aggregation
on the time dimension, the
Vertical Aggrega-
tion Constraint
does not allow using the sum
(κ
nbDamagedTrees
= AVG) because number of trees is
not additive on the time dimension (κ
nbDamagedTrees
∈
AF
ω
= Min(DimensionType(nbDamagedTrees,S
y
SpatialType
AF
∑
AF
ω
AF
c
AF
U
AF
∑
AF
ω
AF
c
AF
Ω
AF
ω
AF
ω
AF
c
measure (SpatialType(AF
U
, AF
∑
) = AF
∑
). For
example, when using the union, it is possible
to sum number of trees as it is additive (AF
∑
):
SpatialType(UNION, AF
∑
) = AF
∑
(see Figure 5).
. When using spatial disaggregations (AF
Ω
), it
is not possible to sum alphanumeric attributes
values of geographic measures, but it should be
possible to use average (AF
ω
) or count (AF
c
)
(SpatialType(AF
Ω
, AF
∑
)= AF
ω
). For example,
when using intersection, it is not possible to use
sum, even if number of trees is additive (AF
∑
):
SpatialType(INTERSECTION, AF
∑
) = AF
ω
(see
Figure 6). .
Finally, if the alphanumeric attribute is not
additive (AF
ω
or AF
c
) and spatial aggregation is
used, then it is not possible to add alphanumeric
attribute values (SpatialType(AF
U
, AF
ω
) = AF
ω
and SpatialType(AF
U
, AF
c
)= AF
c
).
Correct Geographic Aggregation Mode
Before defining the Correct GeographicAggrega-
tion Mode, we need to introduce the concept of
overlay
. The GIS operator overlay takes as inputs
two maps and overlays them one on the top of the
other to form a new map. The
Union Overlay
is an
operator that takes as inputs 2 maps and returns a
map whose geometries are the set of all disjoint
geometries obtained by applying the topological
Figure 8. Union overlay
Union
Overlay
1
=
A
A0
A1
A2
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