ISPRS Workshop on Service and Application of Spatial Data Infrastructure, XXXVI(4/W6), Oct.14-16, Hangzhou, China 
should vary continuously with scale. The scale range between 
when a representation instance occurs and when it dies, is 
considered as its scale life cycle; while its spatial geometry and 
attributes which stay constant in this life cycle are taken as its 
states. In figure 3[d], the wide and horizontal line segment 
represents the state of a representation instance, while its length 
shows the life cycle of this representation instance. In figure 
3[a], RI1 at scale SI and SI1 at scale S3 have the same spatial 
geometry and attributes, so they should belong to the same 
representation instance; but as for RI4 at scale SI and RI5 at 
scale S2, they belongs to different representation instances in 
that they are simplified in spatial geometry. 
abed 
(a) Representational Instances (b) Hierarchical Structures (c)PN 
Structures (d)States and Scale Lifecycle 
Figure 3. Models of Multi-Scale Representation 
Therefore, as for a cartographic entity, its life cycle can be 
obtained by summing life cycles of all its representation entities 
together. This paper is intended to focus on representation 
instances, and make research on their states, scale events and 
correlations between these states and events. Scale events relate 
inevitably to states, in that it is the scale event that changes a 
state of a representation instance to another state. Seen from a 
reasoning aspect, a scale point is an event’s location in the one 
dimensional space; while a scale zone is the scale range 
represented by a straight line between these scale points. The 
one-dimensional topology between one-dimensional scale zones 
is named scale topology, which includes relations between two 
one-dimensional scale zones, such as the first zone meeting 
with the second, intersecting it, being apart from it, being 
contained by it and so on. 
3.3 A multi-scale Representation Model Based on Petri net 
Pet Net has place, transition, and arc as its elements, which are 
respectively used to describe states of a representation instance, 
its scale events, and relations between these states and events. 
In this way, not only a multi-scale map is represented, and the 
topology between scale zones can also be explicitly represented. 
In figure 4, a circle represents a state, described by a scale zone; 
a wide short line represents an event, described by a scale point 
Si (some arbitrary scale, not specified one); a straight line 
shows the relation between states and events. 
When it comes to the multi-scale hierarchical model, its scale 
variable can only choose finite (non-scalable) scales; while in 
our PN-based multi-scale model, the scale variable Sc can make 
continuous changes in the valid scale ranges, providing 
theoretic bases for the implementation of a scalable map. 
The resolution of representation instances represented in current 
tree/graph-based multi-scale hierarchical representation model 
is only in conformance with the sampling interval. There are 
three scales in figure 3b, SI, S3 and S5. Snapshots at scale SI 
are RIK R^ RI3 and RI4; while as for scale S3 there are 
snapshots such as RIK RI2 and RI6, with S5 having only one 
snapshot. Seven edges should be recorded to save relations 
between representation instances. However, changes of details 
at scale S2 and S4 are ignored, such as the simplification event 
changing RI4 at scale SI to RI5 at scale S2, and the 
amalgamating event changing both RI5 and RI6 at scale S3 to 
RI7 at scale S4, both of which show that cartographic data vary 
greatly with scale. RI1 and RI2 are repeatedly stored at scale S1 
and scale S3, thus giving difficulty in data updating. 
The PN-based multi-scale representation model records 
relations between basic scale events and representation 
instances with high resolution, with these events defining both 
the starting scale value and the ending scale value of a state of a 
representation instance. In figure3c, as for the number of edges 
and the number of representation instances, PN model seems 
the same to the hierarchical model, but it can described twice 
the amount of detail as the hierarchical one, thus reducing data 
redundancy (unfilled polygons in the figure). 
4. THE IMPLEMENTATION OF OUR PETRI NET 
BASED MULTI-SCALE MODEL 
A multi-scale model based on extended E-R model is proposed 
by Wang Yanhui (Wang, 2003), including three fundamental 
elements: entity, attribute and relation. A entity may be just a 
entity of basic types (point, line, area), and also can be some 
complex one composed of these basic entities, such as a city, a 
building, a road and so on; attribute involves spatial attribute 
and non-spatial attribute; as for the relation, it can be divided 
into two types, spatial relation and non-spatial relation, made up 
of four basic semantic types (aggregation, generalization, 
classification, association), which can effectively reflect 
semantic relations between different representations involved in 
cartographic generalization. If Petri Net is used to represent this 
model, entities and relations expressed in E-R model will turn 
to location and transition in the PN model, while restrictions 
between entities and relations in E-R model will correspond to 
directional arcs in the PN model. However, this multi-scale 
model based on extended E-R model revolves around snapshots 
of a specified scale point, but our PN-based multi-scale model 
is oriented to representation instances with “scale lifetime”.