Download Interpreting Tissot indicatrices

Principles of Cartography
 The Earth and Its Coordinate System
 Map Projections
 Selecting a Map Projection
 Scale and Generalization
http://montgomerycollege.edu/Departments/planet/M_AS102/coordinates/EarthLatLong.gif
http://maic.jmu.edu/sic/images/projections.gif
http://go.owu.edu/~jbkrygie/krygier_html/geog_222/geog_222_lo/geog_222_lo04_gr/scale.jp
g
Geodesy
 The science of earth measurement
 Approximations of the shape of the earth
o Sphere
o Ellipsoid
 Approximate shape of earth
o Geoid
 Most precise shape
 Flattened at the pole
 Extended at the equator
 Includes surface irregularities
http://jaeger.earthsci.unimelb.edu.au/ImageLibrary/Favourites/Page
s/monim_1300.html
https://www.e-education.psu.edu/files/geog482/image/ellipsoid_diagram.jpg
http://go.owu.edu/~jbkrygie/krygier_html/geog_353/geog_353_lo/geog_353_lo05_gr/projprocess.jpg
Datums
 A starting point
 Gives context to locations on the earth’s surface
 Defines the size and shape of earth (such as a reference
ellipsoid) and some sort of “tie point” that fixes the ellipsoid
to the to surface of the earth or the center of the earth
http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html
Not everyone uses the
same ellipsoid.
Airy is used in the UK,
North America uses
Clarke, but everyone
uses the WGS
(Worldwide, Global
Positioning System).
http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html
Geodesic datums and coordinate reference systems
 Geodetic datums define the reference systems that describe the size
and shape of the earth. Hundreds of different datums have been
used to frame position descriptions since the first estimates of the
earth's size were made by Aristotle. Datums have evolved from
those describing a spherical earth to ellipsoidal models derived
from years of satellite measurements.
 Modern geodetic datums range from flat-earth models used for
plane surveying to complex models used for international
applications which completely describe the size, shape, orientation,
gravity field, and angular velocity of the earth. While cartography,
surveying, navigation, and astronomy all make use of geodetic
datums, the science of geodesy is the central discipline for the topic.
 Referencing geodetic coordinates to the wrong datum can result in
position errors of hundreds of meters. Different nations and
agencies use different datums as the basis for coordinate systems
used to identify positions in geographic information systems,
precise positioning systems, and navigation systems. The diversity
of datums in use today and the technological advancements that
have made possible global positioning measurements with submeter accuracies requires careful datum selection and careful
conversion between coordinates in different datums.
 Geodetic datums and the coordinate reference systems based on
them were developed to describe geographic positions for
surveying, mapping, and navigation. Through a long history, the
"figure of the earth" was refined from flat-earth models to spherical
models of sufficient accuracy to allow global exploration,
navigation and mapping. True geodetic datums were employed only
after the late 1700s when measurements showed that the earth was
ellipsoidal in shape.
Ha ha!
“In the realm of thematic mapping, the focus
is on examining spatial patterns and
distributions, and so knowledge of the
precise direction, distance and area is not
critical.”
Given the scale of most thematic maps issues of geodesy rarely
enter into our world. In thematic mapping the assumption is that
the earth is a perfect sphere which drastically simplifies our
lives in terms of mathematics and creating or selecting a map
projection.
Basic Coordinate Systems





There are many basic coordinate systems.
These systems can represent points in two-dimensional or
three-dimensional space.
René Descartes (1596-1650) introduced systems of
coordinates based on orthogonal (right angle) coordinates.
These two and three-dimensional systems used in analytic
geometry are often referred to as Cartesian systems.
Similar systems based on angles from baselines are often
referred to as polar systems.
http://www.ncgia.ucsb.edu/education/curricula/giscc/units/u014/figures/figure01.gif
http://upload.wikimedia.org/wikipedia/commons/thumb/2/2c/3D_coordinate_system
.svg/487px-3D_coordinate_system.svg.png
http://eusoils.jrc.ec.europa.eu/gisco_dbm/dbm/img/ch3-5_fig2.jpg
Global Systems
 Latitude and Longitude
o The most commonly used coordinate system today is the
latitude, longitude, and height system.
o The Prime Meridian and the Equator are the reference planes
used to define latitude and longitude.
