Cylindrical Projections

ALASKA 27
Important Notes:

NOT FOR CARTOGRAPHIC USE. Use only to import legacy data that might have been saved in this system and then transform to a new coordinate system

Information:
The Alaska State Plane 27 is part of the State Plane Coordinate System (SPCS). See Guam27 for more information.

The Alaska 27 projection does not require any parameters.

BEHRMANN

The Behrmann projection is a variation of the generic Equal Area Cylindrical, in which the latitude of the standard parallel is always 30 degrees. It was originally presented by Walter Behrmann in Berlin in 1910.
 

The Equal-Area Cylindrical projection represents an orthographic projection of a sphere onto a cylinder. Like other regular cylindrical projections, the graticule of the normal Equal-Area Cylindrical projection consists of straight equally spaced vertical meridians perpendicular to straight unequally spaced horizontal parallels. To achieve equality of area, the parallels are spaced form the Equator in proportion to the sine of the latitude. This is the simplest equal-area projection. 

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing

Usage:
World maps only.

CASSINI

The Cassini projection is a cylindrical projection. It is neither equal-area nor conformal. The central meridian, each meridian 90 degrees from the central meridian and the Equator are straight lines. Other meridians and parallels are complex curves. Scale is true along the central meridian and along lines perpendicular to the central meridian. Scale is nearly constant but not true along lines parallel to the central meridian.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of true scale

Usage:
Large–scale maps of areas predominantly north–south in extent. Used by the UK Ordance Survey.

Notes:
Also known as Cassini-Soldner projection.

DANISH SYSTEM 34

Important Notes:

NOT RECOMMENDED FOR CARTOGRAPHIC USE. This projection uses Westing instead of the regular Easting. Maps created in this system in Adobe Illustrator would look flipped in the east/west direction. Use this projection only to import source data in this system and then transform to a different choice, or for export.

Information:

This projection is a variation of the Transverse Mercator projection used in Denmark, and is also referred to as UTS34. The projection consists of a base UTM (zones 32 & 33) calculation, which is then adjusted by an order 11 polynomial. The polynomials used in the Danish System 34 projection were developed by K. Poder and K. Engsager of Kort & Matrikelstyrelsen. The polynomial coefficients can be obtained by contacting Kort & Matrikelstyrelsen.

Note that this projection was superseded in 1999, by a newer version that uses an order 13 polynomial to further adjust the results achieved using this projection.

Parameters: 

		Jyland	Sjælland	Bornholm	National
region	Region	“j”, “J”, or “1”	“s”, “S”, or “2”	“b”, “B”, or “3”	“u”, “U”, or “4”

Usage:
Maps of Denmark

DANISH SYSTEM 34 (1999)

Important Notes:

NOT RECOMMENDED FOR CARTOGRAPHIC USE. This projection uses Westing instead of the regular Easting. Maps created in this system in Adobe Illustrator would look flipped in the east/west direction. Use this projection only to import source data in this system and then transform to a different choice, or for export.

Information:

This projection is a variation of the Transverse Mercator projection used in Denmark. The projection consists of a base UTM (zones 32 & 33) calculation, which is then adjusted by an order 11 polynomial, and then further adjusted by an order 13 polynomial. The polynomials used in the Danish System 34 projection were developed by K. Poder and K. Engsager of Kort & Matrikelstyrelsen. The polynomial coefficients can be obtained by contacting Kort & Matrikelstyrelsen.

Note that a previous version of this projection was used up until 1999, based solely on the order 11 polynomial. This newer version is a further refinement of those results using the additional order 13 polynomial. 

Parameters:

		Jyland	Sjælland	Bornholm	National
region	Region	“j”, “J”, or “1”	“s”, “S”, or “2”	“b”, “B”, or “3”	“u”, “U”, or “4”

Usage:
Maps of Denmark

EGYSEGES ORSZAGOS WTEULET (EOV)

The Egyseges Orszagos Vetulet (EOV) is a conformal cylindrical projection in transversal position used uniformly for the Hungarian civilian base maps and, in general, for Spatial Informatics. The projection is Conformal Cylindrical and is referenced to the GRS 1967 ellipsoid. One zone covers the whole territory of Hungary in an East-West direction.

