Projections
Video Transcript
Slide 1
So now that we know about how to
measure the Earth and how to locate
things on its surface. Let’s discuss how
the world becomes a flat map using
projections.
Introduction
to GIS
PROJECTIONS
Slide 2
A projection is a systematic
transformation of the three
dimensional earth onto a two
dimensional developable surface. All
projections include distortion and not
one projection is the best universal
projection for all purposes. In this
lecture we’ll talk a little bit more
about map projections in general.
Map Projections
Slide 3
Back to the first video… The problem
that cartographers have is that when
you take a sphere or spheroid and try
to lay it out flat - something's going to
give. Just like taking an orange peel
and trying to flatten it out… something
gets distorted and it's virtually
impossible to do without breaking the
surface in at least a few places.
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Projections
Slide 4
Any projected flat map or parts of a
map can have the following
characteristics:
True direction
True distances
True areas
True shapes
Or DADS… Direction, Area, Distance,
Shape.
Distortion
True Direction
Azimuthal
True Distance
Equidistant
True Area
Equal Area
True Shapes
Conformal
Maps typically can’t have all of these
characteristics at one time. So when
you choose a projection you are
deciding which of these characteristics
you want to retain or that will have
the least amount of distortion. As such
we can use these properties to
describe a projection’s distortion - At
least one or up to all four of these
properties may be distorted on a
projected flat map.
Typically projections are named based
on the characteristics that they
maintain. For example maps that have
true direction are called Azimuthal.
Equidistant maps have true distances
Equal area maps have true areas
Conformal maps have true shapes
So when you have a Lambert
Conformal Conic Projection, you know
that it is best when you need True
Shapes, other characteristics will be
distorted to a greater extent. But what
does Conical mean? That comes next!
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Slide 5
So when you have a Lambert
Conformal Conic Projection, you know
that it is best when you need True
Shapes, other characteristics will be
distorted to a greater extent. The
distortion also depends on your
Developable surface…
Lambert Conformal Conic Projection
Slide 6
A developable surface is a surface that
can be flattened onto a plane without
any distortion. That means there's no
stretching, no compression depending on how we flatten the
earth and which projection type we
use, the developable surface will be
different.
Developable Surface
If we use a plane we have a point of
tangency and areas touching the plane
are not distorted.
If we use a cylinder any location that is
tangent or secant to the sphere to the
sphere (touches the sphere perfectly)
will not be distorted.
Finally if we use a cone to flatten the
earth any area that is tangent or
secant to the cone will also not be
distorted.
In all of these examples, there's only
one point or one line (depending on
the method used) in which there is no
distortion. As you move further away
from the point or line, the distortion
increases. We use the developable
surface to classify different types of
projections. Let’s look at the different
types of projections more closely.
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Slide 7
Back to our Lambert Conformal Conic
Projection, The conic means that the
developable surface of this projection
is a cone and the parts of the world
that are least distorted are along the
standard parallels or points of
tangency indicated here. Not all of the
names are this easy… but there are
plenty of resources out there that list
projections and their distortions.
Lambert Conformal Conic Projection
Slide 8
let’s look at cylindrical projections.
Imagine placing a movie screen
around the globe in a cylinder shape.
The projection results in areas very
close to the equator having very little
distortion however, closer to the poles
the area is more distorted. For
example Greenland appears to be
many times larger than it really is.
One of the most common cylindrical
projections is the Mercator projection.
The Mercator projection is conformal tangent along the equator and has
straight lines. There is no convergence
at the polls. This means that along the
equator the distortion it is minimal,
however, as you move further away
from the equator either north or
south, the amount of distortion
increases.
This type of projection is very useful
for navigation. At or near the equator
any straight line drawn is a true
compass heading otherwise known as
a rhumb line. It is truly a directional
map.
Cylindrical Projections
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Slide 9
Slide 10
A conical projection is created by
placing a conical shaped screen on a
globe. The resulting semicircular map
is more accurate than a cylindrical
projection map. The further we travel
down the map. The more distorted
and less accurate the map becomes.
Conical Projections are used for midlatitude areas that have an east-west
orientation. They're very useful for
projecting areas such as the United
States which is mid-latitude and has
an east west orientation. The lines of
latitude where the cone touches the
earth are called standard parallels.
Conical Projections
Azimuthal or plane projections are
created by placing an imaginary
screen directly above or below a
globe. While not commonly used, it
retains area, direction, and distance
properties. Because of this, it can be
useful for maps showing population
density, political boundaries and
oceanic mapping. As you can see from
these examples, azimuthal projections
have a point of tangency compared to
conical or cylindrical projections which
have lines as tangential points. This
means that there's only one POINT
that minimizes distortion in an
azimuthal projection.
Azimuthal or Plane
Projections
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Slide 11
There are many different types of
interrupted projections. They tend to
depict continents as accurately as
possible by leaving blank or empty
space and less important areas such as
oceans. So the ocean may be cut out
of the map but the land area will be
more accurate. These types of
projections are often called orange
peel maps because they distinctly
resemble that flattened orange peel
we looked at earlier. Interrupted
projections can be used for equal
aerial world maps and are used very
commonly with raster data. The
United States Geological Survey
(USGS) Center for Earth Resources
Observation and Science (EROS)
Center provides data in Goode’s
homolosine projection which is an
interrupted projection.
Interrupted Projections
So with all these choices how do we
decide? In the next video we will look
at ways your GIS software can help
you with projections.
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