Maps as NumbersMaps as Numbers

Getting Started with GISGetting Started with GIS

Chapter 3Chapter 3

Chapter 3: Maps as NumbersChapter 3: Maps as Numbers

3.1 Representing Maps as Numbers 3.1 Representing Maps as Numbers 3.2 Structuring Attributes 3.2 Structuring Attributes 3.3 Structuring Maps 3.3 Structuring Maps 3.4 Why Topology Matters 3.4 Why Topology Matters 3.5 Formats for GIS Data 3.5 Formats for GIS Data 3.6 Exchanging Data 3.6 Exchanging Data

Maps as NumbersMaps as Numbers

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

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

The Data ModelThe Data Model

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

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

Rasters and vectors can be Rasters and vectors can be flat files … if they are simpleflat files … if they are simple

Vector-based line

Raster-based line

4753456 6234124753436 6234244753462 6234784753432 6234824753405 6234294753401 6235084753462 6235554753398 623634

00000000000000000001100000100000101010000101000011001000010100000000100010001000000010001000010000010001000000100010000100000001011100100000000100001110000000000000000000000000

Flat File

Flat File

Features and MapsFeatures and Maps

A GIS map is a scaled-down digital A GIS map is a scaled-down digital representation of point, line, area, and representation of point, line, area, and volume features.volume features.

While most GIS systems can handle While most GIS systems can handle raster and vector, only one is used for raster and vector, only one is used for the internal organization of spatial data.the internal organization of spatial data.

A raster data model uses a grid.A raster data model uses a grid.

One grid cell is one unit or holds one attribute. One grid cell is one unit or holds one attribute. Every cell has a value, even if it is “missing.” Every cell has a value, even if it is “missing.” A cell can hold a number or an index value standing A cell can hold a number or an index value standing

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

ground units.ground units.

Generic structure for a grid Generic structure for a grid

Figure 3.1 Generic structure for a grid.

Row

s

Columns

Gridcell

Grid extent

Resolution

The mixed pixel problemThe 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

Grids and missing dataGrids and missing data

Figure 3.8 GIS data layer as a grid with a large section of “missing data,” in thiscase, the zeros in the ocean off of New York and New Jersey.

RASTERRASTER

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

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

Grids are good only at very localized topology, and weak Grids are good only at very localized topology, and weak otherwise.otherwise.

Grids are a natural for scanned or remotely sensed data.Grids are a natural for scanned or remotely sensed data. Grids suffer from the mixed pixel problem.Grids suffer from the mixed pixel problem. Grids must often include redundant or missing data.Grids must often include redundant or missing data. Grid compression techniques used in GIS are run-length Grid compression techniques used in GIS are run-length

encoding and quad trees.encoding and quad trees.

The Vector ModelThe Vector Model

A vector data model uses points stored by their real A vector data model uses points stored by their real (earth) coordinates. (earth) coordinates.

Lines and areas are built from sequences of points in Lines and areas are built from sequences of points in order. order.

Lines have a direction to the ordering of the points. Lines have a direction to the ordering of the points. Polygons can be built from points or lines. Polygons can be built from points or lines.

Vectors can store information about topology.Vectors can store information about topology.

Vectors: pro and conVectors: pro and con

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

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

and tablet digitizers.and tablet digitizers. Vectors are not good at continuous coverages or Vectors are not good at continuous coverages or

plotters that fill areas.plotters that fill areas.

TOPOLOGYTOPOLOGY

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

elimination.elimination. Rarely are maps topologically clean when digitized or Rarely are maps topologically clean when digitized or

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

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

eliminated.eliminated.

Topology MattersTopology Matters

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

Complete topology makes map overlay Complete topology makes map overlay feasible.feasible.

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

FORMATSFORMATS

Most GIS systems can import different Most GIS systems can import different data formats, or use utility programs to data formats, or use utility programs to convert them.convert them.

Data formats can be industry standard, Data formats can be industry standard, commonly accepted or standard.commonly accepted or standard.

EXCHANGEEXCHANGE

Most GISs use many formats and one data structure.Most GISs use many formats and one data structure. If a GIS supports many data structures, changing structures If a GIS supports many data structures, changing structures

becomes the user’s responsibility.becomes the user’s responsibility. Changing vector to raster is easy; raster to vector is hard.Changing vector to raster is easy; raster to vector is hard. Data also are often exchanged or transferred between different Data also are often exchanged or transferred between different

GIS packages and computer systems.GIS packages and computer systems. The history of GIS data exchange is chaotic and has been The history of GIS data exchange is chaotic and has been

wasteful.wasteful.

Vector to raster exchange errorsVector to raster exchange errors

Transfer StandardsTransfer Standards

GIS Data ExchangeGIS Data Exchange

Data exchange by translation (export and import) can lead to significant Data exchange by translation (export and import) can lead to significant errors in attributes and in geometry.errors in attributes and in geometry.

In the United States, the SDTS was evolved to facilitate data transfer.In the United States, the SDTS was evolved to facilitate data transfer. SDTS became a federal standard (FIPS 173) in 1992.SDTS became a federal standard (FIPS 173) in 1992. SDTS contains a terminology, a set of references, a list of features, a SDTS contains a terminology, a set of references, a list of features, a

transfer mechanism, and an accuracy standard.transfer mechanism, and an accuracy standard. Both DLG and TIGER data are available in SDTS format.Both DLG and TIGER data are available in SDTS format. Other standards efforts are DIGEST, DX-90, the Tri-Service Spatial Other standards efforts are DIGEST, DX-90, the Tri-Service Spatial

Data Standards, and many other international standards.Data Standards, and many other international standards. Efficient data exchange is important for the future of GIS.Efficient data exchange is important for the future of GIS.