Rectangular polyconic projection: Difference between revisions

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{{Short description|Pseudoconical compromise map projection}}

The '''rectangular polyconic''' projection is a [[map projection]] developed in the mid 1800s and used in large scale British military mapping of the period. It belongs to the [[polyconic projection class]], which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Sometimes the rectangular polyconic is called the '''War Office''' projection due to its development and use by the British [[War Office]].<ref name = "Flattening">

[[File:Rectangular polyconic projection SW.jpg|300px|thumb|Rectangular polyconic projection of the world, with correct scale along the equator.]]

The '''rectangular polyconic''' projection is a [[map projection]] developedwas first mentioned in 1853 by the mid[[United 1800sStates Coast and usedGeodetic inSurvey|United largeStates scaleCoast BritishSurvey]], militarywhere mappingit was developed and used for portions of the periodU.S. exceeding about one square degree. It belongs to the [[polyconic projection class]], which consists of map projections whose parallels are non-concentric circular arcs except for the equator, which is straight. Sometimes the rectangular polyconic is called the '''War Office''' projection due to its development and use by the British [[War Office]] for topographic maps.<ref name = "Flattening">

{{ cite book

| title = Flattening the Earth: Two Thousand Years of Map Projections

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The rectangular polyconic has one specifiable latitude (along with the latitude of opposite sign) along which scale is correct. The scale is also true on the central meridian of the projection. Meridians are spaced such that they meet the parallels at right angles in equatorial aspect; this trait accounts for the name ''rectangular''.

The projection is defined by:<ref name = "Album">{{cite book

| title = An Album of Map Projections

| volume = U.S. Geological Survey Professional Paper 1453

| last = Snyder

| first = John P.

| year = 1989

| publisher = United States Government Printing Office

| url = https://pubs.usgs.gov/pp/1453/report.pdf

| archive-url = https://web.archive.org/web/20170222004111/https://pubs.usgs.gov/pp/1453/report.pdf

| archive-date = 2017-02-22

| url-status = bot: unknown

| access-date = 2018-01-15

}}</ref>{{rp|225}}{{rp|110}}

:<math>

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*''φ''{{sub|0}} is the latitude chosen to be the origin along ''λ''{{sub|0}};

*''φ''{{sub|1}} is the latitude whose parallel is chosen to have correct scale.

To avoid division by zero, the formulas above are extended so that if ''φ''&nbsp;=&nbsp;0 then ''x''&nbsp;=&nbsp;''λ2A'' and ''y''&nbsp;−=&nbsp;−''λφ''{{sub|0}}. andIf ''yφ''{{sub|1}}=&nbsp;0 then ''A''&nbsp;=&nbsp;{{sfrac|1|2}}(''λ''&nbsp;−&nbsp;''φλ''{{sub|0}}).

==See also==

{{Portal|Atlas}}

* [[List of map projections]]

* [[American polyconic projection]]

==References==

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==External links==

* [https://www.mapthematics.com/ProjectionsList.php?Projection=129194#rectangular%20polyconic Mapthematics page describing the rectangular polyconic projection.]

{{Map Projectionsprojections}}

[[Category:Map projections]]

{{cartography-stub}}