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. An equal-area map projection cannot be conformal, nor can a conformal map projection 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 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
- McBryde-Thomas Flat-Polar Quartic Projection[5]
- Gall–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
- ↑ "INSPIRE helpdesk | INSPIRE". https://inspire.ec.europa.eu/forum/discussion/view/10928/use-of-the-equal-area-grid-grid-etrs89-laea.
- ↑ http://scorus.org/wp-content/uploads/2012/10/2010JurmalaP4.5.pdf[|permanent dead link|dead link}}]
- ↑ IBGE (2016), “Grade Estatística”. Arquivo
grade_estatistica.pdfem FTP ou HTTP, http://geoftp.ibge.gov.br/recortes_para_fins_estatisticos/grade_estatistica/censo_2010[bare URL] - ↑ Tsoulos, Lysandros (2003). "An Equal Area Projection for Statistical Mapping in the EU". Map projections for Europe. Joint Research Centre, European Commission. pp. 50–55. https://www.researchgate.net/publication/236852866.
- ↑ "McBryde-Thomas Flat-Polar Quartic Projection - MATLAB". https://www.mathworks.com/help/map/flatplrq.html.
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