Map Projection Overview
Peter H. Dana
These materials may be used for study, research, and education in notforprofit
applications. All commercial rights are reserved. Please credit the author,
Peter H. Dana, The Geographer's Craft Project, Department of Geography,
The University of Colorado at Boulder. Copyright © 1999 Peter H. Dana.
This page is available in a framed
version. For convenience, a Full
Table of Contents is provided.
Revised: 12/15/99
Associated Overviews
Introduction

Map projections are attempts to portray the surface of the earth or a portion
of the earth on a flat surface. Some distortions of conformality, distance,
direction, scale, and area always result from this process. Some projections
minimize distortions in some of these properties at the expense of maximizing
errors in others. Some projection are attempts to only moderately distort
all of these properties.

Conformality

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.

Distance

A map is equidistant when it portrays distances from the center of the
projection to any other place on the map.

Direction

A map preserves direction when azimuths (angles from a point on a line
to another point) are portrayed correctly in all directions.

Scale

Scale is the relationship between a distance portrayed on a map and the
same distance on the Earth.

Area

When a map portrays areas over the entire map so that all mapped areas
have the same proportional relationship to the areas on the Earth that
they represent, the map is an equalarea map.

Different map projections result in different spatial relationships between
regions.

Map projections fall into four general classes.

Cylindrical projections result from projecting a spherical surface onto
a cylinder.

When the cylinder is tangent to the sphere contact is along a great circle
(the circle formed on the surface of the Earth by a plane passing through
the center of the Earth)..

In the secant case, the cylinder touches the sphere along two lines, both
small circles (a circle formed on the surface of the Earth by a plane not
passing through the center of the Earth).

When the cylinder upon which the sphere is projected is at right angles
to the poles, the cylinder and resulting projection are transverse.

When the cylinder is at some other, nonorthogonal, angle with respect
to the poles, the cylinder and resulting projection is oblique.

Conic projections result from projecting a spherical surface onto a cone.

When the cone is tangent to the sphere contact is along a small circle.

In the secant case, the cone touches the sphere along two lines, one a
great circle, the other a small circle.

Azimuthal projections result from projecting a spherical surface onto a
plane.

When the plane is tangent to the sphere contact is at a single point on
the surface of the Earth.

In the secant case, the plane touches the sphere along a small circle if
the plane does not pass through the center of the earth, when it will touch
along a great circle.

Miscellaneous projections include unprojected ones such as rectangular
latitude and longitude grids and other examples of that do not fall into
the cylindrical, conic, or azimuthal categories
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Selected Map Projections
Cylindrical Projections

Cylindrical Equal Area

Cylindrical EqualArea projections have straight meridians and parallels,
the meridians are equally spaced, the parallels unequally spaced. There
are normal, transverse, and oblique cylindrical equalarea projections.
Scale is true along the central line (the equator for normal, the central
meridian for transverse, and a selected line for oblique) and along two
lines equidistant from the central line. Shape and scale distortions increase
near points 90 degrees from the central line.

Behrmann Cylindrical EqualArea

Gall's Stereographic Cylindrical

Gall's stereographic cylindrical projection results from projecting the
earth's surface from the equator onto a secant cylinder intersected by
the globe at 45 degrees north and 45 degrees south. This projection moderately
distorts distance, shape, direction, and area.

Gall's
Sterographic Cylindrical

Peters

The Peters projection is a cylindrical equalarea projection that deemphasizes
area exaggerations in high latitudes by shifting the standard parallels
to 45 or 47 degrees.

Peters

Mercator

The Mercator projection has straight meridians and parallels that intersect
at right angles. Scale is true at the equator or at two standard parallels
equidistant from the equator. The projection is often used for marine navigation
because all straight lines on the map are lines of constant azimuth.

Mercator

Miller Cylindrical

The Miller projection has straight meridians and parallels that meet at
right angles, but straight lines are not of constant azimuth. Shapes and
areas are distorted. Directions are true only along the equator. The projection
avoids the scale exaggerations of the Mercator map.

Miller
Cylindrical

Oblique Mercator

Oblique Mercator projections are used to portray regions along great circles.
Distances are true along a great circle defined by the tangent line formed
by the sphere and the oblique cylinder, elsewhere distance, shape, and
areas are distorted. Once used to map Landsat images (now replaced by the
Space Oblique Mercator), this projection is used for areas that are long,
thin zones at a diagonal with respect to north, such as Alaska State Plane
Zone 5001.

Oblique
Mercator (Alaska State Plane Zone 5001)

Transverse Mercator

Transverse Mercator projections result from projecting the sphere onto
a cylinder tangent to a central meridian. Transverse Mercator maps are
often used to portray areas with larger northsouth than eastwest extent.
Distortion of scale, distance, direction and area increase away from the
central meridian.

Many national grid systems are based on the Transverse Mercator projection

The British National Grid (BNG) is based on the National Grid System of
England, administered by the British Ordnance Survey. The true origin of
the system is at 49 degrees north latitude and 2 degrees west longitude.
The false origin is 400 km west and 100 km north. Scale at the central
meridian is 0.9996. The first BNG designator defines a 500 km square. The
second designator defines a 100 km square. The remaining numeric characters
define 10 km, 1 km, 100 m, 10 m, or 1 m eastings and northings.

