Maps as Numbers

• GIS requires that both data and maps be represented as numbers.

• The GIS places data into the computer’s memory in a physical data structure (i.e. files and directories).

• Files can be written in binary or as ASCII text.• Binary is faster to read and smaller, ASCII can

be read by humans and edited but uses more space.

Organizing Data and Information

• Information can be organized as lists, numbers, tables, text, pictures, maps, or indexes.

• Clusters of information called data can be stored together as a database.

• A database is stored in a computer as files.

The GIS Database

• In a database, we store attributes as column headers and records as rows.

• The contents of an attribute for one record is a value.

• A value can be numerical or text.

Flat File Database

Record Value Value Value

Attribute Attribute Attribute

Record Value Value Value

Record Value Value Value

The GIS Database (cont)

• Data in a GIS must contain a geographic reference to a map, such as latitude and longitude.

• The GIS cross-references the attribute data with the map data, allowing searches based on either or both.

• The cross-reference is a link.

Feature Attribute Table

Fields

Records

Representation and Data Structures

Real world - phenomena that exist

Data model - an abstraction, identifying those phenomena and properties we deem relevant for our applications Data and file structures - computer representation and storage scheme of the data model, often shown as diagrams and lists

Representation and data structures

Important to note the selection process as we move from real world to data model...this reflects our conceptualization, and affects much of what we can do

Terms

Entities - those "things" in the real world we wish to represent (Rivers, buildings, soil types, wetlands) Objects - our representation in a data model, which generally includes both geometric information (spatial data) and descriptive information (aspatial or attribute data).

Entity

Object

A data model represents reality

The Data Model

• A logical data model is how data are organized for use by the GIS.

• GISs have traditionally used either raster or vector for maps.

Data ModelsRepresentation and Data Structures

Data Model – An consistent way of defining and representing spatial objects in a database, and of representing the relationships among the objects.

A data model includes at least two parts –

Coordinate data - pairs or triplets of numbers that define location

Attribute data - text, numbers, images, or other “non-

spatial” data

Discrete and Continuous Space

Vector Data model – Discrete space

Raster Data model – Continuous or discrete space

A raster data model uses a grid

• One grid cell is one unit or holds one attribute.

• Every cell has a value, even if it is “missing.” • A cell can hold a number or an index value

standing for an attribute.• A cell has a resolution, given as the cell size in

ground units.

Generic structure for a grid

Rows

Columns

Gridcell

Grid extent

Resolution23 Cell Value

Points as Cells

Line as a Sequence of Cells

Polygon as a Zone of Cells

The mixed pixel problem

W GW

W W G

W W G

W GG

W W G

W G G

W GE

W E G

E E G

Water dominates Winner takes all Edges separate

Raster – The Mixed Pixel Problem

Landcover map –Two classes, land or water

Cell A is straightforward

What category to assignFor B, C, or D?

Raster – The Storage Space/Resolution Tradeoff

Decreasing the Cell Size by one-half causes aFour-fold increase in the storage space required

Rasters – Discrete or Continuous Features

discrete continuous

RASTER

• Grids are poor at representing points, lines and areas, but good at surfaces.

• Grids are a natural for scanned or remotely sensed data.

• Grids suffer from the mixed pixel problem.

Vector format

Point - a pair of x and y coordinates(x1,y1)

Line - a sequence of points

Polygon - a closed set of lines

Node

vertex

Vector data are defined spatially:

Vectors Define Discrete Features

Representation – Enforced Uniformity

VECTOR• Vector data evolved the arc/node model in the 1960s.• In the arc/node model, an area consist of lines and a line consists of

points.• Points, lines, and areas can each be stored in their own files, with links

between them.• The topological vector model uses the line (arc) as a basic unit. Areas

(polygons) are built up from arcs.• The endpoint of a line (arc) is called a node. Arc junctions are only at

nodes.• Stored with the arc is the topology (i.e. the connecting arcs and left

and right polygons).

Basic arc topology

n1

n2

1

23A

B

Arc From To PL PR n1x n1y n2x n2y

1 n1 n2 A B x y x y

Topological Arcs File

TOPOLOGY

• Topological data structures dominate GIS software.• Topology allows automated error detection and

elimination.• Rarely are maps topologically clean when digitized or

imported.• A GIS has to be able to build topology from

unconnected arcs.• Nodes that are close together are snapped.• Slivers due to double digitizing and overlay are

eliminated.

Topology Matters

• The tolerances controlling snapping, elimination, and merging must be considered carefully, because they can move features.

• Complete topology makes map overlay feasible.

• Topology allows many GIS operations to be done without accessing the point files.

Although Raster is FasterVector is Correcter

• Vector can represent point, line, and area features very accurately.

• Vectors are far more efficient than grids.• Vectors work well with pen and light-

plotting devices and tablet digitizers.• Vectors are not good at continuous

coverages or plotters that fill areas.

No Decision is Final – We Can Convert

Comparisons, raster v.s. vector

 

Characteristics Positional Precision

 Attribute Precision

 Analytical Capabilities   Data Structures

 Storage Requirements Coordinate conversion Network Analyses

 Output Quality

   

 Can be Precise

 Defined by cell size

 Poor for continuous data

 Good for continuous data

Good for spatial query, adjacency, area, shape analyses. Poor for continuous data. Most analyses limited to intersections. Slower overlays.

Spatial query more difficult, good for local neighborhoods, continuous variable modeling. Rapid overlays.

 Often complex

 Often quite simple

 Relatively small

 Often quite large

 Usually well-supported

 Often difficult, slow

 Easily handled

 Often difficult

 Very good, map like

 Fair to poor - aliasing

Vector Raster

Raster-Vector Data Model

Raster

Vector

Real World