The equidistant conic projection is a
conic map projection commonly used for maps of small countries as well as for larger regions such as the continental United States that are elongated east-to-west.
[
Also known as the simple conic projection, a rudimentary version was described during the 2nd century CE by the Greek astronomer and geographer ]Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importanc ...
in his work ''Geography
Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...
''.
The projection has the useful property that distances along the meridians are proportionately correct, and distances are also correct along two standard parallels that the mapmaker has chosen. The two standard parallels are also free of distortion.
For maps of regions elongated east-to-west (such as the continental United States) the standard parallels are chosen to be about a sixth of the way inside the northern and southern limits of interest. This way distortion is minimized throughout the region of interest.
Transformation
Coordinates from a spherical datum
In the pursuit of knowledge, data (; ) is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted. ...
can be transformed to an equidistant conic projection with rectangular coordinates
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...
by using the following formulas, where ''λ'' is the longitude, ''λ'' the reference longitude, ''φ'' the latitude, ''φ'' the reference latitude, and ''φ'' and ''φ'' the standard parallels:
:
where
:
:
:
:
Constants ''n'', ''G'', and ''ρ'' need only be determined once for the entire map. If one standard parallel is used (i.e. ''φ'' = ''φ''), the formula for ''n'' above is indeterminate, but then
:
The reference point (λ'', φ'') with longitude ''λ'' and latitude ''φ'', transforms to the ''x,y'' origin at (0,0) in the rectangular coordinate system.
The Y axis maps the central meridian ''λ'', with ''y'' increasing northwards, which is orthogonal to the X axis mapping the central parallel ''φ'', with ''x'' increasing eastwards.
Other versions of these transformation formulae include parameters to offset the map coordinates so that all ''x,y'' values are positive, as well as a scaling parameter relating the radius of the sphere (earth) to the units used on the map.
The formulae used for ellipsoidal datums are more involved.
See also
* List of map projections
This is a summary of map projections that have articles of their own on Wikipedia or that are otherwise notable
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References
Sources
*
External links
Table of examples and properties of all common projections
from radicalcartography.net
Map projections
Equidistant projections
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