British
National Grid 100 km Squares

The Universal Transverse Mercator (UTM) projection is used to define horizontal,
positions worldwide by dividing the surface of the Earth into 6 degree
zones, each mapped by the Transverse Mercator projection with a central
meridian in the center of the zone. UTM zone numbers designate 6 degree
longitudinal strips extending from 80 degrees South latitude to 84 degrees
North latitude. UTM zone characters designate 8 degree zones extending
north and south from the equator.

UTM
Zones

Eastings are measured from the central meridian (with a 500km false easting
to insure positive coordinates). Northings are measured from the equator
(with a 10,000km false northing for positions south of the equator).

UTM
Zone 14
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Pseudocylindrical Projections

Pseudocylindrical projections resemble cylindrical projections, with straight
and parallel latitude lines and equally spaced meridians, but the other
meridians are curves.

Mollweide

The Mollweide projection, used for world maps, is pseudocylindrical and
equalarea. The central meridian is straight. The 90th meridians are circular
arcs. Parallels are straight, but unequally spaced. Scale is true only
along the standard parallels of 40:44 N and 40:44 S.

Mollweide
Projection

Eckert Projections

Eckert IV Equal Area

The Eckert IV projection, used for world maps, is a pseudocylindrical and
equalarea. The central meridian is straight, the 180th meridians are semicircles,
other meridians are elliptical. Scale is true along the parallel at 40:30
North and South.

Eckert
IV Equal Area

Eckert VI Equal Area

The Eckert VI projection , used for maps of the world, is pseudocylindrical
and equal area. The central meridian and all parallels are at right angles,
all other meridians are sinusoidal curves. Shape distortion increases at
the poles. Scale is correct at standard parallels of 49:16 North and South.

Eckert
VI Equal Area

Robinson

The Robinson projection is based on tables of coordinates, not mathematical
formulas. The projection distorts shape, area, scale, and distance in an
attempt to balance the errors of projection properties.

Robinson

Sinusoidal Equal Area

Sinusoidal equalarea maps have straight parallels at right angles to a
central meridian. Other meridians are sinusoidal curves. Scale is true
only on the central meridian and the parallels. Often used in countries
with a larger northsouth than eastwest extent.

Sinusoidal
Equal Area
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Conic Projections

Albers Equal Area Conic

A conic projection that distorts scale and distance except along standard
parallels. Areas are proportional and directions are true in limited areas.
Used in the United States and other large countries with a larger eastwest
than northsouth extent.

Albers
EqualArea Conic

Equidistant Conic

Direction, area, and shape are distorted away from standard parallels.
Used for portrayals of areas near to, but on one side of, the equator.

Equidistant
Conic

Lambert Conformal Conic

Polyconic

The polyconic projection was used for most of the earlier USGS topographic
quadrangles. The projection is based on an infinite number of cones tangent
to an infinite number of parallels. The central meridian is straight. Other
meridians are complex curves. The parallels are nonconcentric circles.
Scale is true along each parallel and along the central meridian.

Polyconic
(North America)
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Azimuthal Projections

Azimuthal Equidistant

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.

Azimuthal
Equidistant

Lambert Azimuthal Equal Area

The Lambert azimuthal equalarea 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.

Lambert
Azimuthal Equal Area

Orthographic

Orthographic projections are used for perspective views of hemispheres.
Area and shape are distorted. Distances are true along the equator and
other parallels.

Oblique
Aspect Orthographic Projection

Stereographic

Stereographic projections are used for navigation in polar regions. Directions
are true from the center point and scale increases away from the center
point as does distortion in area and shape.

North
Polar Stereographic
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Miscellaneous Projections

Unprojected Maps

Texas StateWide Projection

In 1992, the Cartographic Standards Working Group proposed a Texas StateWide
Map Projection Standard for the GIS Standards Committee of the GIS Planning
Council for the Department of Information Sciences.

Earlier maps had often used projections designed for the continental United
States

The new projection was designed to allow statewide mapping with a minimum
of scale distortion. A Lambert Conformal Conic Projection was proposed
with an origin at 31:10 North, 100:00 West and with standard parallels
at 27:25 North and 34:55 North. For plane coordinate use a false Easting
and Northing of 1,000,000 meters were defined for the origin.

Space Oblique Mercator

The Space Oblique Mercator is a projection designed to show the curved
groundtrack of Landsat images. There is little distortion along the groundtrack
but only within the narrow band (about 15 degrees) of the Landsat image.

Space
Oblique Mercator
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References

Muehrcke, Phillip C. 1986. Map use: reading, analysis, interpretation.
Madison, WI: JP Publications.

Snyder, John P. 1987. Map projections: a working manual.USGS Professional
Paper 1395. Washington, DC: United States Government Printing Office.

Many of the maps on this page were produced using MapInfo's MapInfo
and Golden Software's MapViewer and Surfer for Windows.
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