Latitude and Longitude
combine aspects of planar
coordinate systems
(Cartesian) with angular
measurement to
accommodate the
spherical shape of the
earth.
http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html
http://www.colorado.edu/geography/gcraft/notes/coordsys/coordsys_f.html
http://media.tiscali.co.uk/images/feeds/hutchinson/ency/c01522.jpg
Latitude
 The location on the earth’s surface between the equator and
either the North or South Pole.
 Latitude is a function of the angle between the horizon and
the North Star (or some other fixed star).
 As you travel towards the pole the angle increases.
 Latitude is designated in angular degrees N or S from 0° at
the equator to 90° at the poles.
 The surface designation for each degree of latitude is about
69.2 miles
 Latitude lines are parallel to the equator and to each other.
 The equator is a great circle, dividing the earth into two
equal parts.
 All other lines of latitude are small circles.
Longitude
 Earth rotates on its axis every 24 hours therefore any point on the
earth moves through 360 angular degrees in a day’s time or 15° in
each hour.
 In order to measure longitude you need a fixed point of reference
and accurate time keeping to determine the difference in time
between the local time and the point of reference.
 This time can be converted into degrees and thus position.
 The base line or reference for longitude is the Prime Meridian (as
of 1884) and has an angular designation of 0°
 Longitude position is designated as 0° to 180° east or west of the
prime meridian for a total of 360°
 The 180° meridian is the international date line
 Lines of longitude are not equally spaced
 At the equator each degree is 69.2 miles, but the distance narrows
towards the poles until the lines converge. This is called the
convergence of meridians.
Why do we care?
Familiarity with the spherical geographic grid and the
characteristics of the arrangement of meridians and parallels is
important in estimating graticule distortion on the flat map.
http://ian.macky.net/pat/gallery/scale.gif
Map Projections
A map projection is a way to represent the curved surface of the Earth
on the flat surface of a map. A good globe can provide the most
accurate representation of the Earth. However, a globe isn't practical
for many of the functions for which we require maps. Map projections
allow us to represent some or all of the Earth's surface, at a wide
variety of scales, on a flat, easily transportable surface, such as a sheet
of paper. Map projections also apply to digital map data, which can be
presented on a computer screen.
There are hundreds of different map projections. The process of
transferring information from the Earth to a map causes every
projection to distort at least one aspect of the real world – either shape,
area, distance, or direction.
Each map projection has advantages and disadvantages; the appropriate
projection for a map depends on the scale of the map, and on the
purposes for which it will be used. For example, a projection may have
unacceptable distortions if used to map the entire country, but may be
an excellent choice for a large-scale (detailed) map of a county. The
properties of a map projection may also influence some of the design
features of the map. Some projections are good for small areas, some
are good for mapping areas with a large east-west extent, and some are
better for mapping areas with a large north-south extent.
http://www-atlas.usgs.gov/articles/mapping/a_projections.html
Basic Types of Projections
Projections are developed from “developable surfaces.”
Developable surfaces are surfaces that can be flattened to for a
plane without compressing or tearing any part of it. Three
commonly used developable surfaces for map projections are the
cylinder, cone and plane.
Developable surfaces may be described as tangent or secant case
Tangent Case: Describes a developable surface that intersects the
reference globe along one line, usually a parallel line of latitude.
Secant Case: Describes a developable surface that intersects the
reference globe along two separate lines, usually two parallel lines
of latitude.
The CONE, CYLINDER and PLANE are developable geometric
shapes. The curved surface of the Earth can be projected on to
these shapes that can be unrolled to make a flat map.
http://www.geography.ccsu.edu/kyem/GEOG256/Map_projections/Projection_2_files/image001.gif
http://www.innovativegis.com/basis/pfprimer/Topic7/Topic7-3.gif
Map Projection Properties
A map projection is a method of portraying the two-dimensional curved
surface of the Earth on a flat planar surface. Projections are created to
preserve one or several measurements of the following qualities:
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
Area
Shape
Direction
Bearing
Distance
Scale
Each projection handles the conversion of these properties from the
curved surface of a globe to the flat surface of map differently.
The purpose of the map is of primary importance in choosing a
projection to illustrate spatial patterns of Earth phenomena. For
instance, the Mercator projection was long used for navigation or maps
of equatorial regions.
The cylindrical Mercator projection projects the globe onto a cylinder
tangent to the Equator. Large areas become distorted which increases
toward away from the Equator. Distances are true only along the
Equator; special scales are provided for other latitudes for
measurement.
The Robinson projection uses tabular coordinates rather than
mathematical formulas to make earth features look the "right" size and
shape. A better balance of size and shape result is a more accurate
picture of high-latitude lands like Russia, Soviet and Canada.
