Map Projection

Map Projection
§ Curved surface (3D)
2D Flat Surface
§ Approaches to transfer the spherical earth on
a two dimensional surface
§ Some distortions will always occur
Projection cont.
n
Visualize a light shining through the
Earth onto a surface
Distortions
n
Fitting sphere to plane causes
stretching or shrinking of features
Types of Distortion
Shape
n Area
n Distance
n Direction
n
Projection properties
n
Conformal
n
n
Equal- area
n
n
maintains area
Equidistant
n
n
maintains shape
maintains distance
Azimuthal (Planar)
n
maintains some directions
Example
Mercator Projection
(Shape Preserved)
Mollweide Projection (Area preserved)
Developable Surfaces
n
Can be flattened without distortion
n
n
n
n
n
Cylinders
Cones
Planes
Other
A point or line of contact is created
when surface is combined with a
sphere
Developable surfaces
contacting spheres
n
Tangent
n
n
Secant
n
n
n
projection surface touches sphere
surface cuts through sphere
No distortion at contact points
Increases away from contact points
Example
Lambert’s Conformal Conic
From James R.
Smith,page 194
Cylindrical Projection
n
Projecting a spherical surface onto a
cylinder
• Longitudes equally spaced
• Latitudes unequally spaced
• Scale is true along equator
• Shape and scale distortions
increase near poles
• Best for equatorial or low
latitudes
Cylinder touches sphere along
Rotate cylinder to reduce two lines - both small circles
distortion along a line
- UTM is based on this
- Cylinder right angles to the pole
Conic projections
- result from projecting a spherical surface onto a cone.
Best for mid- latitudes with
an East- West orientation
like Canada
Azimuthal (Planar) projections
- result from projecting a spherical surface onto a plane.
•Best for polar or circular regions
•Direction always true from center
Common Projections
n
n
n
n
n
Mercator
Universal Transverse Mercator
Albers Equal Area
Lambert’s Conformal Conic
Azimuthal Equidistant
Mercator Projection
-Projected on a cylinder
-Any straight line is a
line of constant
direction (rhumb line)
-Used for navigation
-True Directions,
-Conformal (angles and
shapes true in small
areas) but not equal area
or equidistant
-Cylindrical
Universal Transverse Mercator
§ Divides the earth from latitudes 84N to 80S
in 60 vertical zones that are 6 deg wide.
§ Zones are numbered starting at 180th
meridian in eastward direction
§ Each zone is divided into sections of 8 deg
latitude each
§ Eastings (from Central meridian) and
Northings(from equator) can be designated
for each zone
§ UTM preserves Area, Distance and Shape
well.
Universal Transverse Mercator
Albers Equal Area
• Conic (Secant case)
• Well-suited for areas that
are mainly east-west in
extent
• Areas - True
• Directions - Reasonably
accurate in limited regions
• Distances and Scale True
only along standard
parallels
• Map - not conformal
• Used for Thematic maps
Lambert Conformal Conic
• Conic (Secant case)
• Distances - True only along
standard parallels
• Map - Conformal but not equal
area or equidistant
• Area and Shape - Distortion
minimal at std. parallels
• Directions - Reasonably
accurate
• Shape - True for small areas
• To map large ocean Areas and
regions in E-W extent
Different map projections result in different spatial relationships between regions.
Azimuthal Equidistant
• Extent - World; Eq/midlat/Polar
• Distances measured from
centre are true; Distortion of
other properties increases
from centre point
• Useful for showing airline
distances from centre point
• Useful for seismic & radio
work
Choosing a projection
n
n
Often mandated by organization
Or intended use:
n
n
n
Thematic = equal- area
Presentation = conformal (also equal- area)
Navigation = Mercator, true direction or
equidistant
Choosing, cont.
n
n
n
n
Extent
Location
Predominant extent
Projection supports spheroid/
datums?
Combining data
n
n
n
Data must be in common coordinate
system
Must know projection AND GCS
(datum)
Ex. Both in UTM, zone 10,
n
n
1 is NAD27, 1 is NAD83 -Y coordinates up to 200 meters off
COMMON MAP PROJECTIONS
Equal Area – Goode’s Homolosine
From Robinson, Sixth Edition, page 81
COMMON MAP PROJECTIONS
Special Purpose
Equidistant Cylindrical/Plane Chart
From Robinson, Sixth Edition, page 86
COMMON MAP PROJECTIONS
Special Purpose – Simple Conic
From Robinson, Sixth Edition, page 87
COMMON MAP PROJECTIONS
Special Purpose - Polyconic
From Robinson, Sixth Edition, page 88, 89
The distribution of scale
factors on a polyconic
projection in the vacinity of
40° latitude. N-S SF values
away from the central
meridian are approximate.
Note that the section of the
projection which is used for a
standard 7.5-minute
quadrangle map would be 1/8
degree E-W and N-S along
the central meridian.
COMMON MAP PROJECTIONS
Special Purpose
Space
Robinson’s
Oblique
Mercator