Mapping and Projections
Web resources:
Geographer’s Craft, Department of Geography, University of
Colorado at Boulder - particularly Peter H. Dana’s part
http://www.colorado.edu/geography/gcraft/contents.html
Laurie Garo, Map Projections module, in Virtual Geography
Department, U. of Texas at Austin (hosted at U. of Colorado)
http://www.colorado.edu/geography/virtdept/contents.html
Map Projections
•Basic problem:
–Earth is round
–Paper is flat
Conformal
Equivalent or Equal Area
Equidistant
Equidistant Cylindrical
Map from Carlo Futuri
Solving the Problem
• How do you represent a curved surface on
a flat surface?
– Bonehead way - just plot latitude vs.
longitude as cartesian rectangular
coordinates
– Projection - fit a flat surface around (or
through) a sphere, and trace the
pertinent information on it
Unprojected map
Types of projections
• Three main families:
– Cylindrical - wrap sheet of paper around
globe in cylinder shape
• Also pseudocylindrical - like cylindrical but the
sheet of paper bends inward at the poles
– Conic - form sheet of paper into a cone and
insert globe
• Also polyconic - multiple cones
– Azimuthal - place flat sheet of paper next to
globe; project features out onto it
Cylindrical Projection
Cylindrical Projection
• Formed by wrapping a large, flat plane
around the globe to form a cylinder.
• Transfer latitude, longitude, shapes onto
cylinder, then unfolded into a flat plane.
• Typically used to represent the entire
world; often projected from center of
globe with equator as tangent line
• Most types show parallels and meridians
forming straight perpendicular lines.
Cylindrical Projection
Pseudocylindrical Projection
• Projection surface is not rectangular
• Instead, it curves inwards at the
poles.
• Latitude lines are straight; central
meridian is straight, but other
meridians are curved (concave
toward the central meridian).
• Often used for world maps
Pseudocylindrical Projection
Pseudocylindrical Projection
Pseudocylindrical Projection
Conic Projection
Conic Projection
• Points from the globe are transferred to a
cone fit around the sphere.
• Usually, the pointy end of the cone is
directly over the north or south pole, but
you can do it anywhere.
• Can represent both hemispheres, but
distortion increases the farther along the
cone you go
Conic Projection
• Often used to project areas that have a
greater east-west extent than northsouth, e.g., the United States.
• When projected from the center of the
globe, conic projections typically show
parallels forming arcs concave toward the
North or South pole, and meridians are
either straight or curved and radiate
outwards from the direction of the point
of the cone.
Conic Projection
Equidistant Conic Projection
Albers Equal Area Conic
Polyconic Projection
• Complex projection, used originally by
USGS for quadrangle maps of U.S.
• Uses an infinite number of cones applied
to an infinite number of tangents across a
given hemisphere
• Reduces distortion, but harder to
conceptualize and produce
Polyconic Projection
Polyconic Projection
(centered at equator, 90ºW)
Azimuthal (Planar) Projection
Azimuthal or Planar Projection
• Globe grid is projected onto a flat plane
• Plane is normally placed above the north
or south pole, so normally only one
hemisphere, or a portion of it, is
represented
• When projected from the center of the
globe, a typical polar azimuthal projection
shows circular latitude lines with radiating
longitude lines
Azimuthal Projection
Azimuthal Projection
Oblique Azimuthal Projection
Orthographic
sort of means
viewed from
infinite distance
Types of projections
• Tangent
– Flat surface only touches globe along one
circular line (or at one point for Azimuthal)
• Secant
– Flat surface passes through globe; touches
surface at two circular lines (or in one circle
for Azimuthal)
– Some projection is inward rather than
outward
– Reduces distortion of large areas
Tangent Projection
Secant Projection
Secant Projection
Robinson Projection
Goode’s Interrupted Homolosine Projection
Tissot indicators
• Tissot’s idea - to see the effects of
distortion, show what shape small circles
on the surface of the globe take after
projection
• This shows shape, scale, area, and other
distortions
Tissot Indicators – Mercator (Conformal)
Image from http://quantdec.com/tissot
Tissot Indicators – Peters Equal Area
Image from http://quantdec.com/tissot
Tissot Indicators – Azimuthal Equidistant
Image from http://quantdec.com/tissot
Tissot Indicators
Silly Projections
Web sites to visit:
• http://www.guilford.edu/geology/Geo340.html