ISPRS Workshop on Service and Application of Spatial Data Infrastructure, XXXVI(4/W6), Oct.14-16, Hangzhou, China 
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This model can not only organically associates states, events 
and their relations with each other, but also can implement 
queries based on states, events and relations, and also is tailored 
to both multi-scale based analyses and data update applied in 
G1S and cartographic databases. This querying functionality can 
be divided according to the structure of PN as follows: 1) state- 
based queries, used to query states of representation instances of 
the same cartographic entity at different scales; 2) event-based 
queries, used for queries of events which change states of 
representation instances; 3) relation-based queries, intended to 
query relations between states and events of representation 
instances. In another aspect, this functionality can also be 
divided into two following types by the scale concept: (1) scale 
point queries, i.e. scale snapshot queries; (2) scale zone queries, 
queries of cartographic objects which have scale events in a 
certain scale zone. This PN-based multi-scale model, as a model 
for database organization and storage, can reduce data 
redundancy and therefore save more storage space compared 
with the hierarchical model. But because of the complexity of 
PN model, it takes more time than the hierarchical one when 
applied to query scale snapshots. Data source in our experiment 
is obtained from figure3, with Eventl, Event2, Event3, Event4, 
respectively at scale 1:10,000, scale 1:50,000, scale 1:100,000, 
and scale 1:500,000. Tables of states, events, and directional 
arcs can be created with Maplnfo (Figure 5). 
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50,000 
□ Event3 AicJEvent3,RI2) 
A/c(Event3,RI7) 
100.000 
□ Event4 i Arc(Event4.RI1) 
1 — 
Arc(Event4.RI8| 
■ I 
500,000 _ 
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□ 
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□ 
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□ 
Arc(E venti,RI4) 
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NULL 
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Arc(Event2.RI3) 
RI3 
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□ RI2 NULL Event3 
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□ RI3 NULL Event2 
Arc(Evcnt2.RI6) 
RI8 
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Arc|Event3,RI6 
□ RI5 Eventi Event2 
Afc|Event3.RI6| 
RI6 
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RI8 
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Figure 5. The Tables of the Petri Net-based Multi-Scale Model 
in Maplnfo 
Figureó. The Snapshot Querying Operation on any Scale 
Scale snapshot queries are made to exemplify how this PN- 
based multi-scale model can implement scalable scales. Here we 
can input three “random” scales (1: 11000, 1:80000 and 
1:110000) to query three snapshots (See figure 6). But these 
queries can’t be implemented in the hierarchical multi-scale 
model, which only supports queries of snapshots at a specified 
scale. 
Queries of states of specified representation instances can track 
changes and events evoked when these representation instances 
vary with scale, and further provide convenience to update in 
cartography. When update of representation instances of large- 
scale cartographic data is made, multi-scale update can be 
achieved by first using a pointer to search for according 
representation instances of a series of small-scale cartographic 
data and then making updates according to the scale events, 
which further guarantees consistency of multi-scale spatial data. 
Meanwhile, those unchanged representation instances can stay 
constant at a series of scales, which avoids repeated map 
generalization and greatly reduces the amount of labour work 
done by cartographers. 
Spatial objects have six-dimensions, such as x, y, z (in the 
geometrical space), attribute, time, and scale. Time and scale 
can respectively change geographical objects in quantity or in 
quality, with their spatial geometry and attributes changed, thus 
producing geographical objects of different time and scale 
versions. In current GIS, time sequence maps mainly adopt the 
snapshot sequence model, while the scale sequence model uses 
the single sequence scale model. Scale can change attributes of 
a spatial object, through classification, and also can change its 
properties of spatial geometry by simplification, amalgamation, 
segmentation, displacement, deletion, exaggeration, and some 
complex operation. When time doesn’t vary, a cartographic 
object only changes with scale, forming the scale sequence 
model. This still holds for the scale. A cartographic object can 
only change with time, if scale doesn’t vary, forming time 
sequence model. Time possesses basic properties such as states, 
events, and relations just as scale does, so our Petri Net model 
can also be used to represent these properties of time, with place, 
transition, and directional arc respectively corresponding to its 
state, event and relation (Yin, 2004). 
5. CONCLUSIONS 
In current multi-scale representation, how to build and manage 
relations between original features in GIS and their derived 
representation instances becomes a really hard problem]. By 
combining benefits of both multi-scale representation and the 
Petri Net model, a Petri-net based multi-scale representation is 
put forward in this paper, which can explicitly express the same 
geographical feature’s representation instances, and scale events, 
and relations between them as well. It is experimented that 
queries of scalable scale snapshots can be effectively 
implemented in our proposed model, giving benefits to the 
updating of multi-scale maps. 
REFERENCES 
Frye, C. And Eicher, C.L, 2003. Modeling Active Database- 
Driven Cartography Within Gis Databases. Proc. of the 21st Int. 
Cartographic Conf (ICC), Durban, South Africa, pp. 1872-1879.