The current implementation for the "EgysegesOrszagosVetulet" Projection does not require any user defined Parameters.

Usage:
Hungarian civilian base maps and Spatial Informatics.

EQUAL-AREA CYLINDRICAL

The Equal-Area Cylindrical projection represents an orthographic projection of a sphere onto a cylinder. Like other regular cylindrical projections, the graticule of the normal Equal-Area Cylindrical projection consists of straight equally spaced vertical meridians perpendicular to straight unequally spaced horizontal parallels. To achieve equality of area, the parallels are spaced form the Equator in proportion to the sine of the latitude. This is the simplest equal-area projection.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of standard parallel

Usage:
Maps of equatorial regions.

Notes:
Also known as Equal-Area or Lambert Cylindrical Equal-Area.

EQUIDISTANT CYLINDRICAL

The Equidistant Cylindrical projection is probably the simplest of all map projections to construct and one of the oldest. Meridians and parallels are equidistant straight lines, intersecting at right angles.
Poles are shown as lines. This projection is used only in spherical form.

If the Equator is made the standard parallel, true to scale and free of distortion, the meridians are spaced at the same distances as the parallels, and the graticule appears square. This form is often called the Plate Carree or the Simple Cylindrical Projection.

Parameters:

Plate Carrée
central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of true scale	= 0°

Usage:
Often used for city maps or small area maps.

GALL-PETERS

The Gall-Peters projection is a variation of the generic Equal Area Cylindrical, in which the latitude of the standard parallel is always 45 degrees. It was originally presented by James Gall in 1855, and is also known as the Gall Orthographic projection.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing

Usage:
World maps.

GALL STEREOGRAPHIC

The Gall Stereographic projection is a cylindrical perspective projection that is neither conformal nor equal area. It is produced geometrically by projecting the Earth perspectively from the point on the Equator opposite a specified meridian, onto a secant cylinder cutting the globe at latitudes 45° N and S. It was presented by James Gall in 1855. It is sometimes known simply as the Gall projection, or as Gall’s Stereographic projection. This projection is used primarily for world maps in British atlases and some other atlases. It resembles the Mercator, but has less distortion of scale and area near the poles.

The meridians in the Gall Stereographic projection are equally spaced straight parallel lines .77 as long as the Equator. Parallels are unequally spaced straight parallel lines perpendicular to meridians. The poles are represented by straight lines equal in length to the Equator. The projection is symmetrical about any meridian or the Equator. Scale is true along latitudes 45° N and S in all directions, and is constant in any

given direction along any other latitude. There is no distortion at latitudes 45° N and S, but shape, area and scale distortion increase moderately away from these latitudes and become severe at the poles.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing

Usage:
World maps

Notes:

Only a spherical form of this projection is used. The semi-major axis of the ellipsoid specified in the coordinate system datum definition is used as sphere radius.

HOTINE OBLIQUE MERCATOR (DEPRECATED)

Important Notes:

NOT FOR CARTOGRAPHIC USE. Use only to import legacy data that might have been saved in this system and then transform to a new coordinate system. For similar aspects, use the Oblique Mercator projection.

Information:

The Hotine Oblique Mercator (HOM) projection is a cylindrical, conformal map projection. It is similar to the Mercator projection, except that the cylinder is wrapped around the sphere so that it touches the surface along the great circle path chosen for the central line, instead of along the Earth’s equator. Scale becomes infinite 90 degrees from the central line and is true along a chosen central line, along two straight lines parallel to the central line, or along a great circle at an oblique angle. Two cases of the Hotine Oblique Mercator projection are implemented within MAPublisher and Geographic Imager, differing only in their defining parameters.

