Transcript Map Projections and How they are Made Cartography Additional Study Map Projections: http://geology.isu.edu/geostac/Field_Exercise /topomaps/map_proj.htm Round Earth, Flat Maps: http://www.nationalgeographic.com/features /2000/exploration/projections/ Page 1

Map Projections and
How they are Made
Cartography
Additional Study
Map Projections:
http://geology.isu.edu/geostac/Field_Exercise
/topomaps/map_proj.htm
Round Earth, Flat Maps:
http://www.nationalgeographic.com/features
/2000/exploration/projections/
Page 1
Map Projection: From Globe to Map
A map projection is used to portray all or part of the round
Earth on a flat surface. This cannot be done without some
distortion.
Map Projection: From Globe to Map
Every flat map misrepresents
the surface of the Earth in some
way. No map can rival a globe in
truly representing the surface of
the entire Earth.
However, a map or parts of a map can show one or more—but never all—of the
following:
True directions
True distances
True areas
True shapes
Types of Map Projections
.
Map Properties
•Useful map properties:
• preserving distances (equidistance)
•preserving directions
•preserving shape (conformality)
•preserving area (equal area)
Page 2
Types of Map Projections
Map Properties
What is the largest continent?
Most people would say Antarctica. But is it?
See Continents by Land Area.
Equal-Area Projection
Preserving area
Mapped areas have the same proportional
relationship to the areas on Earth
Equal Area
Eckert IV and Eckert VI,
Equal-Area Projection
Preserving area
Mapped areas have the same proportional
relationship to the areas on Earth
Different map projections result in different spatial
relationships between regions.
Equal-Area Projection
Preserving area
Mapped areas have the same proportional
relationship to the areas on Earth
Map Projection: From Globe to Map
A map projection is used to portray all or part of the round
Earth on a flat surface. This cannot be done without some
distortion.
Equidistant Map
An equidistant map projection correctly
represents distances. Distance between two
points are preserved.
Distances and directions to all places are true only from the
center point of projection. Distances are correct between
points along straight lines through the center. All other
distances are incorrect. Distortion of areas and shapes
increases dramatically, the further away one gets from
center point.
Equidistant Map
Distances are true only from the center point of
the projection
Equidistant:
Azimuthal Map, Miller’s Cylindrical Projection, Equidistant
Conic Projections
Equidistant Map
Distances are true only from the center point of
the projection
In this class we will study the Equidistant Azimuthal Map
Equidistant Map
Distances are true only from the center point of
the projection
Equidistant Cylindrical Map
Equidistant Map
Distances are true only from the center point of
the projection
Equidistant: Equidistant Conic Projections
Flat-plane Projection
Azimuthal
Another map projection called an Azimuthal Map, is a
flat-plane projection. It is very accurate where the 'paper
touches the Earth‘. There are no distortions, here. But
the further the 'paper' is away from the surface of the
Earth the greater distortions.
Flat-plane Projection
Azimuthal
Math:
http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html
http://blogs.esri.com/support/blogs/mappingcenter/archive/2
010/09/16/map-projection-animations.aspx
Flat-plane Projection
Azimuthal
Some widely used azimuthal projections are
• Equidistant azimuthal projection
• Gnomonic projection
• Lambert equal-area azimuthal
projection
• Orthographic projection
• Stereographic projection
• Universal polar stereographic projection
Azimuthal Projections
Azimuthal orthographic map with great circle passing through Campinas,
Brazil and Tokyo, Japan
Equidistant Map
Distances are true only from the center point of
the projection
Equidistant: Equidistant Azimuthal Projection
This is a great projection for
preserving area but get outside the
center and shapes become badly
distorted.
Distances and directions to all places are true
only from the center point of projection.
Distances are correct between points along
straight lines through the center. All other
distances are incorrect. Distortion of areas and
shapes increases dramatically, the further
away one gets from center point.
Azimuthal Equidistant
In the north polar aspect, the azimuthal equidistant is
familiar as part of both flag and emblem of the United
Nations Organization, with olive branches replacing
Antarctica.
Equal-area – no
Equidistant – yes
Conformal - no
Azimuthal Equidistant
Azimuthal
Projection
• Equidistant
• Center of map is most accurate
• Benefits:
• Shows great circle
• Distances & direction to all places are true
from center point
• Disadvantages
• Distortion increase as move away from center
• Can only show one hemisphere at a time
• Uses
• Show water currents and wind pattern
• Airplane navigation
• North and South Pole projections
Preserving area
Map Projection: From Globe to Map
The earth is round. The challenge of any world map is to represent a round
earth on a flat surface. There are literally thousands of map projections. Each
has certain strengths and corresponding weaknesses
Choosing among them is an exercise in values clarification: you have to decide
what's important to you. That is generally determined by the way you intend to
use the map.