Greenland is truer to size but compressed.
http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/essentials/maps.html
Comparing distortions…
Lambert Conformal Conic
Projection
Mercator Projection
Tissot Indicatrix
The two maps above illustrate the effect that choosing a projection can
have on how features are displayed on a map. The first map uses the
Mercator projection and the second the Lambert Conformal Conic
projection. Both projections preserve conformality, which is illustrated
by the circular shape of the distortion ellipses on the maps. In the
Lambert projection there is no distortion along the standard parallels;
distortion increases as you move away from the standard parallels. The
area distortion is much greater in the Mercator projection than in the
Lambert as evident by the increasing size of the distortion ellipses as
you move away from the equator. Area distortion in the Lambert
projection is minimal due to the placement of the standard parallels.
Differences in the height and width of the distortion ellipses can be
used to identify the distance distortion. Distortion of distance in the
Lambert projection appears minimal. In the Mercator projection,
distances increase as you move north as evident by the increasing
height and width of the distortion ellipses.
http://www.personal.psu.edu/kwa107/projects/p01_report.htm
Tissot’s Indicatricies
A Tissot indicatrix ("Tiss-oh") displays properties of a map projection
at a point.
A projection cannot preserve all the geometric properties of space at
every point: length, area, angle. The Tissot indicatrix is a figure that
shows how a projection changes the geometry.
Interpreting Tissot indicatrices
A conformal projection preserves local angles. The indicatrix will be a
circle. It might be a different size than the reference circle.
Conversely, wherever the indicatrix is circular, the projection is
conformal.
Tissot indicatrices for the Mercator
projection, showing conformality.
The large distortion at extreme southern
latitudes is evident in the discrepancies
between the gray (reference) circles and
the Tissot indicatrices (blue circles).
An area-preserving transformation preserves local areas. The
indicatrix may be an ellipse. In that case, the expansion along the
major axis will exactly compensate for the contraction along the minor
axis in order to preserve area. (The area of an ellipse is proportional to
the product of its major and minor axis lengths.)
Tissot indicatrices for the Peters
projection, showing its equal-area
property.
The blue ellipses maintain constant
areas, but the amount, degree, and
direction of scale distortion varies
dramatically from north to south,
illustrating the large distortions present
in this projection.
An equidistant transformation preserves distances along some path,
often a parallel or meridian. Along this path, the indicatrix and the
reference circle will intersect.
Tissot indicatrices for an azimuthal
equidistant projection from the south
pole.
The blue ellipses meet the reference
circles at their northern and southern
tips, showing how scale is consistently
preserved along meridians. The
indicatrices make the increased eastwest distortion to the north apparent.
http://www.quantdec.com/tissot/index.htm
Preserving Qualities in the Map Projection
Equivalent map projections
 preserve landmasses in their true proportions, as found on the
earth’s surface.
Alber’s Equivalent
Conic Projection
- Two standard
lines at 30° N and
45° N
http://www.personal.psu.edu/jwr206/albers3.png
Conformal Projections
 preserve angular relationships around a point by preserving scale
relations about that point in all directions.
 Conformal projections do not preserve shapes per se but preserve
the angular relationships so that the scale factor of the map changes
along a path between to points at the same rate.
http://2.bp.blogspot.com/_R4hC30cg9Z4/S-kNj4Vvz8I/AAAAAAAAACA/v7ezl_-nzaE/s1600/conformal.jpg
Equidistant Projections
 Preserve the principal scale from two points on the map to any
other point on the map (example: if the two points are the poles,
then all the meridians are straight lines that have the same principal
scale).
http://matplotlib.sourceforge.net/basemap/doc/html/_images/aeqd_fulldisk.png
http://www.mgaqua.net/AquaDoc/Projections/img/Equidistant%20Cylindrical.jpg
Azimuthal Projections
 Directions or azimuths are preserved from the center of the map to
any other point on the map.
 All straight lines drawn or measured to distant points represent
great circle routes
http://matplotlib.sourceforge.net/basemap/doc/html/_images/nplaea.png
Selecting a Map Projection
Select a class of map…
In theory, the selection of a map projection for a particular area can be
made on the basis of:
 the shape of the area,
 the location (and orientation) of the area, and
 the purpose of the map.
