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
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:
- The topological relationship values of the primitives (e.g. initial node, component etc.) have to appear. Their value has not be field NULLA.
- All the primitives forming the objects have to exist.
- All the relationship indices have to reach the goal, i.e. the data record denoted by the index has to exist.
- None of the object can have relationship denotation referring to itself.
5.6.2. Topological relationship types
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.
- "Incorporating object": Complex objects entirely including simple or combined objects.
- "Incorporated object": It denotes the complex or simple objects making up the complex object or contained in it.
- "Superimposition": When an object is to put above another object because of priority.
- "Underimposition": When an object is to put under another object because of priority.
Between primitives and in connection of objects:
5.6.3. Rules of the topological structuralisation
- "Component": It means, that a certain node forms a point object or that a certain line segment or edges part of a simple line object or that a certain face is part of a simple surface object.
- "Status": It expresses the belonging of an isolated node, an isolated line segment or an isolated edge to a certain face.
- "Initial node", "end node": A node constituting the beginning, end of a certain line edge.
- "Forward", "backward": It means the keeping (sign"+") or alteration (sign "-") of the orientedness of a certain line segment or edge.
Point object: It consist of one node.
- Each object belongs just to one object class and object group.
- Any object can only be classified into one geometrical object type.
- The simple object consist of just primitives.
- The simple object can only be connected with primitive of with the own one identical dimension.
Simple line object:
Simple surface object: It consist of one or more adjacent faces.
- Some simple line object consist of one or more line segments or edges joining sequentially.
- Its orientedness has to be definite and homogeneous.
- The line segments or edges making up the simple line object have to be identical oriented.
- The simple line object can close in itself.
- The complex object consist of simple object(s) and/or complex object(s).
- One object can not be an object encompassing itself and not an object encompassed by itself.
The database DAT manages the nodes in a table.
Line segments and edges:
- The node is an independent point.
- A node can interrupt any edge or line segment just as an "initial", or "end node".
- A node is an "isolated" one, if it does not belong to any edge or line segment.
- More than one node can not have the same x, y coordinates except if they have different heights.
- In one node can be placed optional number of objects.
The database DAT manages the line segments and edges separately in tables.
- The orintedness of the line segment is determined by the sequence of the node indices.
- In order to determine the orientedness of the edge the line segments making up the edge have to be made one-directional (relationship "forward" and "backward").
- Two line segments or two edges are adjacent, if they have a common node.
- The line segment and the edge must not intersect line segment or edge, not itself either. The point of intersection of two line segments or edges is not considered a point of intersection of two lines, but is handled as a node.
- One line segment or edge may be a component of simple line object of optional number.
- One line segment or edge has not even to be a component just of one single simple line object.
- It is about an isolated line object or edge, when it does not join (belong to) none of a border of any face. An isolated line segment or edge does not divide a face.
- It is about a depending line segment or edge, when one of its nodes is on a boundary determining a certain face.
The database DAT manages the faces in one table.
5.6.4. Structural expression of the relationships, tables of relation
- The face may consist of edges of optional number, may contain isolated elements (node, line segment, edge) and depending elements of optional number.
- In order to determine the orientedness of the face the orientedness of edges making up the face is to homogenize.
- The overlapping of two faces is not allowed (when overlapping a separate face is to form).
- Two faces are adjacent, if they have at least one common line segment or edge.
- Each of the isolated nodes, line segments or edges has to belong to a certain face.
- Each of the faces can be component of simple surface object of optional number.
- The face needs not be component of none of an object.
In dependence on the broad range of the relationships the ramification
the relationships is expressed structurally in the database DAT
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
d) With the grid relationship of a degree M:N, which expresses
the simultaneous relationship of more object with more further
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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