76
Michela Bertolotto
Table 4.1. Comparing transmission time of real data with and without progressive transmission
Average response time (s)
level 0
10
level 1
6
level 2
9
total
25
one step transmission
24
4.5 Approaches Based on Topological Operators
Several operators commonly used in map generalization apply changes to the map
topology. For example, a geographical entity can be represented as a region at
higher detail, and as a point at a coarser level. In this case a region-to-point contraction operation can be applied to obtain the generalized version. The dimension of the entity, and consequently its spatial relations with surrounding entities,
changes.
The approaches based on geometric operators seen in Sect. 4.4 do not take these
changes into account. However, in real applications, these operations are needed.
In this section we discuss some progressive transmission prototypes that have been
developed based on operators that apply topological changes.
The framework proposed by Bertolotto and Egenhofer [5, 6] relies on a model
that was initially presented by Puppo and Dettori [17, 39] and then further formalized
in [4]. The model consists of a sequence of map representations of a given area, each
corresponding to a different LOD. Such a sequence is stored on the server and sent
progressively to the client upon request (as described in Sect. 4.3). In [4] a set of
generalization operators have been defined and shown to be minimal and sufficient
to generate consistent generalized maps. The set of operators defined is the following
(see Fig. 4.5):
• Point Abstraction: elimination of an isolated point inside a region
• Line Abstraction: elimination of a line inside a region
• Line-to-point Contraction: contraction of an open line (including its endpoints)
to a point
• Line Merge: fusion of two lines sharing an endpoint into a single line
• Region-to-point Contraction: contraction of a simply connected region (and its
boundary) to a point
• Region Merge: fusion of two regions sharing a boundary line into a single region
• Region-to-line Contraction: reduction of a region (and its bounding lines) to a
line
These operators are defined as functions between map representations. They are
called atomic as they perform atomic changes on the map. Complex generalization
Michela Bertolotto
Table 4.1. Comparing transmission time of real data with and without progressive transmission
Average response time (s)
level 0
10
level 1
6
level 2
9
total
25
one step transmission
24
4.5 Approaches Based on Topological Operators
Several operators commonly used in map generalization apply changes to the map
topology. For example, a geographical entity can be represented as a region at
higher detail, and as a point at a coarser level. In this case a region-to-point contraction operation can be applied to obtain the generalized version. The dimension of the entity, and consequently its spatial relations with surrounding entities,
changes.
The approaches based on geometric operators seen in Sect. 4.4 do not take these
changes into account. However, in real applications, these operations are needed.
In this section we discuss some progressive transmission prototypes that have been
developed based on operators that apply topological changes.
The framework proposed by Bertolotto and Egenhofer [5, 6] relies on a model
that was initially presented by Puppo and Dettori [17, 39] and then further formalized
in [4]. The model consists of a sequence of map representations of a given area, each
corresponding to a different LOD. Such a sequence is stored on the server and sent
progressively to the client upon request (as described in Sect. 4.3). In [4] a set of
generalization operators have been defined and shown to be minimal and sufficient
to generate consistent generalized maps. The set of operators defined is the following
(see Fig. 4.5):
• Point Abstraction: elimination of an isolated point inside a region
• Line Abstraction: elimination of a line inside a region
• Line-to-point Contraction: contraction of an open line (including its endpoints)
to a point
• Line Merge: fusion of two lines sharing an endpoint into a single line
• Region-to-point Contraction: contraction of a simply connected region (and its
boundary) to a point
• Region Merge: fusion of two regions sharing a boundary line into a single region
• Region-to-line Contraction: reduction of a region (and its bounding lines) to a
line
These operators are defined as functions between map representations. They are
called atomic as they perform atomic changes on the map. Complex generalization