gis bootcamp

Some of this material was presented by Bruce Stauffer, Advanced Technology Solutions, Inc., and Todd Bacastow, Penn State, at a PA GIS Conference

Seminar, June 2001

GIS BOOTCAMP

Todd Bacastow


Seminar, June 2001

Geography matters!

• ‘Geographic Information’ is information which can be related to specific locations.

• Most human activity depends on geographic information.


Seminar, June 2001

Topic 1: What is GIS?

• Dozens of possible definitionsSome emphasise the technology

The Hardware The Software

Others focus on applications Other terms often encountered: LIS,

AM/FM, Geo-information systems, etc. May emphasise different roles for the

system, e.g. spatial decision support system, spatial database system, etc.


Seminar, June 2001

One definition of GIS (Dueker and Kjerne,

1989)

• “Geographic Information Systems - A system of hardware, software, data, people, organizations and institutional arrangements for collecting, storing, analysing, and disseminating information about areas of the Earth”


Seminar, June 2001

Geographic Information System

• Concepts such as location, direction, distance, proximity, adjacency provide links between different data Geographic information usually broken down

into three linked components of Space Time Attribute


Seminar, June 2001


• An Information System is a set of processes, executed on raw data, to produce information which will be useful in decision-making


Seminar, June 2001


• In a system the whole is greater than the sum of its parts (Aristotle, C4th BC)

GIS is a convergence of technological fields and traditional disciplines

Not just technology: the data, people and institutional context are as much part of GIS as are the computers and software


Seminar, June 2001

GIS is the convergence of many disciplines:

• Geography

• Cartography

• Remote Sensing

• Photogrammetry

• Surveying

• Geodesy

• Statistics

• Operations Research

• Computer Science

• Mathematics

• Civil Engineering

• Business management

• Behavioural science

• Etc….


Seminar, June 2001

GIS as a tool

• Majority view of GIS

• Focus is on hardware, software and routines

• A technocentric perspective

• The favoured viewpoint of the system vendors


Seminar, June 2001

GIS as science

• Emphasis is on data, human uses, contexts

• A more academic perspective

• Geographic information science is the “science behind the systems”

• Includes concepts of spatial reasoning, cognition, human-machine communication, visualisation, data modelling, etc.


Seminar, June 2001

GIS is a product of a particular culture

• Most GIS developed in Europe/N. AmericaUSA: Arc/Info, ArcView, Intergraph,

Bentley, Autodesk, MAP, GRASS... Canada: Caris, Spans, GeoVision...France: GeoConcept, Carto 2-D...UK: Smallworld, GIMMS, Laserscan...Netherlands: ILWIS, PC Raster...


Seminar, June 2001

GIS is a commercial product

• Developments often driven by commercial considerations, less by scientific ones

• Vendor’s decisions usually based on questions of profitability

• Critical evaluation of proprietary GIS is rare


Seminar, June 2001

Boundaries of GIS are being pushed back

• GIS techniques and concepts increasingly seen in other areas and applications:“Office” type softwareIn-car navigation and other route-

finding systemsMultimedia presentationsThe InternetWAP, SMS, & MMS phone technology


Seminar, June 2001

What GIS is not

• GIS is not simply the technology: it also has a (growing and important) conceptual base

• GIS can not produce good results from bad data or poor conceptual frameworks

• GIS is not simply a program to produce maps

• GIS is not a substitute for thinking! • GIS is not the universal answer to all

problems!


Seminar, June 2001

Topic 2: Sources of Spatial Data


Seminar, June 2001

Data input - a major bottleneck

• Costs of input often >80% of project costs

• Labor intensive, tedious, error-prone

• Construction of the database may become an end in itself the project may not move on to

analysis of the data collected• Essential to find ways to reduce

costs, maximise accuracy


Seminar, June 2001

Manual data conversion involves three stages

• State 1: GeocodingThe conversion of analogue maps to

digital form

• Stage 2: Entering attribute valuese.g. the heights to associate with

digitised contour lines

• State 3: Linking attribute data to their own geocoded features


Seminar, June 2001

Digital map data: three possible situations.

• The data we want already existHopefully we can find and buy them

(or they may even be free!)

• Data exist but not in digital formWill require conversion from

analogue format

• Data do not exist at allWill need to collect the data

ourselves by remote sensing, field data collection, etc.


