Boggs eumorphic projection: Difference between revisions
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{{Short description|Pseudocylindrical equal-area map projection}} |
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[[File:Boggs eumorphic projection SW.JPG|300px|thumb|Boggs eumorphic projection of the world.]] |
[[File:Boggs eumorphic projection SW.JPG|300px|thumb|Boggs eumorphic projection of the world.]] |
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[[File:Boggs eumorphic projection Tissot.svg|300px|thumb|Tissot indicatrix on Boggs eumorphic projection, 15° graticule, gradations every 10° of angular deformation.]] |
[[File:Boggs eumorphic projection Tissot.svg|300px|thumb|[[Tissot indicatrix]] on Boggs eumorphic projection, 15° graticule, gradations every 10° of angular deformation.]] |
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The '''Boggs eumorphic projection''' is a [[Map projection#Pseudocylindrical|pseudocylindrical]], [[ |
The '''Boggs eumorphic projection''' is a [[Map projection#Pseudocylindrical|pseudocylindrical]], [[equal-area projection|equal-area]] [[map projection]] used for [[world map]]s. Normally it is presented with [[Interrupted projection|multiple interruption]]s. Its equal-area property makes it useful for presenting spatial distribution of phenomena. The projection was developed in 1929 by [[Samuel Whittemore Boggs]] (1889–1954) to provide an alternative to the [[Mercator projection|Mercator]] projection for portraying global areal relationships. Boggs was geographer for the [[United States Department of State]] from 1924 until his death.<ref name="Snyder93"/> The Boggs eumorphic projection has been used occasionally in textbooks and atlases.<ref name="Wong65"/> |
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Boggs generally repeated regions in two different lobes of the interrupted map in order to show Greenland or eastern Russia undivided. He preferred his interrupted version, and named it "eumorphic”, meaning |
Boggs generally repeated regions in two different lobes of the [[Interrupted projection|interrupted map]] in order to show Greenland or eastern Russia undivided. He preferred his interrupted version, and named it "eumorphic”, meaning "goodly shaped" (in Boggs's own words). The projection's mathematical development was completed by [[Oscar S. Adams]] of the [[United States Coast and Geodetic Survey]].<ref name="Snyder93"/> |
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==Formulas== |
==Formulas== |
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The projection averages the ''y''-coordinates of the [[Mollweide projection]] and the [[Sinusoidal projection]] for a given geographic coordinate in order to obtain its own ''y''-coordinate. The ''x''-coordinate is then forced by the constraints of the equal-area property and the pseudocylindric class. |
The projection averages the ''y''-coordinates of the [[Mollweide projection]] and the [[Sinusoidal projection]] for a given geographic coordinate in order to obtain its own ''y''-coordinate. The ''x''-coordinate is then forced by the constraints of the equal-area property and the pseudocylindric class. |
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Given a radius of sphere ''R'', an adjustment ''k'' = 1.00138, a central meridian ''λ'' |
Given a radius of sphere ''R'', an adjustment ''k'' = 1.00138, a central meridian ''λ''<sub>0</sub> and a point with geographical latitude ''φ'' and longitude ''λ'', plane coordinates ''x'' and ''y'' can be computed using the following formulas: |
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: <math>x = |
: <math>\begin{align} x &= 2Rk \frac{\lambda - \lambda_0}{\sec \varphi + \frac{\pi \sqrt{2}}{4} \sec \theta}, \\ |
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y &= R\frac{\varphi + \sqrt{2} \sin \theta}{2k} \end{align}</math> |
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where |
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: |
: <math>2\theta + \sin 2\theta = \pi \sin \varphi</math> |
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''θ'' can be solved for numerically using [[Newton's method]]. The adjustment ''k'' shifts the points of no distortion to 40°N/S at each lobe's central meridian.<ref name="Snyder89" /> |
''θ'' can be solved for numerically using [[Newton's method]]. The adjustment ''k'' shifts the points of no distortion to 40°N/S at each lobe's central meridian.<ref name="Snyder89" /> |
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==See also== |
==See also== |
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{{Portal|Atlas}} |
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* [[List of map projections]] |
* [[List of map projections]] |
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* [[Goode homolosine projection]] |