Hotine Oblique Mercator projection parameters:

false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
latitude_of_true_scale	Latitude of true scale
scale_factor	Scale reduction factor at the centre of the projection
standard_longitude1	Standard longitude of 1st point
standard_longitude2	Standard longitude of 2nd point
standard_latitude1	Standard latitude of 1st point
standard_latitude2	Standard latitude of 2nd point

Hotine Oblique Mercator (1 Point) projection parameters:

azimuth	Azimuth of the central line
azimuth_skew	Skew azimuth
central_meridian	Longitude at the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
scale_factor	Scale reduction factor at the centre of the projection

There are two variations of the Hotine Oblique Mercator (1 Point) projection type. These are mathematically identical in terms of results returned. The only difference is that the Hotine Oblique Mercator (1 Point) Method 2 version uses hyperbolic functions in the underlying mathematical computations.

HYPERBOLIC CASSINI-SOLDNER

A modified form of the standard Cassini-Soldner projection known as the Hyperbolic Cassini-Soldner is used for the island of Vanua Levu, Fiji.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of true scale

Usage:
Maps of the Island of Vanua Levu, Fiji.

LABORDE

The Laborde Projection is an Oblique Mercator projection that is primarily used in Madagascar. It is a cylindrical, conformal map projection similar to the Mercator system, except the cylinder is wrapped around the sphere so that it touches the surface along the great circle path at a chosen azimuth from the centerline. It was adopted for use in the Madagascar grid system in 1926.

Parameters: 

azimuth	Azimuth of the central line
azimuth_skew	Skew azimuth
central_meridian	Origin longitude (centerline)
false_easting	False easting
false_northing	False northing
latitude_of_origin	Origin latitude
scale_factor	Scale reduction factor at the centre of the projection

Usage:
Maps of Madagascar.

MERCATOR

The Mercator projection is a cylindrical, conformal map projection in which meridians and parallels are straight lines that cross at 90-degree angles. Angular relationships are preserved. To preserve conformality, parallels are placed increasingly farther apart with increasing distance from the equator.

This results in extreme distortion at high latitudes. Scale is true along the equator or along two parallels equidistant from the equator.

Using these parameters, there are two different variations of the Mercator projection that can be supported.

Parameters: 

		Variant 1	Variant 2
central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of true scale	Ignored, always using Equator	Used to calculate scale factor at the Equator
scale_factor	Scale scale factor	≠ 1	= 1

Usage:
Despite its drawbacks, the Mercator projection is quite useful for navigation because rhumb lines, which show constant direction, are straight. The Mercator projection is also appropriate for conformal maps of equatorial regions.

MILLER CYLINDRICAL

Meridians and parallels are straight lines, intersecting at right angles on the Miller Cylindrical projection. Poles are shown as lines. This projection is used only in spherical form and provides a compromise between Mercator and other cylindrical projections.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
spherical_radius	Radius of the sphere (e.g. 6378137)

Usage:
World maps

Notes:

Only a spherical form of this projection is supported. The specified geodetic datum is required to perform geodetic datum shifts into other coordinate systems.

OBLIQUE MERCATOR AZIMUTH

The Oblique Mercator projection is a cylindrical, conformal map projection. It is similar to the Mercator projection, except that the cylinder is wrapped around the ellipsoid so that it touches the surface along the great circle path chosen for the central line, instead of along the earth's equator. Scale becomes infinite 90 degrees from the central line and is true along a chosen central line, along two straight lines parallel to the central line, or along a great circle at an oblique angle. In this variation of the Oblique Mercator projection, a point and an azimuth define the central line where the cylinder touches the ellipsoid.

The planar points determined by this projection may be left “unrectified” (u, v coordinates) formula) or they may be “rectified” (x, y coordinates) by rotating the coordinates by a certain angle. This angle can be user defined or calculated so that the y axis is parallel to the central meridian or meridian of natural origin (see diagram next page). The parameter settings below show how to set up one option or the other.

By default, the X,Y coordinates are relative to the natural origin. If the center_flag parameter is set to 1, the coordinates are shifted to the centre of the projection (see diagram next page).

By default, the azimuth is the angle at the centre of projection. If the azimuth_is_gamma flag is set to 1, the azimuth parameter value will define the angle at the natural origin of the projection (see diagram next page).

Parameters:

Oblique Mercator Azimuth notations:
This simplified diagram shows the meaning of some of the parameters described above.

