MAP
PROJECTIONS
Cartographic Design for GIS (Geog. 340)
Prof. Hugh Howard
American River College
MAP PROJECTION
DEFINED
MAP PROJECTION
•
•
Method by which Earth’s geographic
coordinates are converted to projected
(Cartesian) coordinates
The “flattening” of Earth onto a plane
Geographic Coordinates (lon,lat)
Projected (Cartesian) Coordinates (x,y)
MAP PROJECTION
•
A great challenge faced by ancient
(and modern) cartographers
– Ancient Babylonians introduced the idea
of scale, and 360 degrees in a circle
– Ancient Greeks introduced the idea of
meridians and parallels (diaphragma)
– Claudius Ptolemy introduced the idea of
map projections in the 2nd century AD
Claudius Ptolemy,
2nd Century AD
MAP PROJECTION
•
How are projections created?
– Today, most projections are created
mathematically using computers
– A Reference Globe is created as a scale
model of Earth
– A “rule” is derived that can be applied to
every point on the globe
MAP PROJECTION
•
Projective Geometry has been used to
create projections, and still serves as a
conceptual explanation
– A semi-transparent
reference globe is fitted
with a Point of Projection
– Surface of reference globe
is projected onto a
Developable Surface
– Surface is traced on
developable surface
PROJECTION CLASSES
(According to Projective Geometry)
PROJECTION CLASSES
Classification According to Projective Geometry
Developable
Surface
THREE CLASSES
Planar
Cylindrical
Conic
Good for:
Polar regions
PROJECTION CLASSES
Classification According to Projective Geometry
Developable
Surface
THREE CLASSES
Planar
Cylindrical
Conic
Good for:
Equatorial regions
PROJECTION CLASSES
Classification According to Projective Geometry
Developable
Surface
THREE CLASSES
Planar
Cylindrical
Conic
Good for:
Midlatitude regions
Originally developed
by Claudius Ptolemy,
2nd Century AD
PROJECTION CLASSES
Classification According to Projective Geometry
THREE CLASSES
Planar
Cylindrical
Conic
Mathematical Projections
Some projections are developed
mathematically, not according to
projective geometry; developable
surfaces are not involved.
Pseudocylindrical, Sinusoidal, etc.
PROJECTION
CASE and ASPECT
PROJECTION CASE
•
Case
– Describes how the developable surface is
positioned, relative to the reference globe
– Tangent
– Secant
PROJECTION CASE
•
Case (cont.)
– Lines of contact are Standard Lines
Standard Lines have same
scale as reference globe
Distortion increases away
from Standard Lines
PROJECTION ASPECT
•
Aspect
– The orientation of the developable
surface, relative to the reference globe
Polar/Transverse Aspect
Equatorial Aspect
(Mercator)
Oblique Aspect
(Oblique Mercator)
(Transverse Mercator)
PROJECTION CLASSES
(According to Properties Preserved)
PROJECTION CLASSES
Classification According to Properties Preserved
• Distortion always results from the
projection process
– The larger the area of Earth projected, the
greater the distortion
– Smaller areas are subject to less distortion
Large Area
(strongly curved)
Smaller Area (closer to flat)
PROJECTION CLASSES
Classification According to Properties Preserved
• Types of distortion:
– Angle (shape)
– Area
– Distance
– Direction
PROJECTION CLASSES
Classification According to Properties Preserved
• Projections can be classified
according to the type of distortion
they do not produce…
• Projections can be classified by the
Properties They Preserve
– Angle (shape)
– Area
– Distance
– Direction
PROJECTION CLASSES
Classification According to Properties Preserved
• Conformal projections:
– Preserve Angles (shapes of small areas)
• Equivalent (Equal Area) projections:
– Preserve relative sizes of Areas
• Equidistant projections:
– Preserve Distances…
• Azimuthal projections:
– Preserve Directions…
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Good for:
Topographic maps
Weather maps
Navigational maps
Conformal: Lambert Conformal Conic
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Good for:
Topographic maps
Weather maps
Navigational maps
Conformal: Mercator
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Good for:
Thematic maps
Political maps
Equivalent: Eckert IV
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Good for:
Thematic maps
Political maps
Equivalent: Sinusoidal
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Conformal and Equal Area
projections are mutually exclusive
!
No projection can be both conformal
and Equal Area
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Conformal and Equivalent projections
are mutually exclusive
No projection can be both conformal
and Equivalent
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Good for:
Airline distance maps
Seismic maps
Distances are correct from
the center of the projection,
to all other locations
(and along standard lines)
Equidistant: Azimuthal Equidistant
PROJECTION CLASSES
Classification According to Properties Preserved
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Directions are correct from
the center of the projection,
to all other locations
(and along standard lines)
Good for:
Navigational maps
Azimuthal: Loximuthal
PROJECTION CLASSES
Classification According to Properties Preserved
Compromise Projections
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Distort shape, size, distance, and direction,
but distribute distortion in a way that looks natural
Good for:
Non-critical
applications
Robinson
PROJECTION CLASSES
Classification According to Properties Preserved
Compromise Projections
FOUR CLASSES
Conformal
Equivalent
Equidistant
Azimuthal
Good for:
General, non-critical
applications
Distort shape, size, distance, and direction,
but distribute distortion in a way that looks natural
Van der Grinten
Winkel Tripel
SELECTING an
APPROPRIATE
PROJECTION
SELECTING A PROJECTION
•
Selection of an appropriate projection
requires consideration of
–
–
–
–
–
–
Data
Symbolization method
Intended audience
Region of Earth
Map scale
Level of generalization, etc.
SELECTING A PROJECTION
•
John Snyder’s Guidelines provide a
hierarchical mechanism for choosing
projections, based on
– Region to be mapped (world, hemisphere,
continent or smaller)
– Desired projection property (conformal,
equivalent, azimuthal, equidistant)
– Desired projection characteristic
(class, case, aspect)
SELECTING A PROJECTION
•
World Map of Literacy Rates (choropleth)
Preserves relative areas
of enumeration units
SELECTING A PROJECTION
SELECTING A PROJECTION
•
Map of Russian Population (proportional
symbol and dot)
Preserves relative areas
of enumeration units
SELECTING A PROJECTION
Standard Parallels
located ~1/6 from top,
and ~1/6 from bottom
Central Meridian located
midway of E-W extent
SELECTING A PROJECTION
•
Map of Kansas Tornado Paths (flow)
Angular relationships of
paths are important
No need to preserve
relative areas of
enumeration units
SELECTING A PROJECTION
Lambert Conformal Conic
SELECTING A PROJECTION
Albers Equal Area Conic
Virtually no difference!
The smaller the area, the
less important the projection!
SELECTING A PROJECTION
Lambert Conformal Conic
Lambert Conformal Conic
would be the correct
choice…
MAP
PROJECTIONS
Cartographic Design for GIS (Geog. 340)
Prof. Hugh Howard
American River College