GEO 465/565 - Lecture 5
Maps as Numbers - Part 1

Maps as Numbers

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

The GIS places data into the computers 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.

The Data Model

A conceptual description (mental model) of how data are organized for use by the GIS

entities ---> objects

GISs have traditionally used either field or object data models for maps and the flat-file data model for attributes.

Attribute data

Attribute data are stored logically in flat files

i.e., matrix of numbers and values stored in rows and columns, like a spreadsheet

DBMSs use many different methods to store and manage flat files

Rasters and vectors can be flat files ... if they are simple - GRAPHIC

A field data model uses a grid data structure.

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 - GRAPHIC

The mixed pixel problem - GRAPHIC

Run Length Encoding

based on spatial autocorrelation

nearby things tend to be more similar than distant things

data entered as pairs

run length & value

40 items instead of 70

Rasters are faster...

A raster or grid maps directly onto a programming computer memory structure called an array.

Good for representing continuous surfaces.

Rasters are a natural for scanned or remotely sensed data

Rasters are easy to understand, easy to read and write, and easy to draw on the screen.

Spatial analytical operations are faster

Compression is easier using techniques such as Run Length Encoding and quadtrees


Rasters are poor at representing points, lines and areas

Points and lines in raster format have to move to a cell center

Lines can become fat. Areas may need separately coded edges

Good only at very localized topology, and weak otherwise

Suffer from the mixed pixel problem

Must often include redundant or missing data

Each cell can be owned by only one feature

The Vector Model

An object data model uses point/line/polygon data structures stored by their real (Earth) coordinates.

Lines are built from sequences of points in order.

Lines have a direction according to the ordering of the points.

Polygons can be built from points or lines.

Object data model gave rise to the arc/node data structure in the 1960s

The endpoint of a line (arc) is called a node. Arc junctions are only at nodes

Vector Data Structure Featuring Arcs and Nodes - GRAPHIC

Arc-Node Combo Eliminates Redundancy of Storage - GRAPHIC

Vectors and Topology

Vectors without topology are spaghetti structures

Points, lines, and areas can each be stored in their own files, with links between them

Stored with the arc is the topology (i.e. the connecting arcs and left and right polygons)

Relationships are computed and stored


Arc/node map data structure with file - GRAPHIC

Topology, GIS, and You

Topological data structures dominate GIS software

Rarely are maps topologically clean when digitized or imported

A GIS has to be able to BUILD topology from unconnected arcs

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

Nodes that are close together are snapped - GRAPHIC

Slivers due to double digitizing and overlay can be eliminated - GRAPHIC

The bounding rectangle - GRAPHIC

Why Topology Matters

Topology allows automated error detection and elimination

Complete topology makes map overlay feasible

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

Topology makes spatial analysis possible

"Rasters are faster, but vectors are 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 as good with continuous coverages or plotters that fill areas

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