5.6. Relationships, topology

The other group of the knowledge describing the objects is the relationship , which is a thematical and geometrical connection between two or more objects or a geometrical relation of one object and the primitives between each other. For its abstract denotation the term relationship type, for its concrete denotation the term relationship occurrence are used respectively. In the relationship one side contains the feature of the other side intended for identification as a characteristics intended for linkage.

The database DAT is topological structured, accordingly an extra role is played by the topology, which is part of the concept relationship and which describes the multi way geometrical relationship existing between the objects and primitives.

Of the relationships this standard accentuates the description of the topological (geometrical) relationships. The structure of the thematical relations does not need here a separate description, because in the case of the DAT, on the level of the data model there did not be formulated general requirements as to the relationships and because the thematical relationships have to be retrievable in the physically existing database on base of the attributes by use of the actual retrieval language in compliance of the actual need.

5.6.1. General logical consistency

Each of the objects and their primitives are linked with each other structure-like, logically consistent. For doing so the fulfillment of the following condition is needed:

5.6.2. Topological relationship types

Between objects:

By applying the topological relationships "superimposition" and "underimposition" chain-like to two or more objects or part of object being incidentally above each other the order of the priority (e.g. which type of line valid for an object should be displayed) can unambiguously be designated.

Between primitives and in connection of objects:

5.6.3. Rules of the topological structuralisation

General rules:

Point object: It consist of one node.

Simple line object:

Simple surface object: It consist of one or more adjacent faces.

Complex object


The database DAT manages the nodes in a table.

Line segments and edges:

The database DAT manages the line segments and edges separately in tables.


The database DAT manages the faces in one table.

5.6.4. Structural expression of the relationships, tables of relation

In dependence on the broad range of the relationships the ramification the relationships is expressed structurally in the database DAT as follows:
a) With the mutual relationship of a degree 1:1, which can be described between two objects.
b) With the hierarchical inhomogeneous relationship of a degree 1:N, which exists among concrete objects of more object sorts.
c) With the hierarchical inhomogeneous relationship of a degree 1:N, which exist among more concrete objects belonging to one objects sort.
d) With the grid relationship of a degree M:N, which expresses the simultaneous relationship of more object with more further objects.

The above structural relationships in the database DAT needs to be expressed by means of a so called table of relation to be compiled by relationship types (and properly by object sorts and by primitives). The first column of the table of relation the identifiers of the superordinate and its second column the ones of the objects subordinate to the former one contains respectively. In this way we get to the concretum of the relationships, to the relationship occurrences.

The building in the tables of relationship into the database DAT is in consideration of the topological relationship compulsory, in case of thematical relationships optional.

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