Brazil on an Azimuthal
Kazakhstan on a Conic
Tunisia on a Cylindrical
\http://www.geo.hunter.cuny.edu/~jochen/GTECH201/
Lectures/Lec6concepts/Map%20coordinate%20system
s/How%20to%20choose%20a%20projection_files/ima
ge012.gif
Ideally, the general shape of the mapping area should match with the
distortion pattern of a specific projection. If an area is approximately
circular it is possible to create a map that minimizes distortion for that
area on the basis of an azimuthal projection. The cylindrical projection
is best for a rectangular area and a conic projection for a triangular area
(figure below).
The choice of the map projection class (cylindrical, conical or
azimuthal) depends largely on the general shape of the mapping area.
http://gisremote.blogspot.com/2008_02_10_archive.html
Select your aspect…
Map aspect refers to the
placement of a projection’s
center with respect to the
earth’s surface: common
aspects are equatorial,
polar, and oblique.
http://www.mathworks.com/help/toolbox/map/cyl-aspect-types.gif
The choice of the aspect of a map projection depends largely on the
location (and orientation) of the geographic area to be mapped.
Optimal is when the projection centre coincides with centre of the area,
or when the projection plane is located along the main axis of the area
to be mapped.
Once the class and aspect of the map projection have been selected, the
distortion property of the map projection has to be chosen. The most
appropriate type of distortion property for a map depends largely on the
purpose for which it will be used.
Consider the properties of the map projection…
For example…
Map projections with a conformal distortion property represent angles
and local shapes correctly, but as the region becomes larger, they show
considerable area distortions. An example is the Mercator projection.
Although Greenland is only one-eighth the size of South America,
Greenland appears to be larger. Maps used for the measurement of
angles (e.g. aeronautical charts, topographic maps) often make use of a
conformal map projection.
The Mercator projection is a cylindrical map projection with a conformal
property. The area distortions are significant towards the polar regions. An
example, Greenland appears to be larger but is only one-eighth the size of
South America.
Map projections with a equal-area distortion property on the other
hand, represent areas correctly, but as the region becomes larger, it
shows considerable distortions of angles and consequently shapes.
Maps which are to be used for measuring areas (e.g. distribution maps)
often make use of an equal-area map projection.
The cylindrical equal-area projection after Lambert is a cylindrical map
projection with an equal-area property. The shape distortions are
significant towards the polar regions.
The equidistant distortion property is achievable only to a limited
degree. That is, true distances can be shown only from one or two
points to any other point on the map or in certain directions.
If a map is true to scale along the meridians (i.e. no distortion in NorthSouth direction) the map is equidistant along the meridians (e.g. the
equidistant cylindrical projection in the figure below).
If a map is true to scale along all parallels we say the map is equidistant
along the parallels (i.e. no distortion in East-West direction). Maps
which require correct distances measured from the centre of the map to
any point (e.g. air-route, radio or seismic maps) or maps which require
reasonable area and angle distortions (several thematic maps) often
make use of an equidistant map projection.
The equidistant cylindrical projection (also called Plate Carrée
projection) is a cylindrical map projection with an equidistant property.
The map is equidistant (true to scale) along the meridians (in NorthSouth direction). Both shape and area are reasonably well preserved
with the exception of the polar regions.
Once the class and aspect of a map projection have been selected, the
choice of the property of a map projection has to be made on the basis
of the purpose of the map.
The ideal map projection for any country would either be an azimuthal,
cylindrical, or conic projection, depending on the shape of the area,
with a secant projection plane located along the main axis of the
country or the area of interest. The selected distortion property depends
largely on the purpose of the map.
http://www.kartografie.nl/geometrics/map%20projections/body.htm
Some simplified guidelines…
 If you want to show a country or region on or near the equator
use a cylindrical projection
Africa on a Cylindrical Equal-Area
projection with true-scale standard
parallels at 20° N and S
http://www.gis.psu.edu/projection/chap5figs.html
 If you want to show a country or region in the temperate zones,
use a conic projection.
A Lambert Conformal Conic projection of the U.S. based on truescale standard parallels at 33° and 45° N.
http://www.gis.psu.edu/projection/chap5figs.html
 If you want show a country or a region near the poles, use an
azimuthal projection.
The azimuthal Equidistant
projection is also known as the
Postel, and the Zenithal Equidistant.
 If you want to show a country or region with minimal
distortion in the map projection, change the aspect of the map
projection so that the area of interest is in the center of the
map.
http://www.kartografie.nl/geometrics/map%20projections/body.htm
When working with world maps,
o If you want to make a statistical map of the world an equalarea pseudo cylindrical projection is a good choice.