 

 

Usage:
Conformal mapping of regions that have an oblique orientation. Traditionally used for maps of Malaysia.

Notes:
Accurate only within 15° from the line of tangency (central line above).

The case when center_flag=0 (using natural origin as centre) corresponds to the Hotine Oblique Mercator method in EPSG standards. If center_ flag=1 (using the centre of projection as centre), the projection corresponds to the Oblique Mercator method in EPSG standards.

OBLIQUE MERCATOR TWO POINTS

This variation of the Oblique Mercator projection uses two points to define the central line where the cylinder touches the ellipsoid (see diagram on the previous page for the definition of the central line). See Oblique Mercator Azimuth for more information.

Usage:

Conformal mapping of regions that have an oblique orientation. Traditionally used for maps of Malaysia.

Notes:
Accurate only within 15° from the line of tangency (central line).

Parameters: 

 

In this case the central meridian is defined as the intersection of the central line (line connecting the two points defined by their latitude and longitude) and the latitude of origin.

POPULAR VISUALIZATION PSEUDO-MERCATOR

This method is utilised by some popular web mapping and visualisation applications. It applies standard Mercator (Spherical) formulas to ellipsoidal coordinates and the sphere radius is taken to be the semi-major axis of the ellipsoid. This approach only approximates the more rigorous application of ellipsoidal formulas to ellipsoidal coordinates.

Parameters:

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of true scale

Usage:
Google Earth/Map data (image geometry). Note that KML files use the WGS84 geodesic coordinate system.

Notes:
Unlike either the spherical or ellipsoidal Mercator projection methods, this method is not conformal: scale factor varies as a function of azimuth, which creates angular distortion. Despite angular distortion there is no convergence in the meridian.

SPACE OBLIQUE MERCATOR

Important Notes:

NOT FOR CARTOGRAPHIC USE. This projection is specific to individual Landsat scenes — the projection parameters depend on the Landsat satellite type and position at the time of capture. As such, it is supposed to be used to only import images rather than to create new cartography.

Information:

The Space Oblique Mercator (SOM) projection is a modified cylindrical projection with the map surface defined by a satellite orbit. The SOM is an extremely complicated projection. We urge you to refer to "Map Projections a Working Manual" by Snyder for a detailed explanation. The parameters are rather complicated and will vary depending on the Landsat satellite number (1, 2, 3, 4 or 5) and on the time of capture of the imagery (position of the satellite at the time.).

Parameters:

central_meridian	Origin longitude (centerline)
satellite_a	Semi-major axis of the satellite orbit
satellite_e	Eccentricity of the satellite orbit
satellite_gamma	Longitude of the perigee relative to the ascending node
satellite_incl	Inclination of the satellite orbit
satellite_long0	Geodetic longitude of the ascending node at time=0 (start of image capture)
satellite_p1	Length of Earth's rotation with respect to the precessed ascending node
satellite_p2	Time required for revolution of the satellite

Usage:
The SOM projection was designed especially for continuous mapping of satellite imagery.

SWISS OBLIQUE MERCATOR

The Swiss Oblique Mercator projection is a particular case of an Oblique Mercator projection, which in turn differs from the Mercator and Transverse Mercator projections in that the central line with true scale is neither the equator (as in the Mercator), nor a meridian (as in the Transverse Mercator), and is chosen to suit the region to be mapped. In the Swiss Oblique Mercator this line has an azimuth of 90 degrees and contains the centre of the projection.

The "SwissObliqueMercator" projection has no parameters.

Usage:
Maps of Switzerland

TRANSVERSE MERCATOR

The Transverse Mercator projection is similar to the Mercator Projection, except that the axis of the projection cylinder is rotated 90 degrees from the polar axis. This projection does not have the straight meridians and straight parallels of the Mercator projection, except for the central meridian, the two meridians 90 degrees away, and the equator. Nor does the Transverse Mercator projection have the straight rhumb lines of the Mercator projection; rather, it is a conformal projection. Scale is true along the central meridian or along two straight lines equidistant from and parallel to the central meridian.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
scale_factor	Scale reduction factor at the central meridian

Usage:

This projection is used in the State Plane Coordinate System for states with predominant north-south extent. It is also the geometric basis for the UTM Coordinate System (see UTM map zones in Appendix).

