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These are some projections that preserve area:
* Azimuthal
** Lambert azimuthal equal-area
** Wiechel
* Conic
**
cartography
Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an i ...
, an equal-area projection is a map projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...
that preserves area measure, generally distorting shapes in order to do that. Equal-area maps are also called equivalent or authalic. An equal-area map projection cannot be conformal, nor can a conformal map projection
In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection, i.e. the projection is a conformal map in the mathema ...
be equal-area.
Several equivalent projections were developed in an attempt to minimize the distortion of countries and continents of planet Earth, keeping the area constant. Equivalent projections are widely used for thematic maps showing scenario distribution such as population, farmland distribution, forested areas, etc.
Description
Equal area representation implies that aregion of interest
A region of interest (often abbreviated ROI) is a sample within a data set identified for a particular purpose. The concept of a ROI is commonly used in many application areas. For example, in medical imaging, the boundaries of a tumor may be def ...
in a particular portion of the map will share the same proportion of area as in any other part of the map.
Statistical grid
The term "statistical grid" refers to a discrete grid (global or local) of an equal-area surface representation, used for data visualization, geocode and statistical spatial analysis.IBGE (2016), “Grade Estatística”. Arquivograde_estatistica.pdf em FTP ou HTTP, http://geoftp.ibge.gov.br/recortes_para_fins_estatisticos/grade_estatistica/censo_2010
List of equal-area projections
These are some projections that preserve area:
* Azimuthal
** Lambert azimuthal equal-area
** Wiechel
* Conic
** Albers Albers is a Dutch and Low German patronymic surname, meaning " Albert's son". Notable people with the surname include:
;Academics
* Heinrich Albers-Schönberg (1865–1921), German gynecologist and radiologist
* :de:Johann Abraham Albers (1772– ...
** Lambert equal-area conic projection
The Lambert equal-area conic projection (named after Johann Heinrich Lambert), is a conic, equal area map projection that represents one pole as a point. Albers projection is a generalization of this projection with two standard parallel.
"Dir ...
* Pseudoconical
** Bonne
** Bottomley
** Werner
* Cylindrical
** Lambert cylindrical equal-area (0°)
** Behrmann (30°)
** Hobo–Dyer (37°30′)
** Gall–Peters (45°)
* Pseudocylindrical
** Boggs eumorphic
** Collignon
** Eckert II, IV and VI
** Equal Earth
** Goode's homolosine
** Mollweide
** Sinusoidal
** Tobler hyperelliptical
* Eckert-Greifendorff
* McBryde-Thomas Flat-Polar Quartic Projection
* Hammer
* Strebe 1995
* Snyder equal-area projection Snyder equal-area projection is a polyhedral map projection used in the '' ISEA (Icosahedral Snyder Equal Area) discrete global grids''. It is named for John P. Snyder, who developed the projection in the 1990s.
Snyder, J. P. (1992), “An Equa ...
, used for geodesic grid
A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron.
Construction
A geodesic grid is a global Earth reference that uses triangular tiles based on the subdivision of a polyhedron (usually the icosahedron, a ...
s.
See also
* Equiareal map (mathematics) *Measure-preserving dynamical system
In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special cas ...
* Geodesic polygon area
References