Seminar, June 2001

Data exist in digital form

•To be useful, have to be in right format, resolution, etc.

•Metadata can inform us as to fitness for purposeunfortunately such information

not always availablemay lead to misinterpretation,

false expectations about accuracy


Seminar, June 2001

Sources of digital map data

• National Mapping Organization

• Other government agencies

• Commercial data vendors


Seminar, June 2001

Standards

•standards may be set to assure uniformity within a

single data set or across several data sets

ensure the data can be shared across different hardware and software platforms


Seminar, June 2001

Some popular standards for digital

map data include• For Vector

data DXF and DWG NTF DLG TIGER SDTF DIGEST .E00 (Arc

Export) format Shapefiles

• For Raster dataBILBSQDEMTIFF JPEGBMP


Seminar, June 2001

Data exist but not in digital form

• Need tools to convert analogue maps or other source documents to digital format

• Digitizing may be performed manually or through automation Manual methods tedious & error

prone Automated techniques may create

bigger editing problems later


Seminar, June 2001

What if the Data do not exist at all?

• Field data captureMay be done manually (e.g. direct

survey), automatically (e.g. automatic data loggers, etc.) or a combination of the two

• Remote sensingIncludes satellite imagery,

geophysical survey, air photosMay be used as alternative source of

data


Seminar, June 2001

Criteria for choosing modes of input

• Type of data sourceimages favour scanningmaps can be scanned or digitised

• Database model of the GISscanning easier for raster, digitising

for vector• Density of data

dense linework makes for difficult digitizing

• Expected applications of the GIS implementation


Seminar, June 2001

Integrating different data sources: issues

• Formatsmany different format standards exist a good GIS can accept and generate

datasets in a wide range of standard formats


Seminar, June 2001


• Projections Many ways exist to represent curved surface

of the earth on a flat map Some projections are very common A good GIS can convert data from one

projection to another, or to latitude/longitude Input derived from maps by scanning or

digitizing retains the original map's projection

With data from different sources, a GIS database often contains information in more than one projection, and must use conversion routines if data are to be integrated or compared


Seminar, June 2001


• Scaledata may be input at a variety of

scalesscale is an important indicator of

accuracymaps of the same area at different

scales will often show the same features

variation in scales can be a major problem in integrating data


Seminar, June 2001


• Resampling rastersRaster data from different sources

may use different pixel sizes, orientations, positions, projections

Resampling is the process of interpolating information from one set of pixels to another

Resampling to larger pixels is comparatively safe, resampling to smaller pixels is very dangerous


Seminar, June 2001

Topic 3: Representing Spatial Entities


Seminar, June 2001

Representing Spatial Entities

• The object-focused approachBased on recognition of discrete

objects or entitiesMay be layer-based or object-

orientedUsually represented by Vector GIS


Seminar, June 2001

Two ways of representing space in a GIS

• The Tesseral (field-oriented) approachTypically seen in Raster GISAlso in some other models


Seminar, June 2001

Vector data models

• Based on the recognition of discrete objects or entities

• The location/boundaries of these objects defined with respect to some coordinate system

• Emphasis is on boundaries, space within and between boundaries implied

• Objects are usually defined in terms of points, lines and areas

• Complex graphic objects are seen as amalgamations of simpler ones

• Typical Vector GIS include ARC/INFO, MapInfo Intergraph MGE


Seminar, June 2001


Seminar, June 2001

Separation of Locational and Attribute data

• In vector GIS, geographic information is represented in terms ofLocational / geometric data

(“where?”)Attribute information (“what?”)Relationships between objects and

attributes


Seminar, June 2001

The vector data model

• Fundamental spatial primitive is a pointDefined by a single x,y coordinate

pair

• Points can be used to locate spatial objectsrepresent Vertices (single = “vertex”)

defining a linerepresent Nodes defining start- or

end-points on lines, junctions where lines meet, etc.


Seminar, June 2001

The vector data model

• Sequences of points can be used to define lines

• Lines themselves can be aggregated to represent Networks Boundaries of polygons and regionsTopographic features (contours,

breaks of slope, etc.).


Seminar, June 2001

Topology

• An essential element of vector GIS

• A distinct branch of mathematics

• Defines spatial relationships between objectsAdjacency, connectivity,

containment, etc.