Pseudo-cylindrical projections are projections in which the parallels are
represented by parallel straight lines and the meridians by curves. The
central meridian is the only meridian that is straight.
Robinson's pseudocylindrical
projection. Shapes
and areas are
reasonable well
preserved.
http://www.kartografie.nl/geometrics/map%20projections/body.htm
o If you want to make a world map that others can take off
right off a web page and use in a GIS program select the
Plate Carrée or equi-rectangular projection.
http://www.gisanalyst.com/projects/labs/export/3040_lab6_plate_carree.jpg
Now that you are familiar with the basic classes of maps and some of
the advantages and disadvantages of different types of projections,
before you select a projection think very hard about the purpose of the
map. For your purpose is it more important to show accurate area,
shape, direction, distance or scale? Or do any of these matter?
The following is a relatively short list of types of projections, their
characteristics and uses. This may be of help to you in selecting a map
projection. Also review “A Summary of Map Projections in ArcView,”
which may further help narrow your decision. You may access this
document through the webpage or directly through the following link.
http://info.wlu.ca/~wwwgeog/special/geomatics/html/arcprojections.htm
Map Projections Grouped By Class
Projection
Description
Cylindrical
Central cylindrical
Map projection is perspective but not conformal nor equal area. Projected perspectively
from the center of the Earth onto a cylinder tangent to the equator. Only used for teaching
purposes.
Equidistant cylindrical Also known as simple cylindrical or Plate Carrée. The projection is equidistant in the
direction of the meridians. Parallels and meridians (half as long as the parallels) are equally
spaced straight lines forming square blocks. This projection maps longitude and latitude
directly into x and y, hence is sometimes called the latitude-longitude projection. In Google
Earth used for display of imagery. The transverse version is known as the Cassini
projection.
Equirectangular
Also known as Plate rectangle, a variant of Plate Carrée. Used for raster maps which store
information of the whole world: each pixel represents a rectangular block of latitudelongitude coordinates.
Gall-Peters
Similar to Lambert's cylindrical equal-area projection, but with standard parallels at 45
degrees North and South.
Lambert cylindrical
equal-area
It is of little use for world maps because of the distortions. Mainly used for educational
purposes.
Miller cylindrical
Modified Mercator projection proposed by O.M. Miller. Compromise between Mercator
and other cylindrical projections. Shape, area and scale distortion increases moderately
away from the equator. Used in numerous world maps.
Mollweide
Pseudo-cylindrical projection. Map is equal area. Occasionally used in thematic world
maps.
Mercator
Conformal map projection. Designed for navigational use; standard for marine charts.
Recommended use for conformal mapping of regions predominantly bordering the equator.
Often inappropriately used as a world map.
Trasverse Mercator
Also called Gauss Conformal, or Gauss Krüger. Transverse form (transverse cylinder) of
the Mercator projection. Used for topographic maps at scales from 1: 20,000 to 1: 250,000.
Recommended for conformal mapping of regions that are predominantly north-south in
extent.
Universal Transverse A version of the Transverse Mercator, but one with a secant map surface. It divides the
world into 60 narrow longitudinal zones of 6 degrees. Widely used standard for topographic
Mercator (UTM)
maps and military maps.
Azimuthal
Azimuthal equidistant Distances measured from the centre of the map to any point are correct and the bearing of
any point from the center is correct (this applies to all azimuthal maps). Commonly used in
the polar aspect for maps of polar regions and the Northern and Southern hemispheres. The
oblique aspect is frequently used for world or air-route maps centered on important cities
and occasionally for maps of continents.
Gnomonic
Map is perspective and neither conformal nor equal area. Area, shape, distance and
direction distortions are extreme. It is used to show great circle paths as straight lines and
thus to assist navigators and aviators.
Hammer-Aitoff
A variant of Lambert azimuthal equal-area. Used for thematic maps of the whole world.
Lambert azimuthal
equal-area
Used for maps of continents and hemispheres. Also suited for regions extending equally in
all directions from a center point, such as Asia and the Pacific Ocean. Recommended to the
European Commission for statistical analysis and display.
Orthographic
Known by Egyptians and Greeks 2000 years ago. Map is perspective and neither conformal
nor equal area. Only one hemisphere can be shown. The Earth appears as it would on a
photograph from space.
Stereographic
Apparently invented by Hipparchus (2nd century bc). Used in combination with UTM
projection as Universal Polar Stereographic (UPS) for mapping poles and in navigation
charts for latitudes above 80°. Recommended for conformal mapping of regions that are
approximately circular in shape; a modified version of the stereographic projection is used
in the Netherlands for large-scale and topographic maps.