Notes:

The term Gauss-Kruger, or simply Gauss, refers to coordinate systems in parts of the world, for example, Germany and South America, based on the Transverse Mercator projection.

The Transverse Mercator projection is only reasonably accurate within 15° from the central meridian, distortions appear rapidly outside the 15° band.

TRANSVERSE MERCATOR SOUTH ORIENTED

Important Notes:

NOT FOR RECOMMENDED CARTOGRAPHIC USE. This projection uses Westing and Southing instead of the regular Easting and Northing value, maps created in this system in Adobe Illustrator would look flipped in north/south and east/west directions. Use this projection only to import source data in this system and then transform to a different choice, or for export.

Information:

This is a projection used in the southern hemisphere. It is identical to the standard Transverse Mercator, except that the false easting and northing are interpreted instead as a false westing and southing. See the parameters above.

Usage:
Data from south hemisphere (particularly South Africa and Botswana)

TRANSVERSE MERCATOR EXTENDED

This is a variation of the standard Transverse Mercator projection that is provided for the definition of coordinate systems used in specific counties in the U.S. states of Minnesota and Wisconsin. Within a specific county in one of these states, the ellipsoid must be expanded by an additional amount to account for the average elevation within that county. In the case of a Wisconsin county, the ellipsoid

must also be adjusted based on the average geoid height for that county. For Minnesota counties, the average geoid height should be set to zero.

Parameters: 

Minnesota
average_elevation	Average elevation (Minnesota and Wisconsin)
average_geoid_height	Average geoid height (Wisconsin-only)	0
central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
scale_factor	Scale reduction factor at the centre of the projection

Usage:
County maps of Minnesota and Wisconsin.

TRANSVERSE MERCATOR SNYDER

Important Notes:

NOT FOR RECOMMENDED CARTOGRAPHIC USE. This projection has been superseded by the newer Transverse Mercator projection. Use this projection only to import source data in this system and then transform to a different choice, or to compare results with old data.

Information:

This projection is based on the description and formulae in John P. Snyder's Map Projections-- A Working Manual (U.S. Geological Survey Professional Paper 1395), pp. 60-64.

The parameters are the same as the regular Transverse Mercator projection.

Usage:
Old USGS maps.

TRANSVERSE MERCATOR 27

Important Notes:

NOT FOR CARTOGRAPHIC USE. Use only to import legacy data that might have been saved in this system and then transform to a new coordinate system

Information:
The Transverse Mercator State Plane 27 is part of the State Plane Coordinate System (SPCS). See Guam27 for more information.

The Transverse Mercator 27 projection does not require any parameters.

UNIVERSAL TRANSVERSE MERCATOR

Important Notes:

NOT FOR CARTOGRAPHIC USE. Use only to import data that might have been saved in this system and then transform to a new coordinate system. To create user-defined coordinate systems or to update a standard UTM coordinate system, please use the Transverse Mercator projection method instead. This projection only works on small scale datasets that are contained in one of the grid cell of the system.

Information:

The Universal Transverse Mercator (UTM) projection class is an extension of the Transverse Mercator projection class that allows all UTM zones in a given horizontal datum to be represented by a single Geodetic Datasource object.

The actual Transverse Mercator parameter values to use when converting between geodetic and projected coordinates are determined from the values of the zone and is_north parameters. If the autoset parameter is set to 1, then the zone and is_north parameters will be automatically recomputed each time a conversion from geodetic coordinates is performed, based on the input geodetic coordinates. Conversions from projected coordinates always use the UTM projection currently specified by the parameters.

Parameters:

autoset	Automatically set zone (if set to 1, the other parameters are automatically calculated)
is_north	Currently in northern hemisphere
zone	Current zone number

Usage:
Military Grid Reference System (MGRS) and U.S. National Grid (USNG) coordinate systems are defined with the Universal Transverse Mercator projection and a point style with the appropriate string format option.