• Essential for most vector GIS operations


Seminar, June 2001

Advantages and disadvantages of the vector

approach• Lower data volumes

• More adaptable to variations in scale/resolution of phenomena

• Tends to be more suited to social and economic applications

• Disadvantages: Less adaptable to uncertainty, fuzziness Often no “lowest common denominator” of

aerial unit .


Seminar, June 2001

Objects versus layers

• Major point of discussion in GIS since mid-1980s

• Alternative strategies for vector representation of geographic space a “stacked” sequence of layers a collection of discrete objects

• Difference in how contents of the database represents the real world

• Echoes wider developments in Computer Science


Seminar, June 2001

The Object view

• More closely mirrors natural ways of seeing the world

• Objects usually used in speaking, writing, thinking about the world

• Objects are fundamental to our understanding of geography

• Object-oriented approaches may offer data storage and processing advantages


Seminar, June 2001

What are these objects?

• Graphics objects can be points, lines, areas

• Geographic objects can be roads, houses, hills, etc.

• A space can be occupied by many, or no, objects A river is an object (has an identity, name,

coordinates, properties, etc.) A line is an object (also has an identity,

name, coordinates, properties, etc.)


Seminar, June 2001

Applications of object view:

• Utilities and facilities managementConcept of empty space littered with objects

fits many needs of managing infrastructureTwo or more objects may occupy same

horizontal position, separated verticallySmaller objects may be part of larger ones

(e.g. pipes as part of networks) and vice versa

Idea of a variable measured everywhere on Earth has little relevance


Seminar, June 2001

The Layer view

• Locations specified by a system of coordinates

• Geography of real world conceptualised as a series of variables (soils, land use, elevation, etc.)

• Each layer in the database represents a particular variable


Seminar, June 2001

The Layer view

• Layer view often more compatible with theories of atmospheric, ocean processes

• Object view is less compatible with concept of continuous change

• Good for resource management applications

• Much data for environmental modelling derived from remote sensing Implies a layer view


Seminar, June 2001

Disadvantages

• The layer approach usually requires many different files to represent each layer

• Some files contain the actual data

• Some contain registration information

• Some contain topological information to construct complex geometries from more primitive ones


Seminar, June 2001

Applications of layer view

• Resource managementgeographic variation can be

described by relatively small amount of variables

conceptualisation reasonably constant between scales

movement of individuals can lead to difficulties of representation and tracking across layers


Seminar, June 2001

Tesseral approaches to GIS


Seminar, June 2001

Tesseral geometries

• From the Greek, tetara or Latin tessella = a tile

• Tessallations are “sets of connected discrete two-dimensional units” thus mosaics or tilings of space

• May be regular or irregular

• Focus is on space occupancy

• Emphasis is on areas, boundaries are implied


Seminar, June 2001

Conceptual basis: creating a tessallation

• Define a geographic area of interest

• Undertake sampling of the entire area

• Each point is space is assigned a value

• The data are separated into a set of vertical thematic layers

• One item of information stored for each location within a single layer


Seminar, June 2001

Types of tessallation

• Regular tessalationsRasters

• Irregular tessalationsQuadtreesVoronoi TessalationsTriangulated Irregular Networks

(TINs)


Seminar, June 2001

The raster

• “Raster Data are spatial data expressed as a matrix of cells or pixels, with spatial positioning implicit in the ordering of the pixels” (AGI 1994)

• Raster data structure widely used in GIS e.g. IDRISI, GRASS, Arc/Info’s GRID module


Seminar, June 2001


Seminar, June 2001

The geometry of a raster• Square cell

Adjacency defined by edges and corners

Connectivity to four neighbouring cells

Uniform orientation throughout the matrix

Strong self-similarity Easy decomposition into identically-

shaped unitsVery efficient way of packing space


Seminar, June 2001

Why use rasters?

• Raster data from other disciplines

• Ideal for representing continuous variations in space

• Common way of structuring digital elevation data

• Assumes no prior knowledge of the phenomenon

• Uniform, regular sampling of reality


Seminar, June 2001

Why use rasters?

