Classes of Map Projection

There are several ways to classify the wide variety of map projections. One of the most common classifications is by distortion characteristics: which properties of the Earth does the projection maintain? Which does it distort?

Classification based on distortion characteristics
A projection that maintains accurate relative sizes is called an equal area, or equivalent projection. These projections are used for maps that show distributions or other phenomena where showing area accurately is important. Examples are the Lambert Azimuthal Equal-Area projection and the Albers Equal-Area Conic projection.

An Azimuthal Equal-Area projection The National Atlas of the United States uses a Lambert Azimuthal Equal-Area projection to display information in the online Map Maker. In addition to its equal-area properties, this projection also shows true directions from the center point of the map. This means that the projection works well for mapping areas that extend equally from the center point, such as North America.

Mercator projection on a globe and map. Mercator projection A projection that maintains angular relationships and accurate shapes over small areas is called a conformal projection. These projections are used where angular relationships are important, such as for navigational or meteorological charts. Examples are the Mercator projection and the Lambert Conformal Conic projection. The U.S. Geological Survey uses a conformal projection for many of its topographic maps.

A projection that maintains accurate distances from the center of the projection or along given lines is called an equidistant projection. These projections are used for radio and seismic mapping, and for navigation. Examples are the Equidistant Conic projection and the Equirectangular projection. The Azimuthal Equidistant projection is the projection used for the emblem of the United Nations.

A projection that maintains accurate directions (and therefore angular relationships) from a given central point is called an azimuthal or zenithal projection. These projections are used for aeronautical charts and other maps where directional relationships are important. Examples are the Gnomonic projection and the Lambert Azimuthal Equal-Area projection.

A map projection may combine several of these characteristics, or may be a compromise that distorts all the properties of shape, area, distance, and direction, within some acceptable limit. Examples of compromise projections are the Winkel Tripel projection and the Robinson projection, often used for world maps.

Classification based on developable surface.

Map projections can also be classified based on the shape of the developable surface to which the Earth’s surface is projected. A developable surface is a simple geometric form capable of being flattened without stretching, such as a cylinder, cone, or plane.Cylindrical projection showing tangent at a selected line and secant along two lines.

 

Cylindrical projection.

For example, a cylindrical projection projects information from the spherical Earth to a cylinder. The cylinder may be either tangent to the Earth along a selected line, or may be secant (intersect the Earth) along two lines. Imagine that once the Earth’s surface is projected, the cylinder is unwrapped to form a flat surface. The lines where the cylinder is tangent or secant are the places with the least distortion.

Transverse and oblique mercator projections on a cylinder and map.A Mercator projection is created using a cylinder tangent at the equator. A Transverse Mercator projection is created using a cylinder that is tangent at a selected meridian. An Oblique Mercator projection is created using a cylinder that is tangent along a great circle other than the equator or a meridian.
Polyconic projection on a globe and map.

Polyconic projection A conic projection projects information from the spherical Earth to a cone that is either tangent to the Earth at a single parallel, or that is secant at two standard parallels. Once the projection is complete, the cone is unwrapped to form a flat surface. The lines where the cone is tangent or secant are the places with the least distortion. A polyconic projection uses a series of cones to reduce distortion.

A planar projection projects information to a plane. The plane may be either tangent or secant.


Commonly Used Map Projection Terms


Azimuth—The angle, measured in degrees, between a base line radiating from a center point and another line radiating from the same point. Normally, the base line points North, and degrees are measured clockwise from the base line.

Azimuthal—A map projection in which the direction from a given central point to any other point is shown correctly. Also called a zenithal projection.

Aspect—The placement of a projection system relative to the Earth’s axis. A polar aspect is tangent at the pole, an equatorial aspect is tangent at the Equator, and an oblique aspect is tangent anywhere else. (The word “aspect” has replaced the word “case” in the modern cartographic literature.)

Cartesian coordinate system —A coordinate system in which a point’s location is described by its distances from a set of perpendicular lines that intersect at an origin, either two lines in a plane or three in space.

Conformal—A map projection in which the angles at each point are preserved. This means that the shapes of small areas are maintained accurately. The size of most areas, however, is distorted.

Conic—A map projection where the Earth’s surface is projected onto a tangent or secant cone, which is then cut from apex to base and laid flat.
Conic Projection on a globe and map. One shows tangent at a single parallel and the other secant at two parallels.

Cylindrical—A map projection where the Earth’s surface is projected onto a tangent or secant cylinder, which is then cut lengthwise and laid flat.

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Map Projection


A map projection is a way to represent the curved surface of the Earth on the flat surface of a map. A good globe can provide the most accurate representation of the Earth. However, a globe isn’t practical for many of the functions for which we require maps. Map projections allow us to represent some or all of the Earth’s surface, at a wide variety of scales, on a flat, easily transportable surface, such as a sheet of paper. Map projections also apply to digital map data, which can be presented on a computer screen.

There are hundreds of different map projections. The process of transferring information from the Earth to a map causes every projection to distort at least one aspect of the real world – either shape, area, distance, or direction.

Each map projection has advantages and disadvantages; the appropriate projection for a map depends on the scale of the map, and on the purposes for which it will be used. For example, a projection may have unacceptable distortions if used to map the entire country, but may be an excellent choice for a large-scale (detailed) map of a county. The properties of a map projection may also influence some of the design features of the map. Some projections are good for small areas, some are good for mapping areas with a large east-west extent, and some are better for mapping areas with a large north-south extent.