Countries Arguing Over Maps
Mercator
vs
Peters
Shapes
vs
Size
Conformal
vs
Equal-Area
Conformal Maps
Preserving shape
Meridians and Parallels intersect at right angle
Conformal Maps
 When the scale of a map at any point on the map
is the same in any direction, the projection is
conformal. Meridians (lines of longitude) and
parallels (lines of latitude) intersect at right
angles. Shape is preserved locally on conformal
maps.
Conformal Maps
Preserving shape
Meridians and Parallels intersect at right angle
Famous Conformal Maps
Mercator, Transverse, Oblique Mercator
Distorting Circles in all Projection
Page 3. Document Camera
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
See the math
Cylindrical Projection
Mercator Projection
• Mercator’s Projection
• Cylindrical
• Conformal- preserves shapes
• Parallels and meridians are straight lines intersecting at right
angles
• Compass directions are maintained
• Meridians are equally spaced
• Parallel spacing increases with distance from Equator
• Benefits:
• Preserves angles and shapes
• One square inch on the map represents an equal number
of square miles anywhere in the world.
• Disadvantages
• Sizes are increasing distorted (at high latitudes, especially)
•Uses
• Navigation , air and marine
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Gerardus Mercator (1512-1594).
Frontispiece to Mercator's Atlas sive
Cosmographicae, 1585-1595.
Courtesy of the Library of Congress,
Rare Book Division, Lessing J.
Rosenwald Collection.
In the 16th-century Mercator made a map to help navigators . His conformal
map desired to preserve shapes of land.
This Mercator map is a famous conformal projection.
Notice the longitude and latitude lines are straight and at right angles.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Conformal map projections - each parallel must cross every meridian at
right angles.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Many conformal maps are cylindrical projections.
Conformal
Projections
A conformal map projection preserves the
shape of small areas but distorts their size.
Because longitudes and latitudes are curved on a globe, converting them to
straight lines will cause distortion in size and shape.
What are some benefits of this type of map?
What are some distortions of this type of map?
Conformal
Projections
A conformal map projection preserves the
shape of small areas but distorts their size.
http://makingmaps.owu.edu/mm/MakingMap
sCh05.pdf
Conformal Projections
A conformal map projection preserves the
shape of small areas but distorts their size.
The mapmaker's dilemma is that you cannot show both shape
and size accurately. If you want a true shape for the land
masses you will necessarily sacrifice proportionality, i.e., the
relative sizes will be distorted.
The Mercator projection
portrays Greenland as
larger than Australia; in
actuality, Australia is more
than three and a half times
larger than Greenland.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Greenland is much larger than actual size
Greenland appears to be the same size as Africa, yet Africa’s
land mass is actually 14x larger.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
The Mercator projection creates increasing distortions of size as
you move away from the equator.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Equator
When the Mercator projection was created, the custom among map-makers was to
place the map-maker’s country—in this case, Germany—at the center of the map.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Equator
It is common to have Antarctica cropped off, resulting in Equator not being in the middle of
the map
The Equator is placed 2/3 of the way down the map rather than halfway down. This
arrangement depicts Europe as being larger than South America.
In reality, South America is almost twice the size of Europe.
•Europe is 3.8 million square miles.
•South America is 6.9 million square miles.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Alaska is appears to be three times larger than Mexico,
although Mexico actually is larger than Alaska. On a
Mercator map, Greenland looks larger than China, even
though China actually is four times larger than Greenland.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Antarctica is enormously stretched, if it is shown at all.
It is common to have Antarctica cropped off, resulting in Equator not being in the
middle of the map
When Antarctica is not on the map, the equator is not in the center. This places
the United States, Europe and Russia as prominent countries.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Northern Hemisphere appears larger than it is
Mercator maps seldom extend above the 80°N parallel or below 75°S. Both this
apparent shift of the Equator southwards and the areal exaggeration of higher
latitudes, which mostly coincide with developed nations, have repeatedly incited
disapproval about its supposed bias against the Third World (it was even claimed to aid
racial discrimination by promoting a supposed superiority of Europe, the U.S.S.R. or the
U.S.A.)
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Mercator
vs.
Peters
Shapes
vs.
Size
Conformal
vs.
