Equal-area map

In map projection, equal-area maps preserve area measure, generally distorting shapes in order to do that. Equal-area maps are also called equivalent or authalic.

The equal-area Mollweide projection

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 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.[1][2][3][4]

List of equal-area projections

These are some projections that preserve area:

• Albers conic
• Bonne
• Bottomley
• Collignon
• Cylindrical equal-area
• Eckert II, IV and VI
• Equal Earth
• Gall orthographic (also known as Gall–Peters, or Peters, projection)
• Goode's homolosine
• Hammer
• Hobo–Dyer
• Lambert azimuthal equal-area
• Lambert cylindrical equal-area
• Mollweide
• Sinusoidal
• Strebe 1995
• Snyder's equal-area polyhedral projection, used for geodesic grids.
• Tobler hyperelliptical
• Werner

See also

• Equiareal map (mathematics)
• Measure-preserving dynamical system
• Geodesic polygon area

References

1. https://inspire.ec.europa.eu/forum/discussion/view/10928/use-of-the-equal-area-grid-grid-etrs89-laea
2. http://scorus.org/wp-content/uploads/2012/10/2010JurmalaP4.5.pdf
3. 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
4. https://www.researchgate.net/publication/236852866_An_Equal_Area_Projection_for_Statistical_Mapping_in_the_EU