Some projections have special properties. For example, a Mercator projection has straight rhumb lines and is therefore excellent for navigation, because compass courses are easy to determine.

Developable Surface

The cylinder is an example of developable surface. In mathematics, a developable surface is a surface with zero Gaussian curvature. That is, it is a surface that can be flattened onto a plane without distortion . Conversely, it is a surface which can be made by transforming a plane (i.e. “folding”, “bending”, “rolling”, “cutting” and/or “gluing”). In three dimensions all developable surfaces are ruled surfaces (but not vice versa). There are developable surfaces in R4 which are not ruled.

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Milestones in Remote Sensing

1759
First statements by Lambert (France) of principles underlying photogrammetry
1839
First ever photographs by Daguerre and Nepce, in France
1840
French used photos in making topographic maps.
1850’s
Photographs important in documenting exploration of the U.S. West (through 1870’s).
1855
Maxwell proposed proof of trichromatic color vision by photographic experiments (1861; Sutton).
1858
Pictures of Paris from cameras mounted in free and captive balloons.
1862
Du Hauron analyzed multispectral imagery with single-lens beam splitter technique.
1860’s
Claims of photos for military observations from balloons during American Civil War; none survive.
1870’s
Simple additive color projection and viewing developed.
1880’s
Camera airborne on kites in England, France, Russia.
1895
First color separations produced.
1895
Photos used by Seville in topographical surveys in Canada.
1900
Ives invented three-lens multispectral camera.
1903
Cameras attached to carrier pigeons.
1909
Wilbur Wright took first photos (movies) from an airplane.
1909
Berthon’s lenticular color film process for additive system.
1910
Orel-Zeiss Stereoautograph: precursor to serial stereo-photos.
1915
Aerial photos used by British R.A.F. for reconnaissance, changing tactics of work in W.W.I.
1917
Unites States Signal corps used aerial photos in Mexican border war.
1920
Aerial photos used by petroleum geologists for exploration.
1923
Zeiss Stereoplanegraph.
1924
Multilayered color film developed.
1930
First aerial spectrophotography of the Earth by Krinov and colleagues (Russia).
1930’s
Extensive use of aerial photos in Earth sciences and agriculture.
1931
Testing of aerial IR sensitive film from stratospheric balloon.
1935
Kodachrome appeared on market.
1937
Color film used in aerial surveys.
1938
Bausch and Lomb multiplex photogrammetric plotter.
1940
Kelsh plotters came into wide use.
1940
to
1943
Rapid advances in development of black-and-white and color IR (CIR) film for camouflage detection and haze penetration.
1941
Eardley’s Aerial Photos: Their Use and Interpretation published
1940
to
1945
Tremendous strides in aerial photography and photogrammetry resulting from W.W.II military needs.
1944 First edition of AS’s Manual of Photogrammetry.
1944 Military studies of water-depth penetration by two-band aerial photography.
1947 Publication of Krinov’s Spectral Reflectance Properties of Natural Materials.
1950’s Orthophoto mapping became popular.
1952 Color aerial photos used in geological mapping.
1953 Colwell (U.S.) demonstrated detection of disease and stress in vegetation (published 1956).
1950’s Term “Remote Sensing” first used (generally ascribed to Evelyn Pruitt; see footnote on page Intro-1).
1956 Soviets published on spectro-zonal photography for mapping soils.
1960’s Color film entered into common use in aerial photography.
1960 Colwell’s Manual of Photointerpretation and Ray’s Aerial Photographs in Geologic Interpretation and Mapping published.
1960’s Considerable activity in multispectral photography applications.
1960 Wheeler’s colorvision additive multispectral system.
1962 United States and Russian nine-lens multispectral cameras; Itek camera (ten lens) in 1963.
1963 USAF built Additive Color Viewer-Printer
1964 NASA inaugurated programs in testing usefulness of multiband photography for Earth resources.
1965 Multispectral additive color system developed by Yost and Wenderoth.
1967 First practical uses of UV photography.
1967 Two-volume Earth Resources Surveys from Space prepared by U.S. Army Corps of Engineers.
1968 ASP’s Manual of Color Aerial Photography.
1968 SO65 multispectral photography experiment on Apollo-9
1975 Publication of ASP’s Manual of Remote Sensing.
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NDVI

NDVI is the acronym for normalized difference vegetation index. It is a simple formula using two satellite channels. If one band is in the visible region (VIS, for example AVHRR band 1) and one is in the near infrared (NIR, for example AVHRR band 2), then the NDVI is (NIR – VIS)/(NIR + VIS).

Why?
The reason NDVI is related to vegetation is that healthy vegetation reflects very well in the near infrared part of the spectrum.
Green leaves have a reflectance of 20 percent or less in the 0.5 to 0.7 micron range (green to red) and about 60 percent in the 0.7 to 1.3 micron range (near infra-red). The visible channel gives you some degree of atmospheric correction. The value is then normalized to the range -1<=NDVI<=1 to partially account for differences in illumination and surface slope.

 How is it useful?

NDVI provides a crude estimate of vegetation health and a means of monitoring changes in vegetation over time. The possible range of values is between -1 and 1, but the typical range is between about -0.1 (NIR less than VIS for a not very green area) to 0.6 (for a very green area).

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