Pseudocylindrical Projections

CRASTER PARABOLIC

The Craster Parabolic projection is a pseudocylindrical, equal area projection used for thematic world maps in textbooks. It was originally presented by John Evelyn Edmund Craster in 1929. It was further developed by Charles H. Deetz and O.S. Adams in 1934. The central meridian is a straight line half as long as the Equator. Other meridians are equally spaced parabolas intersecting at the poles and concave

toward the central meridian. The parallels are unequally spaced, farthest apart near the Equator. They run perpendicular to the central meridian. This projection is symmetrical about the central meridian or the equator. Scale is true along latitudes 36°46' N and S, and constant along any given latitude.

Parameters: 

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

Usage:
Thematic world maps.

Notes:

This projection is also known as Putniņš P4, and was independently presented in Latvia in 1934.

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.

ECKERT I

The Eckert I projection is a pseudocylindrical projection that is neither conformal nor equal area. This projection was presented by Max Eckert in 1906.

Meridians in this projection are represented by equally spaced converging straight lines broken at the equator. The central meridian is half as long as the Equator. Parallels are represented by equally spaced straight parallel lines that are perpendicular to the central meridian. Poles are represented by lines half as long as the Equator. This projection is symmetrical about the central meridian or the Equator. Scale is true along latitudes 47°10' N and S, and constant along any given latitude or meridian.

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing

Usage:
Generally used for novelty maps of the world showing a straight-line graticule..

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.

ECKERT II

The Eckert II projection is a pseudocylindrical projection that is equal area. This projection was presented by Max Eckert in 1906.

Meridians in this projection are represented by equally spaced converging straight lines broken at the equator. The central meridian is half as long as the Equator. Parallels are represented by unequally spaced straight parallel lines that are perpendicular to the central meridian. Poles are represented by lines half as long as the Equator. This projection is symmetrical about the central meridian or the Equator. Scale is true along latitudes 55°10' N and S, and constant along any given latitude.

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing

Usage:
Generally used for novelty maps of the world showing a straight-line equal area graticule.

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.

ECKERT III

The Eckert III projection is a pseudocylindrical projection that is neither conformal nor equal area. This projection was presented by Max Eckert in 1906 .

Meridians in this projection are equally spaced semi-ellipses, concave toward the central meridian.

The central meridian is a straight line half as long as the Equator. Parallels are represented by equally spaced straight parallel lines that are perpendicular to the central meridian. Poles are represented by lines half as long as the Equator. This projection is symmetrical about the central meridian or the Equator. Scale is true along latitudes 35°58' N and S, and constant along any given latitude.

Parameters: 

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

Usage:
Primarily used for 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.

ECKERT IV

The Eckert IV projection was created by Max Eckert in 1906.

It is a pseudocylindrical projection whose central meridian is a straight line. 180th meridians of the Eckert IV projection are semicircle, and all other meridians are equally spaced elliptical Arcs. The parallels are unequally spaced straight lines parallel to one another, and the Poles are straight lines half as long as the equator. Scale is true along latitude 40º30' for the Eckert IV.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
spherical_radius	Radius of the sphere

If the spherical_radius parameter is set to a value greater than zero, then it will be used as the radius of the sphere. If this parameter is set to a value less than or equal to zero, then the Semi-Major radius of the Ellipsoid will be used as the radius of the sphere.

Usage:
World maps.

Notes:
Only a spherical form of this projection is used (see parameters).

ECKERT V

The Eckert V projection is a pseudocylindrical projection that is neither conformal nor equal area. This projection was presented by Max Eckert in 1906.

Meridians in this projection are equally spaced sinusoids, concave toward the central meridian. The central meridian is a straight line half as long as the Equator. Parallels are represented by equally spaced straight parallel lines that are perpendicular to the central meridian. Poles are represented by lines half as long as the Equator. This projection is symmetrical about the central meridian or the Equator. Scale is true along latitudes 37°55' N and S, and constant along any given latitude.

Parameters: 

central_meridian	Longitude of origin
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.

ECKERT VI

The Eckert VI projection was created by Max Eckert in 1906. It is a Pseudocylindrical projection whose central meridian is a straight line. Meridians on the Eckert VI projection are equally spaced sinusoidal curves. In both projections, the parallels are unequally spaced straight lines parallel to one another, and the Poles are straight lines half as long as the equator. Scale is true along latitude 49º16' for Eckert VI.