• Often used as common data exchange format

• Raster algorithms often simpler and faster

• Easy to program, less need for special hardware

• Raster systems tend to be cheaper than vector


Seminar, June 2001

Issues and trade-offs

• May give very large data files typical raster databases may contain >

100 layers each layer typically contains hundreds or

thousands of cells

• Many options exist for storing raster data

some are more economical than others in terms of storage space

some more efficient in terms of access and processing speed


Seminar, June 2001

Issues and trade-offs

• Maximum resolution determined by the size of grid

• Less easy to connect tabular (attribute) data to spatial objects

• Raster data lack topology

• Regular geometry of raster cells may not accurately reflect the variations of reality


Seminar, June 2001

Variable-resolution tessalations

• Triangulated Irregular Networks (TINs)Alternative to regular raster for terrain

modellingDeveloped in 1970s Can build surfaces from irregular arrays of

point elevation dataMany commercial GIS now offer TIN

capabilities.


Seminar, June 2001

Topic 4: Coordinates, Datums, and Projections


Seminar, June 2001

Spherical CoordinatesSpherical “grid” is called a graticuleLatitude references north and southLongitude references east/westLine of constant latitude is a parallelLine of constant longitude is a meridianMeridians converge at the poles

Latitude range: 0 to 90 degrees north and southLongitude range: 0 to 180 degrees east and west

0º LatitudeP

rim

e M

erid

ian

0º

Lo

ng

itu

de

Equator

90º N Latitude

90º S Latitude

SouthernHemisphere

NorthernHemisphere

EasternHemisphere

WesternHemisphere

90º W Longitude

0º L

on

git

ud

e

1

80º

Lo

ng

itu

de

90º E Longitude


Seminar, June 2001

Spherical CoordinatesA spherical coordinate measure is expressed in degrees (º), minutes (‘) and seconds (“)

1º = 60’ = 3,600” ; 1’ = 60”

Expressed as:ddd mm ss N/S, ddd mm sss E/W

Note the convention is to express latitude (y) before longitude (x), but computer environments use x,y

• In most digital environments, degrees, minutes and seconds are converted to decimal degrees: degrees + (min/60) + (sec/3600)• Harrisburg International Airport is: 40º12’N, 76 º45’W, or40.20N, 76.75W


Seminar, June 2001

Spherical Coordinates

Eastern and Northern Hemisphere: +x, +y

Eastern and SouthernHemisphere:+x, -y

Western and Northern Hemisphere: -x, +y

Western and SouthernHemisphere:-x, -y


Seminar, June 2001

Cartesian Coordinates

X axis

Y a

xis

0,0 1 2 3 4 5 6 7 8 9

1

2

3

4

5

6

(2.0,3.0)

(4.5, 4.5)

(7.0,2.0)


Seminar, June 2001

Horizontal Datum

North American Datum of 1983• an earth centered datum where the center of

the spheroid is the center of the earth • based on the Geodetic Reference System of

1980 (GRS80): a better approximation of earth’s true size and shape.

• twice as accurate as the NAD27: resulted in controls shifted up to 100 meters

North American Datum of 1927• A local datum centered on the Meades Ranch

in Kansas. Surface of ellipsoid was tangent to the Meades Ranch

• 300,000 permanent control network

• Clarke 1866 spheroid used to define the shape and size of the earth

Meades RanchKansas

EarthCenter

Clarke 1866Center

Clarke 1866 Spheroid

GRS80 Spheroid

Meades RanchKansas

EarthCenter

Clarke 1866Center

Clarke 1866 Spheroid

GRS80 Spheroid

NAD 1927 DATUM

NAD 1983 DATUM


Seminar, June 2001

Vertical Datum

North American Vertical Datum of 1988

• 1929 datum adjusted based on more precise measurements of geoid shape and mean sea levels.

• some bench mark heights changed up to 2 meters, but heights between adjacent benchmarks changed < a few millimeters

• provides better geoid height definitions in order to convert earth centered GPS derived heights

National Geodetic Vertical Datum of 1929

• vertical datum based mean sea level as determined by years of observations at tidal gauging stations

• 585,000 permanently monumented vertical benchmarks interconnected by leveling

Vertical Datum(mean sea level)

Land Mass

Sea Floor

Sea Level


Seminar, June 2001

Projections

To represent a spherical model of the earth on a flat plane requires a map projection!

Projection


Seminar, June 2001

Map ProjectionsZ = rotational axis

Y

X

o a

b

a

Spheroid: a three-dimensional geometric surface generated by rotating an ellipse about one of its axes.

