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generalization process is to increase the distance between
objects by moving the weaker objects. In order to achieve this
goal, the forces acting from the mass center of the object
towards the minimal distance need to be calculated, with the
direction of the force issuing from the stronger object and
affecting the weaker object.
3.3 Implementing Actions of Forces
The actions of forces on each object control and determine its
behavior. A middle object with many forces from surrounding
objects is under higher risk of being deleted if the surrounding
objects are much stronger. Alternatively, based on the type of
the object and its surrounding objects, the object will be
clustered with them if they are all of the same type and endowed
with more or less the same power level. A spatial conflict is
resolved by displacing the weaker object in accordance with the
value and the direction of the unified force affecting it.
4. RESULTS
In this chapter the suggested method is demonstrated on a group
of polygonal entities. A map of buildings in a certain area is
given, each building is described as a closed polygon composed
of a known number of vertices. The numeric parameters for
each object are calculated — the area of the polygon, its
perimeter and its compactness. A convex hull circumscribing
the polygon, and the minimal rectangle circumscribing the
convex hull are computed. The determination of principal axes
enables computing the polygon solidity and thus the orientation
of the surrounding rings for the fitting rings analysis. A
constrained Delaunay Triangufation is applied by forcing the
building edges to become part of the triangle edges formed by
the triangulation, as depicted in Figure 7.
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i 1226 1.2262 1.2264 1.2268 1.2268 1.227 12272
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Figure 7. Constrained Delaunay triangulation
The free surrounding area for each object was calculated as the
sum of the area of the triangles stretched between a given object
and surrounding objects in the intermediate space. The
surrounding objects connected to the free area of the given
object are defined as its "affecting neighbors". Tolerance may
be calculated according to the desired map scale and rings
analysis. The width of the rings is equal to the tolerance value
and the number of rings is calculated as a function of ring
width, object area and its free surrounding area. As depicted in
Figure 8, the number of rings needed for the different buildings
of the given set as shown in the histogram, is about the same for
all buildings.
grammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
| Number of Rings
4
the number of rings
+ ALL 5
e E 45 » 2 10 0
the building number
Figure 8. Number of calculated rings
Thus, each object has its power value calculated as a function
of the density derived from the rings analysis, and shape
parameters. The values of the powers are presented in Figure 9,
as a "colored scheme".
Legend
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Figure 9. Powers values of buildings
Interaction between the building powers produces and is
expressed by forces as shown in Figure 10. Large numerical
values of forces evolving between close objects are a warning of
potential spatial conflict.
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Figure 10. A force solving spatial conflict
The final results are derived from translating the action of forces
to the suitable generalization operator according to the value of
the balance of forces and its direction as follows (Figure 11):
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