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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
  
generalization process in the form of rules, several authors have 
proposed and used constraints in the generalization process (e.g. 
Brassel & Weibel 1988, Ruas & Plazanet 1996, Harrie 1999, 
Ruas 2000). In this study, the generalization process is 
controlled by the power of objects. These powers have been 
determined and thus affect and act according to the process 
rules. The forces that are "developed" in each object as a result 
of the powers action are "translated" according to its value and 
direction to suit the generalization operator in respect to the 
process constraints. 
3.1 Object Power Determination 
An analogy to the interaction among a large number of objects 
can be found in electric field theory. In an electric field each 
"object" acts according to its power, affects its neighbors and is 
in turn affected by them. In this study, it is suggested to 
implement the electric field theory, assuming that the map 
generalization process will be based on "powers" of the map's 
features affecting each other. The “power” is determined as a 
function of the object’s properties, location, and the surrounding 
area and objects. The action of the power’ action controls the 
object’s behavior, thus it has to be calculated carefully, taking 
into account all affecting elements. 
Object Properties 
The aim of this research is to establish a model for a “combined 
generalization”, where the powers are calculated and 
determined in order to be able to highlight the different qualities 
of each individual object. The area is a very important element 
in such a process; since a bigger object has a higher power 
value. Different objects have different factors under the 
cartographic rules (e.g., trees might be moved easier than 
buildings). According to the map type each object has its 
relative importance value (e.g. in a tourist map hotels will be 
more highlighted than private houses). In a similar manner, high 
buildings should be "stronger" than low buildings, and the 
process prefers not to change their shape or move their location. 
Square buildings should be "stronger" than rectangular or 
elongated ones. 
In analogy to the electric field theory, the power contained in 
each object will be calculated as a function of the following 
object properties: 
1. Area: calculated at the scale of the map (size of the 
plotted object or its plotted symbol). 
Shape: calculated as a function of the compactness, 
solidity, and second axes moment ratio: 
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solidity * compactness 
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3. Height: a normalized value, given to 2D objects like 
roads, and single story houses. The value is increased 
for multistory buildings. 
4. Type: an elastic value for each object describing its 
"material" according cartographic rules and map 
content. 
5. Importance in the map: normalized values according 
to the map type. 
213 
Area Surrounding an Object 
The area surrounding an object affects its behavior as well. 
Objects can be located in a dense urban area, or "isolated" in a 
rural area. Objects with a higher density value resulting from 
more objects in the surrounding area should be "stronger" being 
practically unable to change their shape or moved from their 
location. 
The values of all these elements were chosen in proportion to 
the expected power (larger values vs. larger power), and 
therefore, the power can be calculated as follows: 
(10) power = area * shape * hieght * elastic * Im por tan ce * density 
3.2 Forces between Objects 
The forces between neighboring objects express the interaction 
between them. Returning to the electric field theory, each object 
has its "electric charge”, and attraction or rejection forces 
control their movements. When adopting the same behavior or 
interaction model, the forces between the objects in the map are 
computed as follows: 
C D D) 
R 2 
a.b 
(11) Force, , = 
The force between two objects is a direct function of the 
difference between both powers. Thus, the same style and 
power objects won't affect each other. However, there is an 
inverse function expressing the distance between the objects and 
their effect, with close objects having a stronger effect. 
3.2.1 Minimal Distance between Neighboring Objects 
It was determined that the approach should be to calculate the 
distance between objects as the minimal distance between the 
convex hulls circumscribing the objects as shown in Figure 6. 
  
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Figure 6. Minimum distance between convex hulls 
3.2.2 Direction of Forces between Objects 
The critical zones in a map are located where there is minimum 
distance between neighboring objects, especially if that distance 
causes a spatial conflict. The goal of the combined