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Figure 3. Decomposition of geographic measure (Step 1)
alphanumeric and spatial functions used for the
aggregation are dependent: used spatial func-
tion dictates alphanumeric functions that are
allowed for non-spatial attributes. This implies
a redefinition of the OLAP additivity concept
for spatio-multidimensional databases. Existing
spatio-multidimensional models do not complete-
ly investigate this issue, which covers different
research domains: multidimensional databases,
geostatistic models and Geographic Information
Systems (GIS) as discussed in the previous sec-
tion. Let us consider the application of Figure 1,
and let us suppose we need to get information at
the year level. A Roll-Up operation on the year
level aggregates the geographic measures Zone A
and Zone B. In such a situation, how to aggregate
these geographic objects?
Using union to aggregate the geometries, que-
ries like: “ Where and how many trees have been
damaged by some fires during 1978? ” (Query 1)
can be answered.
To calculate the number of damaged trees
aggregating on the time dimension, we propose
to apply the average operator, as the number of
trees is non-additive, and then to sum all these
averages in order to have the total of trees in the
merged zone. More in details, Zone A (resp. Zone
B) is first splitted into two zones (Zone 1 of A and
Zone 2 of A (resp. Zone 1 of B, and Zone 2 of
B)), and then its alphanumeric attributes values
are recalculated (trees and area) (Figure 3). Please
note that a user-defined function is used to calculate
alphanumeric non-derived attributes of geographic
measure. The number of trees is calculated as a
weighted average on the surface. Areas of Zone
1 of A and of Zone 2 of A are the same (55), and
a weighted average on the surface is used for the
number of trees. Then, this latter is the same (10)
for the two new zones. By the same way, spatial
and alphanumeric attributes values of Zone 1 of
B and Zone 2 of B are calculated.
Then, using these geographic objects, we
calculate another set of geographic objects ap-
plying the average to the number of trees for the
geographic objects with the same geometry and
coordinates (Figure 4). We use average because
the aggregation is made on the time dimension,
which requires not counting several times the
same tree. For instance in figure 3, Zone 2 of A
and Zone 1 of B have the same geometry and
coordinates, and some trees (note that the number
of trees varies in time) (Figure 3). Then, from
these two geographic objects, we create a new
geographic object Zone V2 whose geometry is
the same as the ones of Zone 2 of A and Zone 1
of B and whose number of trees is the average
(8=(10+6)/2) (Figure 4).
Finally, we apply union to these zones and sum
the numbers of trees (Figure 5). In particular, the
geometry of Zone E is the union of the geometries
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