Equal-Area
What do each of these map convey about developed countries vs. developing
countries?
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
•The North is 18.9 million square miles.
•The South is 38.6 million square miles.
• The former Soviet Union is 8.7 million square miles.
•Africa is 11.6 million square miles.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Peters Map supporters contend:
This was convenient, psychologically and practically, through
the eras of colonial domination when most of the world powers
were European. It suited them to maintain an image of the
world with Europe at the center and looking much larger than it
really was.
Was this conscious or deliberate? Probably not, as most map
users probably never realized the Eurocentric bias inherent in
their world view.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
These distortions pose significant limitations for any use other than navigation.
Mercator projections present a surrealistic view of the world that makes them
inappropriate choices for use in classrooms or in any application that compares
separate regions of the world.
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
However, in order to keep shapes undistorted…
area of land became distorted.
But Mercator did not care. His map was to help
navigators get from one place to another.
He did not intend for this map to be used for anything
else.
But because some people did not really know their
geography they used this map for education. This
created generations of misinformed students!
This also led to political pride and arguing between
countries. Why?
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Benefits:
• This map is useful for ship and air navigators because it shows true direction and
shape.
• Navigators need to know the shortest route across Earth’s surface between two
points. Such a path is called a great circle on the globe’s surface.
Distortions: size of land and distances near poles
Preserving shape locally
Conformal Projections
A conformal map projection preserves the
shape but distorts their size.
Mercator's projection (created at a time when navigators were sailing on
the oceans in wooden ships, powered by the wind, and navigating by the
stars) was particularly useful because straight lines on his projection were
lines of constant compass bearing. Today the Mercator projection still
remains useful for navigational purposes and is referred to by seafarers
and airline pilots.
Rarely used in world maps nowadays, except by navigators. Rarely used in
teaching geography. But Google Maps needs to be informed! They better
learn geography and history!
Preserving area
Map Projection: From Globe to Map
The earth is round. The challenge of any world map is to represent a round
earth on a flat surface. There are literally thousands of map projections. Each
has certain strengths and corresponding weaknesses
Choosing among them is an exercise in values clarification: you have to decide
what's important to you. That is generally determined by the way you intend to
use the map.
ECylindrical Projection
Homolosine Projection
“Interrupted Map”
Preserving area
Equal-Area Projection
Dr. Arno Peters sought to create a new world map that dramatically improved
the accuracy of how we see the Earth.
The Peters Map is a famous equal-area map.
Preserving area
Equal-Area Projection
A map projection in which quadrilaterals formed by meridians and parallels
have an area on the map proportional to their area on the globe.
This results in showing area of countries, continents, and oceans – according
to their actual area.
Preserving area
Equal-Area Projection
The Peters projection map was first
introduced in Europe in 1974 by Dr. Arno
Peters, a German historian and
cartographer. Dr. Peters created his
projection to aid in developing a realistic
perception of the world. His equal-area
projection corrects the Northern
Hemisphere size bias of the Mercator map.
All areas, both land and water, are of
relatively proportional size: one square
inch anywhere on the map represents
158,000 square miles on the Earth’s
surface.
Some cartographers contend that the
Peters projection wall map is a valuable
educational tool because of its realistic
portrayal of proportion.
Preserving area
Equal-Area Projection
Peters said the Mercator projections unfairly shows some countries larger than they are.
By making an equal-area map, Peters said his new projection would give poorer, less
powerful nations their rightful proportions on a map.
Preserving area
Equal-Area Projection
However, because the Peters map is cylindrical,
just like the Mercator map, it also has
distortion in the polar regions.
Also, there is considerable
distortion along the equator.
The midlatitude region is less
distorted.
Lacks distance accuracy.
Conformal
Projections
A conformal map projection preserves the
shape of small areas but distorts their size.
http://makingmaps.owu.edu/mm/MakingMap
sCh05.pdf
Preserving area
Equal-Area Projection
Several scholars have noted the irony of the accuracy on the mid latitudes,
including Peters Germany, at the expense of the low latitudes, which is where
most of the undeveloped countries are located.
Remember… no flat map can be both conformal and equal-area
Preserving area
Equal-Area Projection
The distances along the 45th parallels north and south are really off.
(No world projection is good at preserving distances everywhere.)
Preserving area
Equal-Area Projection
Peters said there should be one map for the
world and it should be his. The unscholarly
conduct, of Peters, and his refusal to engage
cartographers in thoughtful discussion
contributed to the polarization and impasse.
