cartography Cartography (; from grc, χάρτης , "papyrus, sheet of paper, map"; and , "write") is the study and practice of making and using maps. Combining science, aesthetics and technique, cartography builds on the premise that reality (or an im ...

, the loximuthal projection is a

map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitud ...

introduced by Karl Siemon in 1935, and independently in 1966 by Waldo R. Tobler, who named it. It is characterized by the fact that loxodromes (rhumb lines) from one chosen central point (the intersection of the central

meridian Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...

and central

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...

) are shown straight lines, correct in

azimuth An azimuth (; from ar, اَلسُّمُوت, as-sumūt, the directions) is an angular measurement in a spherical coordinate system. More specifically, it is the horizontal angle from a cardinal direction, most commonly north. Mathematicall ...

from the center, and are "true to scale" in the sense that distances measured along such lines are proportional to lengths of the corresponding rhumb lines on the surface of the Earth. It is neither an

equal-area projection In cartography, an equal-area projection is a map projection that preserves 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, no ...

nor conformal.

Description

A loxodrome on the surface of the Earth is a curve of constant bearing: it meets every parallel of latitude at the same angle. Suppose its bearing is ''θ'' north of east, so, for example, due east is ''θ'' = 0; due north is ''θ'' = a right angle; due west is ''θ'' = a half circle. The loxodrome's whole length as it goes from the south pole to the north pole is fairly routinely seen to be ''R'' csc ''θ'' where ''R'' is the radius of the Earth (in particular if the loxodrome goes straight east, it circles the Earth infinitely many times without getting closer to either pole, so its length is ∞. Let a loxodrome pass through the point whose longitude and latitude are both 0; call this the "central point". Suppose one starts at the central point and travels a certain distance in a certain direction along this loxodrome and arrives at geographic location . Let ''f''(''p'') be the point in the (''x'', ''y'')-plane reached by going that same distance in that same direction from the origin (0, 0). Thus ''f''(''p'') ∈ R × ��, That point ''f''(''p'') is the image of ''p'' on the map. More than one loxodrome goes from the central point to ''p'', but there is a unique shortest one: the one that does not cross the 180° meridian on its way from the central point to ''p''. If one were to include loxodromes crossing the 180° meridian, one would get infinitely many images of the whole Earth, occupying the entire strip R × ��, Using only the unique shortest loxodrome from the central point to each point ''p'' gives only one copy, occupying a sort of oval.

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Loximuthal projection
Map projections {{cartography-stub

Description

See also

References

External links