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In
Equal area representation implies that a
In 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 ...
, equal-area maps preserve 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.
Applications
Equal area representation implies that a region 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 de ...
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 fordata visualization
Data and information visualization (data viz or info viz) is an interdisciplinary field that deals with the graphic representation of data and information. It is a particularly efficient way of communicating when the data or information is nume ...
, geocode
A geocode is a code that represents a geographic entity (location or object). It is a unique identifier of the entity, to distinguish it from others in a finite set of geographic entities. In general the ''geocode'' is a human-readable an ...
and statistical spatial analysis.IBGE (2016), “Grade Estatística”. Arquivo grade_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: * Albers conic *Bonne
Bonne or Bonné can refer to:
People
; Given name
* Bonne of Armagnac (1399 – 1430/35), eldest daughter of Bernard VII, Count of Armagnac and of Bonne of Berry
* Bonne of Artois, (1396-1425), daughter of Philip of Artois, Count of Eu and of Mar ...
* Bottomley Bottomley and its homophone Bottomly are English surnames. They come from the placename formed by combining geographic terms "bottom" and " ley", and which refers to two small settlements each on opposite sides of a hill near Walsden and Halifax, We ...
* Collignon
* Cylindrical equal-area
* Eckert II, IV and VI
* Equal Earth
* McBryde-Thomas Flat-Polar Quartic Projection
* Gall–Peters projection
The Gall–Peters projection is a rectangular, equal-area map projection. Like all equal-area projections, it distorts most shapes. It is a cylindrical equal-area projection with latitudes 45° north and south as the regions on the map that ha ...
* Goode's homolosine
* Hammer
A hammer is a tool, most often a hand tool, consisting of a weighted "head" fixed to a long handle that is swung to deliver an impact to a small area of an object. This can be, for example, to drive nails into wood, to shape metal (as ...
* Hobo–Dyer
* Lambert azimuthal equal-area
* Lambert cylindrical equal-area
* Mollweide
* Sinusoidal
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ...
* Strebe 1995
* Snyder's equal-area polyhedral projection, 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.
* Tobler hyperelliptical
* Werner Werner may refer to:
People
* Werner (name), origin of the name and people with this name as surname and given name
Fictional characters
* Werner (comics), a German comic book character
* Werner Von Croy, a fictional character in the ''Tomb Rai ...
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See also
*Equiareal map (mathematics) In differential geometry, an equiareal map, sometimes called an authalic map, is a smooth map from one surface to another that preserves the areas of figures.
Properties
If ''M'' and ''N'' are two Riemannian (or pseudo-Riemannian) surfaces, then ...
* 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 ca ...
* Geodesic polygon area
The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an ''oblate ellipsoid'', a slightly flattened sphere. A ''geodesi ...
References