It provides an approximate model of the earth’s shape, the first step in constructing a projection


Seminar, June 2001

Map Scale• Options to deal with minimum mapping unit

size at desired design scaleAdopt a larger map scale for the source

Increased cost for acquisition Increased storage for larger data volume

Convert area features to points or lines Evidence of feature is retained Inconsistency in feature representation May give up desired metrics (area, perimeter) May give up overlay analysis options

Eliminate small areas Consistency in feature representation No evidence of omitted features


Seminar, June 2001

PennsylvaniaStatewide Projection

• Projection: Lambert Conformal Conic• Spheroid: GRS80• Central Meridian: 77º 45’ 00.0” W (-77.75)• Standard parallels: 40º 36’ 10.8” N (40.603) 41º 16’ 33.6” N (41.276)• Reference latitude: 39º 19’ 59.9’ N (39.333)

Considerations for selecting a statewide projection for Pennsylvania:• Pennsylvania’s east/west extent is best suited for a conic projection • If you need to preserve area, use Alber’s Equal Area Conic • If you need to shape and angle, use Lambert Conformal Conic • Select two standard parallels that divide the state into approximately even

thirds north to south • Select a central meridian that divides the state approximately into equal halves


Seminar, June 2001

Map Projections

• Transform spherical geographic space to a 2-D planar surface.If it is a map, it has been projected!Eliminates need to carry a globe around in

the pocket!2-D Cartesian coordinate space is better suited

than spherical coordinates when conducting traditional surveys, mapping, and ground measurements.

• Ensures a known relationship between map location and earth location


Seminar, June 2001

Map Projections

CYLINDRICAL PLANARCONIC


Seminar, June 2001

Map Projections• A tangent projection results in 1 standard

parallel

• A secant projection results in 2 standard parallels

• A standard parallel is the mathematical point of intersection between the projection plane and the sphere.

• Scale distortion. The scale is true (1) along the standard

parallel(s). The scale is greater than 1 outside of the

standard parallel(s) On secant projections, the scale is less than 1

between the two standard parallels


Seminar, June 2001

Map Projections

• Any representation of the Earth’s 3-D surface on a 2-D plane involves distortion of one or more of the following:shapeareadistance (scale)direction (angle)


Seminar, June 2001

Map Projections

• There are many map projections • Each one is good at representing one or

more spatial properties• No projection can preserve all four

properties• The goal is to select a projection that best

matches the intended use of the map. • Projection distortion significantly affects

the properties of a small-scale map• Large scale maps are less effected by

projection distortion


Seminar, June 2001

Map Projection Distortion• Conformal projections

Preserve relative angle and shape for small areas, but area is very distorted

For any given point, local scale is constant in all directions

Used for navigation, meteorological charts Examples: Mercator and Lambert Conformal Conic

• Equivalent projections Preserve area but shape and angles are very distorted. A coin placed at any location on the map covers the

same amount of area Use when area conveys meaning (thematic maps

showing density) Examples: Albers Conic Equal Area and Peters

Projection


Seminar, June 2001

Map Projection Distortion

MERCATOR (Conformal)

ROBINSON

PETERS (Equivalent)


Seminar, June 2001

Universal Transverse Mercator (UTM)

DA

EMB

C • The cylinder is made secant to the sphere, cutting into the sphere along the lines AB and DE

• Lines AB and DE are standard meridians 360,000 meters apart. The scale is exact (1) along these lines.

• The scale for the area between the standard meridians is < 1 (scale too small). Outside these meridians, the scale is too large (> 1)

• Line CM is the Central Meridian, which starts and stops at the poles

• The UTM projection is applied every 6º, resulting in 60 UTM zones for the earth (360 / 6 = 60)

• Good projection if map extent falls within a zone. Should not be used if map extent spans multiple zones

• Used as State Plane projection system for states that are predominately N-S orientation (e.g. Vermont, Maine, Idaho)

0 mN10,000,0000 mS

320,

000

mE

EMB

DCA

680,

000

mE

500,

000

mE

0º 00’ 00”

80º 30’

84º 30’


Seminar, June 2001



Seminar, June 2001


Cen

tra l

Me r

idia

n

Cen

tra l

Me r

idia

n

Sta

nd

ard

Me r

idia

n

Sta

nd

ard

Me r

idia

n

Sta

nd

ard

Me r

idia

n

vv

UTM ZONE 17 UTM ZONE 18

81º

W

75º

W

72º

W

78º

W

84º

W

• Pennsylvania falls between two UTM Zones: Zone 17 and 18• Using either zone for a statewide projection causes excessive scale distortion• Defining a custom UTM zone with a Central Meridian at 78º W and Standard

Meridians at 81º W and 75 º W would be a better customized use of the UTM projection for PA.


