Map Projection Overview

Associated Overviews

Table of Contents

• Introduction
• Selected Map Projections
  • Cylindrical Projections
    • Cylindrical Equal Area
      • Behrmann Cylindrical Equal-Area
      • Gall's Stereographic Cylindrical
      • Peters
    • Mercator
    • Miller Cylindrical
    • Oblique Mercator
    • Transverse Mercator
  • Pseudocylindrical Projections
    • Mollweide
    • Eckert Projections
    • Robinson Projection
    • Sinusoidal Projection
  • Conic Projections
    • Albers Equal Area Conic
    • Equidistant Conic
    • Lambert Conformal Conic
    • Polyconic
  • Azimuthal Projections
    • Azimuthal Equidistant
    • Lambert Azimuthal Equal Area
    • Orthographic
    • Stereographic
  • Miscellaneous Projections
    • Unprojected Maps
    • Texas State Wide Projection
    • Space Oblique Mercator
• Links to other related information
  • Laurie Garo's Introduction to Map Projections
  • Karen Mulcahy's Map Projection Home Page
  • Geodetic Datum Overview, Department of Geography, University of Texas at Austin
  • Global Positioning System Overview, Department of Geography, University of Texas at Austin
  • Coordinate Systems Overview, Department of Geography, University of Texas at Austin
  • Home Page, Department of Geography, University of Texas at Austin
• References

Table of Contents

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 equal-area map.
• Different map projections result in different spatial relationships between regions.
  • Three Different Map Projections of the United States
  • Albers Equal Area and Lambert Conformal Conic Projections of North America
• 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)..
      • Projection of a Sphere onto a Cylinder (Tangent Case)
    • 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).
      • Projection of a Sphere onto a Cylinder (Secant Case)
    • When the cylinder upon which the sphere is projected is at right angles to the poles, the cylinder and resulting projection are transverse.
      • Transverse Projection of a Sphere onto a Cylinder (Tangent Case)
    • When the cylinder is at some other, non-orthogonal, angle with respect to the poles, the cylinder and resulting projection is oblique.
      • Oblique Projection of a Sphere onto a Cylinder (Tangent Case)
  • 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.
      • Projection of a Sphere onto a Cone (Tangent Case)
    • In the secant case, the cone touches the sphere along two lines, one a great circle, the other a small circle.
      • Projection of a Sphere onto a Cone (Secant Case)
  • 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.
      • Projection of a Sphere onto a Plane (Tangent Case)
    • 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.
      • Projection of a Sphere onto a Plane (Secant Case)
  • 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

Table of Contents

Selected Map Projections

Cylindrical Projections

• Cylindrical Equal Area
  • Cylindrical Equal-Area projections have straight meridians and parallels, the meridians are equally spaced, the parallels unequally spaced. There are normal, transverse, and oblique cylindrical equal-area 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 Equal-Area
    • Behrmann's cylindrical equal-area projection uses 30:00 North as the parallel of no distortion.
    • Behrmann Cylindrical Equal-Area
  • 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 equal-area projection that de-emphasizes 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 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 north-south than east-west 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 world-wide 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

Table of Contents

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 equal-area. 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 equal-area. The central meridian is straight, the 180th meridians are semi-circles, 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 equal-area 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 north-south than east-west extent.
  • Sinusoidal Equal Area

Table of Contents

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 east-west than north-south extent.
  • Albers Equal-Area 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
  • Area, and shape are distorted away from standard parallels. Directions are true in limited areas. Used for maps of North America.
  • Lambert Conformal Conic (North America)
• 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 non-concentric circles. Scale is true along each parallel and along the central meridian.
  • Polyconic (North America)

Table of Contents

Azimuthal Projections

• Azimuthal Equidistant
  • Azimuthal equidistant projections are sometimes used to show air-route 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 equal-area 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

Table of Contents

Miscellaneous Projections

• Unprojected Maps
  • Unprojected maps include those that are formed by considering longitude and latitude as a simple rectangular coordinate system. Scale, distance, area, and shape are all distorted with the distortion increasing toward the poles.
  • World: Unprojected Latitude and Longitude
  • North America: Unprojected Latitude and Longitude
  • Texas: Unprojected Latitude and Longitude
• Texas State-Wide Projection
  • In 1992, the Cartographic Standards Working Group proposed a Texas State-Wide 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
    • Texas: Lambert Conformal Conic designed for the Continental United States
  • The new projection was designed to allow state-wide 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.
    • Texas: Texas State-Wide Map Projection
• Space Oblique Mercator
  • The Space Oblique Mercator is a projection designed to show the curved ground-track of Landsat images. There is little distortion along the ground-track 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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