* [[Goode homolosine projection]] |
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}}</ref> |
}}</ref> |
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<ref name="Snyder89">{{cite book |
<ref name="Snyder89">{{cite book |
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|title = An Album of Map Projections |
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|last1 = Snyder |
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|first1 = John P. |
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|authorlink1 = John P. Snyder |
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|last2 = Voxland |
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|first2 = Philip M. |
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| ⚫ | |||
|authorlink2 = Philip M. Voxland |
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| location = Denver |
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|year = 1989 |
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| ⚫ | |||
| ⚫ | |||
|location = Denver |
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|series = Professional Paper 1453 |
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| ⚫ | |||
| ⚫ | |||
| accessdate = 2014-09-27 |
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|pages = 221 |
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| ⚫ | |||
| ⚫ | |||
|accessdate = 2014-09-27 |
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|archive-url = https://web.archive.org/web/20100701102858/http://pubs.er.usgs.gov/usgspubs/pp/pp1453 |
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|archive-date = 2010-07-01 |
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|url-status = dead |
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| ⚫ | |||
<ref name="Wong65">{{cite thesis |
<ref name="Wong65">{{cite thesis |
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| title = World map projections in the United States from 1940 to 1960 |
| title = World map projections in the United States from 1940 to 1960 |
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*[http://mapthematics.com/ProjectionsList.php?Projection=45#Boggs%20eumorphic Description and characteristics] |
*[http://mapthematics.com/ProjectionsList.php?Projection=45#Boggs%20eumorphic Description and characteristics] |
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{{Map |
{{Map projections}} |
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[[Category:Cartographic projections]] |
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[[Category:Equal-area projections]] |
[[Category:Equal-area projections]] |
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Latest revision as of 00:22, 1 September 2024
The Boggs eumorphic projection is a pseudocylindrical, equal-area map projection used for world maps. Normally it is presented with multiple interruptions. Its equal-area property makes it useful for presenting spatial distribution of phenomena. The projection was developed in 1929 by Samuel Whittemore Boggs (1889–1954) to provide an alternative to the Mercator projection for portraying global areal relationships. Boggs was geographer for the United States Department of State from 1924 until his death.[1] The Boggs eumorphic projection has been used occasionally in textbooks and atlases.[2]
Boggs generally repeated regions in two different lobes of the interrupted map in order to show Greenland or eastern Russia undivided. He preferred his interrupted version, and named it "eumorphic”, meaning "goodly shaped" (in Boggs's own words). The projection's mathematical development was completed by Oscar S. Adams of the United States Coast and Geodetic Survey.[1]
Formulas
[edit]The projection averages the y-coordinates of the Mollweide projection and the Sinusoidal projection for a given geographic coordinate in order to obtain its own y-coordinate. The x-coordinate is then forced by the constraints of the equal-area property and the pseudocylindric class.
Given a radius of sphere R, an adjustment k = 1.00138, a central meridian λ0 and a point with geographical latitude φ and longitude λ, plane coordinates x and y can be computed using the following formulas:
where
θ can be solved for numerically using Newton's method. The adjustment k shifts the points of no distortion to 40°N/S at each lobe's central meridian.[3]
See also
[edit]References
[edit]- ^ a b Snyder, John P. (1993). Flattening the Earth: 2000 Years of Map Projections. Chicago: University of Chicago Press. p. 199.
- ^ Wong, Frank Kuen Chun (1965). World map projections in the United States from 1940 to 1960 (Thesis). Syracuse: Syracuse University. pp. 84, 105–106.
- ^ Snyder, John P.; Voxland, Philip M. (1989). An Album of Map Projections. Professional Paper 1453. Denver: USGS. p. 221. ISBN 978-0160033681. Archived from the original on 2010-07-01. Retrieved 2014-09-27.