Conical
Albers equal area
conic
It is equal to Lambert's equal area conic, but has two standard parallels (secant cone).
Excellent for mid-latitude distribution maps. The projection does not contain the noticeable
distortions of the Lambert projections. Frequently used for maps of the United States, for
thematic maps and for world atlases.
Lambert conformal
conic
Lambert conformal conic, also called conical orthomorphic (Lambert, 1972). Extensively
used for large-scale mapping of regions predominantly east-west in extent. Further widely
used for topographic maps.
Polyconic
or American polyconic (Hassler, ± 1820). Map is neither conformal nor equal area, but each
parallel is true to scale. The sole projection used for large scale mapping of the United
States by the USGS until the 1950's.
Simple conic
Also known as equidistant conic. Meridians are true to scale (i.e. no distortion in northsouth direction). The most common projection in atlases for small countries.
Other projections
Sinusoidal
Used since 16th century. Also called Sanson-Flamsteed or Mercator equal area projection.
Pseudo-cylindrical projection. Map is equal area. Used in atlas maps of South America and
Africa. Occasionally used for world maps. Modifications are called sinusoidal interrupted
and sinusoidal 3x interrupted.
Van der Grinten
Shows the entire Earth within one circle. All areas, shapes and angles are greatly distorted.
Winkel Tripel
Used in several atlases. A triple compromise of reduced shape, area and distance distortion.
Selected by the National Geographic Society (NGS) for its new reference world map, in
place of the Robinson projection.
http://www.kartografie.nl/geometrics/map%20projections/body.htm
Scale and Generalization
Scale provides an indication of the amount of reduction that has
taken place on a map. Generalization refers to the process of
reducing the information content of maps due to scale change,
map purpose, intended audience or technical constraints.
Cartographic Generalization
Conceptual
Objectives
(Why to generalize)
Cartometric
Evaluation
(When to generalize)
Fundamental
Operations
(How to generalize)
Why Generalization?
 Reduce complexity
 Maintain spatial accuracy of critical components
 Maintain attribute accuracy of critical components
 Maintain aesthetic qualities
 Maintain a logical hierarchy
When to Generalize…
 When there is congestion- too many objects that compressed into
too small a space
 When there is coalescence-when features collide
 When there is conflict-when there is inconsistency among features
 When there is complication-when features become unduly
complicated
How to Generalize…
 Simplification- weed out unnecessary data
http://gis.unbc.ca/courses/geog205/labs/lab2/images/image027.jpg
 Smoothing-shift position of points to improve the appearance of a
feature
http://www.gis.unbc.ca/courses/geog205/lectures/generalization/dougpoik.jpg
 Aggregation-merge point features
and display them as areal units
http://www.gis.unbc.ca/courses/geog205/lectures/generalization/gen2.jpg
 Amalgamation-fuse neighboring polygons
http://www.satprints.com/ProductImages/Minnesota.jpg
http://www.worldmapsinfo.com/mapimage/minnesota.jpg
 Collapse-Convert the geometry
http://www.gis.unbc.ca/courses/geog205/lectures/generalization/index.php
 Refine-reduce multiple sets of features
 Merge-fuse groups of lines
http://1.bp.blogspot.com/_zwaRuUhzrcM/SZbRXWRLGhI/AAAAAAAAAr0/0RI4rslenlc/s320/Picture
6.png
http://www.zonu.com/imapa/inmonacional/images/Satellite_Image_Photo_Sierra_Segura_Sierra_Filabr
es_Sierra_Nevada_Spain.jpg
 Exaggerate-amplify a part of a
feature to make it visible
http://www.dcda.org.uk/Cartography/3detailed.html
 Enhance-change the symbolization to emphasize importance
http://www.lib.utexas.edu/maps/usgs_ref/usgs2.jpg
 Displace-pull features apart to prevent coalescence
http://www.geocomputation.org/2000/GC034/gc034_100.jpg
Issues of generalization increase with reductions in scale. The smaller
the scale, the more generalization will be needed. The level of
generalization is also part and parcel part of the design process dictated
by the purpose of the map and the intended audience.
Whereas the majority of these issues are addressed through the use
feature specific algorithms, fortunately for you, many are now
integrated into GIS software. The issue becomes how to apply them,
and even after you have applied them how much manual readjustment
you may be required to make.