Parameters: 

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing
spherical_radius	Radius of the sphere

If the spherical_radius parameter is set to a value greater than zero, then it will be used as the radius of the sphere. If this parameter is set to a value less than or equal to zero, then the Semi-Major radius of the Ellipsoid will be used as the radius of the sphere.

Usage:
World maps.

Notes:
Only a spherical form of this projection is used (see parameters).

EQUAL EARTH

The Equal Earth projection was created by Bojan Šavriča, Tom Patterson, and Bernhard Jenny. It is an equal area pseudocylindrical projection intended for use in world maps for schools, organizations, or anyone who needs a map showing countries and continents at their true sizes relative to each other.

It has an overall shape similar to that of the Robinson projection. The curved sides of the projection suggest the spherical form of Earth. Straight parallels that make it easier to compare how far north or south places are from the equator. The height-to-width aspect ratio of 1:2.05 is very close to the natural ratio of a sphere, and pole lines are 0.592 times the length of the equator.

Parameters: 

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing

Usage:
World maps.

GOODE HOMOLOSINE

The Goode Homolosine projection is a pseudocylindrical composite projection that is equal area. It is used primarily for world maps in a number of atlases, including Goode’s Atlas (Rand McNally). It was developed by J. Paul Goode in 1923 as a merging of the Mollweide (or Homolographic) and Sinusoidal projections, thus giving rise to the name “Homolosine”.

Each of the six central meridians is a straight line 0.22 as long as the Equator, but not crossing the Equator. Other meridians are equally spaced sinusoidal curves between latitudes 40°44' N and S. The poles are represented by points. Scale is true along every latitude between 40°44' N and S and along the central meridian within the same latitude range.

This Goode Homolosine projection is the uninterrupted version. Some other software may use the interrupted version (e.g. ArcMap) which has a different aspect.

Parameters: 

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing

Usage:
World maps (Goode Atlas).

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.

LOXIMUTHAL

The Loximuthal projection is a pseudocylindrical projection that is neither conformal nor equal area.

It was presented by Karl Siemon in 1935, and independently as “Loximuthal” by Waldo R. Tobler. This projection has the special feature that loxodromes (rhumb lines) from the central point (the intersection of the central meridian and central latitude) are shown straight, true to scale, and correct in azimuth from the centre. The azimuths with respect to rhumb lines that do not pass through the origin, however, are not shown correctly, due to angular distortion on the map projection.

The central meridian in the Loximuthal projection is a straight line generally over half as long as the Equator (depending on the central latitude). Other meridians are depicted as equally spaced complex curves that are concave toward the central meridian and which intersect at the poles. The parallels are equally spaced straight parallel lines running perpendicular to the central meridian. The poles

are represented as points. The projection is symmetrical about the central meridian, and around the Equator in the case where the central latitude is the Equator. Scale is true along the central meridian, and is constant along any given latitude. Distortion varies from moderate to extreme, and is absent only at the intersection of the central latitude and central meridian.

Parameters: 

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin

Usage:
Maps that display loxodromes (rhumb lines)

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.

MCBRIDE THOMAS FLAT POLAR QUARTIC

The McBryde-Thomas Flat-Polar Quartic Projection is a pseudocylindrical, equal area projection. It was presented by F. Webster McBryde and Paul D. Thomas in 1949.

The central meridian is a straight line 0.45 as long as the Equator. Other meridians are fourth-order (quartic) curves that are equally spaced and concave toward the central meridian. The parallels are unequally spaced straight parallel lines, spaced farthest apart near the Equator and running perpendicular to the central meridian. The poles are represented by lines one-third as long as the Equator.

Scale is true along latitudes 33°45' N and S, and is constant along any given latitude. Distortion is severe near the outer meridians at high latitudes. This projection is free of distortion only at the intersection of the central meridian with latitudes 33°45' N and S.

Parameters:

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing

Usage:

It is primarily used for examples in various geography textbooks, and is sometimes known simply as the Flat-Polar Quartic projection.

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.

MOLLWEIDE

The Mollweide projection is a pseudocylindrical equal-area projection. The central meridian is a straight line, 90th meridians are circular arcs, and all other meridians are equally spaced elliptical arcs. Parallels are unequally spaced straight lines, parallel to each other. Poles are shown as points.

