ISPRS Workshop on Service and Application of Spatial Data Infrastructure, XXXVI(4/W6), Oct. 14-16, Hangzhou, China 
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2. BASIC CONCEPTS 
2.1 Scale 
Scale, an important property of spatial data, refers to the 
comparative sizes of both spatial extent and time represented by 
data, so that there is a big difference between information 
densities represented by different scales (Wang, 2001). Scales 
in geography can be interpreted in two aspects, the comparative 
size and the abstract level; while scale is described as “map 
scale” in cartography (Wang, 2003). Scale dimension is 
continuous as time dimension and can be depicted by a 
reference system, .i.e. scale dimension, scale origin, and scale 
value. A line with an arrowhead is used to represent a scale, 
which has its origin and direction (Figure 1). In a map, scale is 
used to describe a scale reference system. Scale direction starts 
from the scale origin that sets at the scale “one to one”, with 
two opposite directions, one negative because of its 
denominator being bigger than one, and the other positive 
because of its denominator being smaller than one. Seen from 
the macro aspect, the first can be considered as the abstraction 
of our real world; while from the micro aspect, the second as the 
magnification of this real world. Scale value can describe scale 
variable in the form of “1 to m”; the larger the denominator, the 
bigger the scale value. There are basic types for scale: scale 
point, and scale zone. Scale point refers to the size of scale 
origin, such as this “1 to 10000” scale point represented as a 
point in our reference axis; scale zone means the scale range 
between two scale points, such as this [1:10000, 1:250000] 
scale zone represented as a line segment in our reference axis. 
Compound scale can be obtained by integrating these basic 
scale types. 
1:1 1:100 1: 1 : ratio 
Figure 1. Reference System of Scale 
2.2 Introduction to Petri Net 
Petri Net (PN) was proposed by C.A.Petri in 1962 as a 
mathematical model for the study on information systems and 
their interrelationships, including place, transition, arc and 
token. With its intuition, visibility and many fine mathematical 
properties, Petri Net has been widely applied to fields such as 
distributed systems, information systems, and discrete event 
systems and so on. 
Formal languages can be used to describe Petri Net, whose 
static structure corresponds to a three-tuple N(P,T,F). It can also 
be represented by a graph, called the Petri Net Graph. In this 
graph, F is the set of arcs linking p and t in two directions, 
among which p and t refers respectively to the element of set P 
and set T, with P the set of places, and T the set of transitions. 
Therefore, the structure graph can be regarded as directional 
two-tuple graph. Place usually refers to the state of this system, 
represented by a circle “ O ”; transition corresponds to the event 
changing the state, represented by a short vertical line “|” ; arc 
links state and event; net structure (P,T;F) describes relations 
between state and event or system rules. Token is added to the 
net graph to enhance Petri Net’s functionality of simulating, not 
only static phenomena but also dynamic one. 
3. A MULTI-SCALE SPACE REPRESENTATION 
MODEL BASED ON PETRI NET 
3.1 Scale Events 
Scale changes cartographic entities by cartographic 
generalization. While the same cartographic entity is 
represented at different scales, its representation instances may 
change in spatial location, shape and type, which evokes events 
such as classification (aggregation or disaggregation), 
simplification (delete, structure simplification or shape 
simplification), exaggeration (displacement, combination, 
segmentation) etc. Representation instances of the same 
cartographic entity may change at different scales (from a large 
scale to a small one) in the process of generalization. Some will 
be deleted, or replaced by other representation instance at a 
different position, or form a new symbol in the integration of 
other symbols. 
The cartographic entity, as element of a map, may have different 
representation instances at different scales (JONES, 1996). Take 
the cartographic entity man-made lake for example. It can have 
different representation instances at different scales, which can 
have different spatial geometry types (such as point, line, and 
area, and even no type) and different attribute types (man-made 
lakes, unsalted lakes, lakes and so on). In map generation, scale 
events happen to representation instances, thus leading to 
changes in their spatial geometry and attributes. Ri(i e n) 
represents some representation instance (Figure 2) and Si (ien) 
refers to some scale. Here, R1 refers to a meadow, with R2 a 
forest, R3, R4, R6, R7 and R8 belonging to vegetation, and R5 
a lake. R1 and R2 at scale SI is changed into a new 
representation instance R3 at scale S2, with their attribute type 
changing accordingly from meadow and forest to vegetation. 
Then R3 at scale S2 is simplified to R4 at scale S3, with shape 
simplification occurring. R5 at scale S3 is first deleted, and then 
changed into R7 and R8 at scale S4, with segmentation 
happening to them. Pointers can be used to describe relations 
between entities and generalization events. 
SI S2 S3 S4 
• r m R &. 
relati \ / \ / ff 
classifica 
simplifie 
exaggerat 
Figure2. Types of Scale Events 
3.2 Basic Principles 
A basic requirement for cartographic databases is to provide 
representation instances of the same cartographic entity at 
different scales and also to relate them with each other (JONES, 
1996). Now that scale is a continuous dimension, representation 
instances of the same cartographic entity at different scales