Seminar, June 2001

Pennsylvania State Plane Coordinate System

• Based on two different applications of the Lambert Conformal Conic Projectionresults in two different zones: a North and

South Zone

• Minimizes scale and angle distortions for use by surveyors

• Local governments are required by State Law to use the PA State Plane Coordinate System


Seminar, June 2001

Pennsylvania State Plane North Zone

Scale: 1.000000

Scale: .9999568

Scale: 1.000000

Standard Parallel

Standard Parallel

Central Parallel

Cen

tral

Mer

idia

n77

º 45

’W

Projection Origin40º 10’N, 77º 45’W

40º 53’N

41º 57’N

41º 25’N


Seminar, June 2001

Pennsylvania State Plane South Zone

Scale: 1.000000

Scale: .9999595

Scale: 1.000000

Standard Parallel

Standard Parallel

Central Parallel

Cen

tral

Mer

idia

n

77º

45’W

Projection Origin39º 20’N, 77º 45’W

39º 56’N

40º 58’N

40º 27’N


Seminar, June 2001

Pennsylvania State Plane Origin Offsets For North and South Zones

X offset: 2,000,000’y offset: 0’

projection origin for both Zones: 2,000,000’, 0’

2,000,000’

x min 1,188,150’y min 153,500’

x max 2,813,400’y max 677,900’

2,000,000’

x min 1,204,600’y min 162,000’

x max 2,805,600’y max 771,700’


Seminar, June 2001

Map Scale

• Map scale: the relationship between map distance (or display distance) and actual ground distance

• Scale Calculations:Scale = map distance / (ground distance x conversion

factor)To determine map scale when map and ground

distances are known: 2.5” on map = 500 feet on ground 2.5/500*12 = 2.5/6,000 = 1:2,400

To determine ground distance when map scale is known:

1:4,800 is same as 1” = 4,800” 1.82” on map: 1 * 1.82 = 4,800*1.82 1.82” = 8,7376” = 728’


Seminar, June 2001

Map Scale

• Scale can be expressed as:Linear scale

Graphic scale bar

Correct if map is enlarged or reduced

Verbal scale statement 1 in = 2,000 ft Frequently used by engineers or architects

Representative fraction (RF) 1:24,000 (ratio is correct with any units) Usually used by cartographers


Seminar, June 2001

Map Scale• Small Scale Maps

Large denominator in RF (1:14,000,000)Maps of continents and world maps

• Medium Scale MapsMedium denominator in RF (1:24,000)USGS Topographic Quadrangles

• Large Scale MapsSmall denominator in RF (1:2,400)Tax maps, utility maps

• The smaller the number in the denominator, the larger the map scale½ is “larger” than ¼ and ¼ is “smaller” than ½


Seminar, June 2001

Map Scale

• Considerations for selection of source scalecostrequired accuracydesired output map scale(s)desired feature representationdensity of features to be displayed


Seminar, June 2001

Map Scale

• In a GIS, scale is a function of:source map scale (compiled scale)desired plot scale(s)

• Digital data can be plotted at any scaleaccuracy is only as good as the original

source scaleresolution of the data will become apparent

if plot scale greatly exceeds source scale


Seminar, June 2001

• Map scale sets boundary for feature resolution

• Feature resolution is defined as :The density of features that can be shown at a given

scale

The amount of detail (density of vertices) that can be used to represent a feature at a given scale

Map Scale

woodsoror

or


Seminar, June 2001

Map Scale

• Feature resolution is defined as :Minimum mapping unit: the smallest area feature

that can be effectively discerned at plot scaleGenerally around .15” as measured on map

1:24,000 (300 ft. on ground = .15” on map) 1:4,800 (60 ft. on ground = .15” on map) 1:2,400 (30 ft. on ground = .15” on map) 1:1,200 (15 ft. on ground = .15” on map)

60’

30’15’ f(scale) =


Seminar, June 2001

Map Scale

• Area features smaller than the minimum mapping unit are:Merged into surrounding data Converted from area to line (drainage)Converted from area to point (cities)Deleted/omitted

LARGER SCALE1:60,000

SMALLER SCALE1:8,000,000

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