Tobler hyperelliptical projection

# Tobler hyperelliptical projection

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Encyclopedia
The Tobler hyperelliptical projection is a family of equal-area pseudocylindrical projections used for mapping the earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

. It is named for Waldo R. Tobler
Waldo R. Tobler
Waldo Tobler is an American-Swiss geographer and cartographer. Tobler's idea that "Everything is related to everything else, but near things are more related to each other" is referred to as the "first law of geography." Tobler is a Professor Emeritus at the University of California, Santa Barbara...

, its inventor, who first described the family in 1973.

In the projection’s normal aspect, the parallels
Circle of latitude
A circle of latitude, on the Earth, is an imaginary east-west circle connecting all locations that share a given latitude...

of latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...

are parallel straight lines whose spacing is calculated to provide the equal-area property; the meridian
Meridian (geography)
A meridian is an imaginary line on the Earth's surface from the North Pole to the South Pole that connects all locations along it with a given longitude. The position of a point along the meridian is given by its latitude. Each meridian is perpendicular to all circles of latitude...

s of longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....

(except for the central meridian, which is a straight line perpendicular to the lines representing parallels) are curves of the form a|x|γ + b|y|γ = 1 (with a dependent on longitude and b constant for a given map), known as superellipse
Superellipse
A superellipse is a geometric figure defined in the Cartesian coordinate system as the set of all points withwhere n, a and b are positive numbers....

s
or Lamé curves. When γ = 2 the projection becomes the Mollweide projection
Mollweide projection
The Mollweide projection is a pseudocylindrical map projection generally used for global maps of the world . Also known as the Babinet projection, homalographic projection, homolographic projection, and elliptical projection...

; when γ=1 it becomes the Collignon projection
Collignon projection
The Collignon projection is an equal-area pseudocylindrical map projection first known to be published by Édouard Collignon in 1865 and subsequently cited by A...

; the limiting case as γ→infinity is the Cylindrical equal-area projection
Cylindrical equal-area projection
In cartography, the cylindrical equal-area projection is a family of cylindrical, equal area map projections.-Cylindrical projections:The term "normal cylindrical projection" is used to refer to any projection in which meridians are mapped to equally spaced vertical lines and circles of latitude ...

(Lambert cylindrical equal-area
Lambert cylindrical equal-area projection
In cartography, the Lambert cylindrical equal-area projection, or Lambert cylindrical projection, is acylindrical, equal area map projection...

, Gall–Peters, or Behrmann projection
Behrmann projection
The Behrmann projection is a cylindrical map projection. This is an orthographic projection onto a cylinder secant at the 30° parallels. It is equal-area, but distortion of shape increases with distance from the standard parallels. Scale is true along the standard parallels and constant between two...

). Values of γ that are favored by Tobler and others are generally greater than 2.