Vector data and topology

This is lecture six

Last week

• Geographic primitives: points (nodes); lines (chains or arc); areas (vectors/polygons); and continuous surfaces.

• Data models (as opposed to data structures). • Difference between field and object models.

Main points in lecture six

• Fields, objects, and vector data models• More detail about the characteristics of the

field model.• Structuring data to enable queries: topology

What is a field?

• A conceptual model of geographic variation • One of several such models • The differences between this and other models are

conceptual, that is, they exist in the human mind.• Fields and objects are examples of the limited

ways in which humans imagine space.• Fields are also models of variation within a spatio-

temporal frame. They are ways of containing and representing space at one point in time.

Familiar fields

• At every point in the frame there exists a single value of a variable

• e.g. a field of temperature • e.g. a field of land surface elevation • e.g. a field of land ownership

Dimensions of fields

• For geographic information, the frame may be defined by:

• two spatial dimensions (x,y) • three spatial dimensions (x,y,z) • spatial dimensions and time (e.g. x,y,t) • The field variable (or attribute) can be thought of

as a function of these dimensions • e.g. z (x,y) might denote elevation as a function of

two spatial dimensions • generally, z(x) is the value (attribute) at the

location defined by the vector x.

The world as a layer cake

• It is possible to think of geographic variation entirely in terms of fields.

• In this way of thinking, geography consists of a number of variables with single values everywhere on the Earth's surface

Fields and reality

• fields can be infinitely complex • it could take an infinite amount of information to

represent a field perfectly • representations of fields must be approximate &• the space available in a digital computer is always

limited • often, representations capture only the coarser

aspects of variation • the details or high-resolution elements are not

captured • they constitute part of the uncertainty of the

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The vector data model

• Vector data models are based on vectors or polygons.

• The polygon is the primitive or basic unit of the vector data model.

Points as basis for objects

• Fundamental primitive is a point. • Polygons are created by connecting points with

straight lines. • Some systems allow points to be connected using

arcs of circles. • Areas are defined by sets of lines • The term polygon is synonymous with area in

vector databases because of the use of straight-line connections between points

Vector Primitives vs. Raster Primitives

Vector applications

• very large vector databases have been built for different purposes

• vector tends to dominate in transportation, utility, marketing applications

• raster and vector both used in resource management applications

Arcs 1• Polygons in one class or layer cannot overlap and must

exhaust the space of a layer. This corresponds with the field view. Every space on the map is “covered.”

• Every piece of boundary line is a common boundary between two areas. This is defined topologically.

• The stretch of common boundary between two junctions (nodes) has various names

• Edge is favored by graph theorists, "vertex" for the junctions

• Chain is the word officially sanctioned by the US National Standard

Arcs 2

• Arc is used by several systems including software from ESRI.

• Arcs have attributes which identify the polygons on either side. These attributes are part of the topological information.

• These are referred to as "left" and "right" by reference to the sequence in which the arc is coded

• Arcs (chains/edges) are fundamental in vector GIS

Storing Areas

• two ways of storing areas: • 1) polygon storage • every polygon is stored as a sequence of

coordinates • although most boundaries are shared between two

adjacent areas, all are input and coded twice, once for each adjacent polygon

• the two different versions of each internal boundary line may not coincide

Storing areas as arcs

• Every arc is stored as a sequence of coordinates

• Areas are built by linking arcs • Only one version of each internal shared

boundary is input and stored • Used in most current vector-based GISs

Database creation for vector data

• Database creation involves several stages: • Input of the spatial data • Input of the attribute data • Linking spatial and attribute data • Spatial data is entered via digitized points and

lines, scanned and vectorized lines or directly from other digital sources

• Once the spatial data has been entered, much work is still needed before it can be used

Objects

• The main competitor to the field conceptualization: objects or discrete entities

• Geography consists of an otherwise empty space littered with discrete entities

• As with fields, this is a question of conceptualization, not digital representation

• A point can lie in any number of entities, including zero

• Entities can be points, lines, areas, or volumes in three or more dimensions

Objects 2

• Entities can have any number of characteristics (attributes) associated with them

• The attributes apply to the entire entity • With object oriented data models, location information is

just stored as one of the object’s properties. • This makes management of data input and output very

simple. • Object can also be used with rasters or grids. • In this instance, the object record would contain reference

to particular cells in the raster coverage.

Advantages of objects

• Scientific models may work with fields, but people may find discrete entities more acceptable,

• More easily understood natural language provides much better ways of talking about discrete entities it is comparatively difficult to describe a field

• As Helen Couclelis writes, "People manipulate objects, but cultivate fields" (Couclelis, 1992)

Topology

• Holes and islands:• areas often have "holes" or areas of different

attributes wholly enclosed within them. We’ll talk more about them at the end of the lecture when we talk about topology.

• the database must be able to deal with these correctly

• this has not always been true of GIS products

What is topology for in GIS?

• Topology is basically information about relationships, about connectivity between areas on a map.

• Another definition of topology is: those characteristics of geometric objects (such as a polygon) which do not depend on measurement in a coordinate system.

Polygons and topology

• Polygons are bounded by chains, and chains are bounded by nodes.

• From these direct relationships, more complex neighbourhood can be built –based on connectivity information. For example, the adjacent polygon is the other object bounded by the same chain (arc).

Connectivity and adjaceny

• Topological characteristics are those which describe connectivity.

• When thinking about topology, the qualitative relationships of connectedness and contiguityare more important that the quantitative attributes such as length and area.

What makes a spatial database topological?

• A spatial database is often called "topological" if one or more of the following relationships have been computed and stored.

• Connectedness of links at intersections.For example: which roads intersect?

• Ordered set of lines (chains) forming each polygon boundary.

• For example: what lines (or arcs) are next to each other?

Cartographic databases

• By contrast, a database is called "cartographic" if the above conditions are absent

• Objects can be manipulated individually • Relationships between them are unavailable

or are considered unimportant

What limits databases cartographic?

• Cartographic databases are less useful for analysis of spatial data.

• They are satisfactory for simple mapping of data. • Many packages designed for mapping only use

cartographic database models.• A cartographic database can usually be converted

to a topological database by computing relationships - the process of "building topology“.

Building topology

• Building topology is often done when digitizing. • Once points are entered and geometric lines are

created, topology must be "built" • This involves calculating and encoding

relationships between the points, lines and areas • This information may be automatically coded into

attribute tables.

Topology rules in ArcGIS

Why have topology?

• When vector data structures were first introduced, computer processing power was limited. This made topological information more important as it prevented the computer from having to calculate information for every query.

• Topology was built in instead of re-calculated. Now, topology has become less important (in principle; most software programs actually still rely on it).