Preserving area
Equal-Area Projection
World mission and aid-giving agencies use the Peters map because it serves to
represent the developing countries at their true proportion. The Peters map has been
widely adopted elsewhere, but remains a curiosity in the United States. Why is this?
Among related factors are these: (1) our resistance to join the rest of the world on the
metric system (even the British have changed from inches and Fahrenheit to
centimeters and Celsius), (2) national surveys showing U.S. schoolchildren have among
the lowest levels of geography awareness of all developed nations, and (3) many
professional cartographers have resented the "politicization" of their field. Arno Peters
was one of the first to assert that maps are unavoidably political.
http://www.petersmap.com/page9.html
Preserving area
Equal-Area Projection
In the 1980’s the American Cartographic Association produces a series of booklet
(including Which Map is Best) sought to educate the public about map projections
and distortion of maps. In 1989 and 1990, after very much debate, seven North
American geographic organizations adopted a resolution:
They rejected all rectangular world maps, and this included both the Mercator and
Peters projections.
Other cartographers said these seven North American geographic organization were
being reactionary and demonstrated immaturity in the profession, given all maps
were political. They said there is good use for both maps.
Preserving area
Equal-Area Projection
The Peters projection map was featured in the
United States television drama The West Wing
(season 2, episode 16), where an actor
explained to the president (actor) why the
Peters map was a proper map for schools. He
said it correctly represents the size of the
countries and give due prominence to
countries in less developed parts of the world
their place on the map.
Preserving area
Equal-Area Projection
The map is also a favorite of military strategist
Thomas Barnett, who has included it in his
presentations of The Brief, which have aired on
C-SPAN in the United States.
Preserving area
Equal-Area Projection
Is the map used today in other places? Yes, it is the primary map when showing
“special purposes” of the world. Equal-area map projections are generally used in
studies of large areas to show relative distributions.
It is best to have correct area when wanting to compare things like literacy rate,
income, pollution, etc, around the world. For example, imagine a display of
population density: if each million people are represented by a small dot, then it
becomes important that each country appears in relative size to other countries, so
that a dense collection of dots means a relatively dense population.
Preserving area
Equal-Area Projection
Cylindrical Projection
Peter’s Projection
• Cylindrical
• Equal-Area
• Benefits:
• Shows all countries in their true size and proportion
• One square inch on the map represents an equal
number of square miles anywhere in the world.
• Disadvantages
• Shapes of countries are distorted. For example,
Africa looks as long and thin as South America
•Uses
Countries Arguing Over Maps
The Mercator vs. Peters controversy is truly a moot point. Both maps are
rectangular projections and are poor representations of the planet. Ignorant
statements like "Only now are the first non-chauvinistic maps being produced
without bias to any one region of the earth. They are 'Peters Maps' from Peters
Atlas of the World" inflame geographers and cartographers alike because they're
lies - all maps show a certain degree of bias but professional map makers have not
promoted a politically incorrect map such as Mercator's - it's a silly "debate."
Matt Rosenberg
Preserving area
Map Projection: From Globe to Map
Is there another equal-area map that may be an option?
Preserving area
Map Projection: From Globe to Map
The earth is round. The challenge of any world map is to represent a round
earth on a flat surface. There are literally thousands of map projections. Each
has certain strengths and corresponding weaknesses
Choosing among them is an exercise in values clarification: you have to decide
what's important to you. That is generally determined by the way you intend to
use the map.
Map Projections – How They are Made
Cylindrical Projections
Cylindrical projections result from projecting a spherical surface onto a cylinder.
Cylindrical Equal-Area projections have straight meridians and parallels, the meridians are
equally spaced, the parallels unequally spaced.
1. Peters Map
 The Peters projection is a cylindrical equal-area projection that
de-emphasizes area exaggerations in high latitudes
2. Mercator

The Mercator projection has straight meridians and parallels that
intersect at right angles. Scale is true at the equator. The projection is
often used for marine navigation.
Map Projections – How They are Made
Conic Projections
Conic projections result from projecting a spherical surface onto a cone.
 Area, and shape are distorted away from standard
parallels. Directions are true in limited areas.
Map Projections – How They are Made
Azimuthal Projections
Azimuthal projections result from projecting a spherical surface onto a plane.
•
Azimuthal equidistant projections are sometimes used to show airroute distances. Distances measured from the center are true. Distortion of
other properties increases away from the center point.
•
The Lambert azimuthal equal-area projection is sometimes used to
map large ocean areas. The central meridian is a straight line, others are
curved. A straight line drawn through the center point is on a great circle.