State Mutation 
The State of Arc al 
  
  
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The State of Arc a2 
  
The State of Arc a5 
The State of Arc a4 SS 
The State of Arc a41 
The State of Arc a42 
  
SS 
  
  
  
The State of Arc a3 
  
  
The Thematic States 
of Polygon A 
The States of Polygon A 
  
Figure 2.5 The State Topology of Polygon A 
3. TWO-LEVEL TIME TOPOLOGIES FOR 
GEOGRAPHIC INFORMATION 
In the real world, we are accustomed to regarding time as a 
line without endpoints that stretches infinitely into the past 
and future. In practice, world time represented in databases 
would begin at the time of the earliest known information 
and end at the time of the most recent information stored 
in the database. 
3.1 The Time Topology for Geographic Objects 
Time is a phenomenon and can only be perceived by its 
effects. From the point of time of view, every object has a 
beginning at some point in time. It also has a lifespan dur- 
ing which the object’s location or theme may change 
independently of the others. Finally, it may die in the sense 
that it does not exist in the real world or has changed into 
another object. The state topology in Figure 2.1 may be 
viewed as a time topology for objects. World time for a 
Duration 
The Durations of Object A OS SE 
t 
geographic object may be viewed as a line, and is punc- 
tuated by the object mutations. An object state may be 
viewed as a line segment that represents the duration of a 
condition, while a mutation is a point that terminates the 
condition and begins the next. Two line segments which 
share a boundary may be viewed as contiguous neighbors 
in time. World time for all geographic objects in a GIS 
database may be viewed as a topology comprised of these 
parallel time lines as shown in Figure 3.1. 
3.2 The Time Topology for a Geographic Object 
From the point of time of view, the state topology for an 
geographic object, such as the state topology of polygon A 
in Figure 2.5, may be viewed as time topology for the 
object. That is, each time line in Figure 3.1 may be viewed 
as the composition of an object's spatial time durations and 
thematic time durations. For example, the time line of 
polygon A may be viewed as the composition of the spatial 
time durations and the thematic time durations of polygon 
A, as shown in Figure 3.2. 
Mutation 
   
a) 
  
The Durations of Object B C 
Hl on ofl fle 
The Durations of Object C 
The Composition of 
    
   
  
  
  
Durations in a GIS Database 
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Figure 3.1 The Time Topology of Geographic Objects 
158