Parameters: 

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
spherical_radius	Radius of the sphere

If the spherical_radius parameter is set to a value greater than zero, then it will be used as the radius of the sphere. If this parameter is set to a value less than or equal to zero, then the Semi-Major radius of the Ellipsoid will be used as the radius of the sphere.

Usage:
Thematic or distribution maps

Notes:
Only a spherical form of this projection is used (see parameters).

QUARTIC AUTHALIC

The Quartic Authalic projection is a pseudocylindrical, equal area projection that is used primarily for world maps. It was first presented by Karl Siemon in 1937, and then later presented independently by Oscar Sherman Adams in 1945. This projection serves as a basis for the McBryde-Thomas Flat Polar Quartic projection.

The central meridian is depicted as a straight line 0.45 as long as the Equator. Other meridians are equally spaced curves, concave toward the central meridian. The parallels are straight parallel lines perpendicular to the central meridian. These are spaced farthest apart near the Equator, but gradually grow closer spaced when moving toward the poles. The poles are represented by points.

Distortion is significant near the outer meridians, at high latitudes, but is less than in the Sinusoidal projection. There is no distortion and scale is true along the Equator. Scale is constant along any given latitude.

Parameters: 

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing

Usage:
Thematic 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.

ROBINSON

The Robinson projection provides a means of showing the entire Earth in an uninterrupted form. The Robinson projection is destined to replace the Van der Grinten projection as the premier projection used by the National Geographic Society.

Parameters: 

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

Usage:

World maps

SINUSOIDAL

The Sinusoidal projection is pseudocylindrical and equal-area. The central meridian is a straight line. All other meridians are shown as equally spaced sinusoidal curves. Parallels are equally spaced straight lines, parallel to each other. Poles are points. Scale is true along central meridian and all parallels.

Parameters: 

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

Usage:

Maps of South America and Africa

TIMES

The Times projection is a pseudo-cylindrical projection that is neither equal area nor conformal. It was first presented by John Moir in 1965.

The central meridian and Equator are depicted as straight lines. All other meridians are equally spaced curves, concave toward the central meridian. The parallels are straight lines perpendicular to the central meridian, increasing in separation away from the Equator. Scale is correct along the two parallels at 45° N and S

Parameters: 

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing

Usage:

It is used to generate the world maps in The Times Atlas of the World, produced by Collins Bartholomew.

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.

WAGNER IV

This equal-area projection was presented by Karlheinz Wagner in 1932. Scale is true along the 42º59' parallels and is constant along any parallel and between any pair of parallels equidistant from the Equator. Distortion is not as extreme near the outer meridians at high latitudes as for pointed-polar pseudocylindrical projections, but there is considerable distortion throughout the polar regions. It is free of distortion only at the two points where the 42º59' parallels intersect the central meridian. This projection is not conformal or equidistant. 

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
spherical_radius	Radius of the sphere

Usage:
Thematic 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.

WAGNER V

The Wagner V is a compromise projection that displays moderate areal distortion. It is neither equal area or equidistant. The projection was presented by Karlheinz Wagner in 1949.

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
spherical_radius	Radius of the sphere

Usage:
Thematic 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.

WINKEL I

The Winkel I projection is a pseudocylindrical projection that is neither conformal nor equal area. Oswald Winkel developed it in 1914 as the average of the Sinusoidal and Equidistant Cylindrical (Equirectangular) projections.

The central meridian is a straight line, while other meridians are equally spaced sinusoidal curves concave toward the central meridian. The parallels are equally spaced straight parallel lines perpendicular to the central meridian. The poles are represented by lines. If the latitude of true scale is chosen to be 50°28', the total area scale will be correct, though local area scales will vary.

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of true scale

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.

WINKEL II

The Winkel II projection is a pseudocylindrical projection that is neither conformal nor equal area. Oswald Winkel developed it in 1918 as the average of the Mollweide and Equidistant Cylindrical (Equirectangular) projections.

The central meridian is a straight line, while other meridians are equally spaced curves concave toward the central meridian. The parallels are equally spaced straight parallel lines perpendicular to the central meridian. The poles are represented by lines. The length of the poles and of the central meridian will depend on the choice of the latitude of true scale. Scale is true along the north and south latitudes specified by the latitude of true scale, but the projection is generally distorted.

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of true scale

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.