Key concepts 1 GIS - Spatial Data Analysis: An Introduction for GIS Users - page 9

Node

Vertex

Figure 2.2 Vector line features used to illustrate network analysis methods in Chapter 6.

into their spatial component and their attribute component. Attributes linked to each
spatial feature are ot en stored using a relational database system (see Section 2.3 for
more on databases) and this is demonstrated in the following subsection.

2.2.3 Topology

h is section is concerned with vector representation of objects and connections
between features. Topology can be dei ned as 'the mathematical study of objects which
are preserved through deformations, twistings and stretchings. (Tearing, however,
is not allowed.)' (Weisstein, 2003, p. 2990). In other words, if a map showing a set of
zones is stretched, zones separated by other zones cannot become neighbours. For this
to be possible, the map would have to be cut (or torn as the quote above indicates) or
folded over on itself (Wise, 2002). In a GIS (as well as a computer-aided design system,
etc.), information on the connections between objects and, where appropriate, neigh-
bouring objects, may be stored. Operations concerned with connections between
objects (e.g. administrative areas or roads) are dependent on information about topo-
logical relationships.
Obviously, to represent a point only the point coordinates are required. In Figure 2.3,
an example of line topology representation is given. In this case, arcs are indicated
with the prei x 'A' and the nodes with the prei x 'N. Changes in the direction of arcs
between nodes are represented by vertices, as shown previously in Figure 2.2. Note
from the table that direction is represented—there is a 'from node' and a 'to node. N3
may, at i rst sight, appear to be a vertex but it connects two distinct arcs—A1 and A2.
Figure 2.4 gives an example of vector polygon topology representation. With this
representation, information on arcs and the polygons to which they belong is con-
tained in one table while information on the area and perimeter of the polygons is
contained in another table. h e table at the top has separate codes for each arc, the