culating the
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c validity of
y; Boolean
ılculation of
sive task for
required for
n techniques
visualization
tific fcature.
ıtation (BR).
entation and
1s have to be
ering a truly
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nd position.
c dealt with
(CSG)
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a model to
a topologic
bjects in a
formal data
a 3D vector
n object, e.g.
n object can
ect Types.
---- Point object: zero-dimensional objects which have
position but no spatial extension.
---- Line object : one-dimensional objects with length as
the only measurable spatial extension, shape and
position.
---- Surface object: two-dimensional object with area and
perimeter as measurable spatial extensions. They can
have a 3D shape.
---- Body object: three-dimensional object with volume
and surface area as measurable spatial extensions. They
are bordered by a surface.
In the FDS each object is represented by an Object
Identifier ( OID ). There are four OID-set: a Point Object
Set , a Line Object set , a Surface Object set and a Body
Object set. Each object has its own Object Identifier,
referred to respectively as PID, LID, SID or BID. Each
OID is linked to two data sets. The first data set contains
all thematic data. The second data set contains the
geometrical information of terrain object.
In FDS , On the top row there is a thematic class label for
each Object Type. The second row gives the four types of
the objects of Object Identifiers. The lower part of the
diagram gives the geometric structure of the FDS. There
are four Geometric Elements which are the clementary
data types of the geometrical part of the FDS.
The relationship between Geometric Element and
Object Types is determined by the following rules:
---- À Point Object is represented by exactly one node.
---- Line Object are constructed by a chain of arcs. For
each Line Object no more than two arcs can be connected
at one node , so that there are no Line Objects with loops
or multiple branches. A Line Object can be a closed
polygon: all nodes connect exactly two arcs.
---- Surface Object are constructed by one or more
connected faces.
--- A Body Object is completely described by its
bordering faces.
The characteristics of topological relationships between
Geometric Object are of importance in GIS data
manipulation and analysis. In the FDS, nine sets of
topological relationship between the four Geometric
Object types can be identified. They are point-line,
point-surface, point-body, line-line, line-surface, linc-
body, surfacc-surface, surface-body, and body-body.
( Table 1.).
Table 1: Topological Relationships between Geometric Object
Line Surface Body
Point is-on is-on is-on
is-insidc
Line intersect is-on is-insidc
connected is-on
intersect
Surface is-neighbor |is-insidc
is-inside is-on
intersect intersect
Body is-inside
is-neighbor
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
Some topological = relationships between Geometric
Object listed in Table 1 can be derived easily from the
basic data model. But some may be difficult. In order to
complete the topological query space and to improve the
efficiency of query processes, some topological data
structure have built into data model.
The analysis of the topological query space reveals that
the two fundamental topological relationships should be
added onto the data model. They are the is-on
relationship between the Node and Face entities, and the
is-inside relationship between the entities of Node and
Body Object. Consequently, the complete data model for
3D spatial data will be constructed.
J Belongs to Belongs to
Belongs to Î Belongs tc
Body Surface Line Point
is in
is in
Fig. 2. A formal data structure (FDS) for 3D vector map
This representation of topological spatial relationships
stress the organization of the geometric objects and some
simple topological relationships. The drawback is that
this set of relationships is neither orthogonal nor
complete. So it is necessary to investigate the formal
description and the smallest set of topological
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