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Vector GIS: Relational Database Procedures with Two-Dimensional Referencing Systems

Related References

In the last lecture, we set out a formal framework for understanding information systems as tools that foster four basic capabilities:

  • Provide structures for representing entities or phenomena (referencing systems.)
  • Provide procedures for associating representations with eachother.
  • Provide procedures for transforming representations
  • Provide facilities for combining the structures and procedures and visualizing information.

We saw how Relational Database Management Systems have achieved a cannonical status as a very reasonable vessel for dealing with a certain set of referencing systems in tabular form. In classical RDBMS referencing systems are largely one-dimensional (ordinal, rational numbers) or categorical (character strings). If you think about it, there are many real-world phenomena can't be represented well with this limited palette!

THe story of Vector Based Geographic Information Systems is the story of how people, who are never satisfied, developed systems for dealing with two-dimensional representations, and how, after fooling around with this for a while, adapted the logic and the infrastructure of relational database management systems to suit their purposes. A very good summary of the history of GIS is provided In the National Consortioum for Geographic Analysis (NCGIA) core Curriculum Unit 23. For a more detailed look at the GSD's role in this, see, Mapping the Unknown: How Computer Mapping at Harvard Became GIS.

It is enlightening and entertaining to consider how elegantly many of the procedures of RDBMS extend into two dimensions, and the degree to which our ability to create useful representations and associations increases geometrically! Have you read Edwin Abbott's Flatland, A ROmance in Many Dimensions? This is thought by many to be the world's first science-fiction book, written in 1883. A wonderful parable of thinking beyond the limits of one's representation system.

In lecture, we will consider the two-dimensional extensions of the classic relational referencing ststems, procedures and logic.

Representation and Referencing Systems

Consider the classic relational referencing systems and their logic:

  • Numbers: rational and ordinal
  • Dates: behave in many ways like numbers
  • Character strings can be merely names, or may represent hierarchal relarionships among classes. -- consider our Standard Industrial Class Code or the interesting spatial classes implied by a Zip code!

To these referencing systems, we will add a simple vocabulary of vector data types.

  • Points
  • Lines
  • Polygons

How will geometry affect the logic of how we can associate our representations?

Consider the basic Single-Table Associations that can be made with these new objects:

Basic Single Table Associative Procedures

  • Spatial Sorts a map is basically a spatial sort
  • Spatial Queries table rows are selected by defining an area on a map
  • Thematic Mapping creating a map with geometric features symbolized according to attributes. The categorical operations used in thematic mapping are not commonly found in ordinary relational databases.

Multi-Table Associative Operations

  • Spatial Selections based on multiple tables Inside, Contains, Intersecting...
  • Spatial Joins between tables based on spatial associations among their entities.

Transformations of Two-Dimensional Entities

  • Conversion of two single tabular coordinate references, X, and Y, to a point reference.
  • Converting a point or a polygon reference to simple, tabular, X and Y fields.
  • Transforming Coordinate Systems
  • Deriving buffer areas around features. This is a means of converting lines and points to polygons
  • Spatial Summary, or Dissolve aggregates the spatial references in a table having a common attribute.
  • Overlay Functions
    • Intersect
    • Union

Reflections on The Relational Assupmtion that Entities are Distinct

Many relational operations and vector-relational ones depend for their internal consistency that entities be distinct, so that (among other reasons) that the result of a join is repeatable. In Plain tabular databases, this is achieved by assuring that the primary key of a table is unique. In vector database, this requires attention to topological rules for creating geometry. For example, two polygons in the same layer must not overlap. For a deeper discussion of this, see Building a Geodatabase (Especially Chapter 4, about topology.

Applications of Distributed Spatial Databases

The next lab and the next lecture will look at ways that these operations can be chained together in complex logical chains of representations and operations that can be used to explore and understand, plan and manage things in the world.

As relational databases permit the integration of disparate databases into a common framework for high-level analysis and planning. Following on this discussion of the potential for distributed database systems, consider some of the implications of these systems when the flexibility and added representational power of spatial referencing systems is added.

This recent (2003) article in the Boston Globe highlights 10 Billion Dollars worth of error, in the Big Dig. In one case, a Central Artery ramp was planned to be in the same place where the re-alignment of the MBTA's green line was planned. Can you imagine how distributed spatial representations could have helped avoid this problem? Consider how a distributed spatial database may help with the many urban design problems that lie ahead in the Big Dig project.

The fact that information resources maintained by different agencies should be coordinated is a no-brainer. But figuring out how to accomplish this boils down to the perennial problem of getting people to agree on what is important and to spend resources to help someone else. There are a couple of examples you might look at:

Vector-Relational Tools

  • Smallworld GIS
  • ESRI-s Geodatabase Model
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