Representation

Objectives of lecture:

1. Models for representation: Raster & Vector
   Vector approach measures space, but topology is as important as position
   Raster can be viewed by point or by area
2. Topology: focus on connectedness (relationships), not exact measurements

Primitives for representation:

Primitives for attributes:

Bits, bytes, words - structured into fields and records (rows and columns?)

Shades of the Geographical Matrix

Primitives for space:

coordinates (measure of location)

Vector: mathematical term for an element of an n-dimensional space (projected onto the coordinate axes; here used for the direct linear connnection between between two points - a holdover from the storage screen era). Representation system permits coordinates with seemingly infinite resolution.

Raster: a cellular model of geometry. Word derives from mechanical sweep of cathode beam inside television tube and similar devices. Becomes attached to resulting scan. Representation system is clear about the limits of resolution (the cell).

The Vector model can be used with `cartographic primitives' (point line area) to represent isolated objects. Each object has its geometric representation...

Connected coverages (networks & categorical coverages) require deeper thinking.

Raster model directly implements space controlled measurement frameworks, but can represent other measurement frameworks as well.

Issues for raster representation:

• Resolution!
• Rules for aggregation
• Projections...

Teminology as explained by the software empire:

How ESRI explains vector and raster. They make the contrast between these two as the organizing principle, though their vector model is really just the isolated object framework.

Understanding Topology:

What it is NOT:

Topography: measurement/representation of earth elevation and related features (a form of general/reference map)

Topology:

study of basic spatial relationships based on intuitive notions of space (those not requiring measurements - just dimensions)

Spatial relationships that are preserved under continuous deformations (invariance again)

In mathematics: both Combinatorial topology (what cartographers use) and Algebraic topology (what databases use); see definition from text.

Unfortunately, it became a marketing issue in the 1980s: your software (meaning your data models) "had" topology or not... It became a buzz word.

How USGS refers to topology

[scroll down, it is the second thing that is "special" about GIS].

• Adjacency is topological if things are connected.
• Containment is purely topological
• Proximity sounds much more metric (near, not far)

The basic spatial relationships: (an aliterative list)

• connectivity
• containment
• contiguity
• connectedness...

Structural relationships of the dimensional objects; mutually constituitive; assemble a connected coverage

1. points (nodes) bound lines
2. lines (chains) bound areas
3. areas (polygons / faces) bound volumes

Topological issues in data structures:

• logical consistency - more basic than positional accuracy (see Data Quality lecture)
• error detection during digitizing (topic discussed in future lecture 18)
• Topology for networks
  • Users CARE about connectivity
  • Orientation of segments: upgrades from topology to graph theory: direction of flow; rules about flow depend on what is transported/linked (eg. water, electricity, data...)
  • "Turn tables" (attributes of nodes or lines incident at nodes)
  • "Events": features (not necessarily temporal!) linked to a position along a link in a network, may apply to some segment of the "line"
  • Planar versus non-planar graphs (treatment of underpasses, etc.)
• Inner rings: the myth of a special problem (Isle Royale: largest island in the larest lake in Nroth America)
  • Old solution: "retraced lines"
  • Shapefile solutions (components of objects) containment flags...
  • Topological simplicity: polygon definitions

Attribute relationships (preview of Chapter 4):

Vector approach implies some form of attribute database to attach to the geometric objects. The 'geographical matrix' rides again, but there are relationships this matrix does not model.