cartography Cartography (; from , '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 imagined reality) can ...

, the loximuthal projection is a

map projection In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, ...

introduced by Karl Siemon in 1935, and independently in 1966 by Waldo R. Tobler, who named it. It is characterized by the fact that

loxodrome In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant azimuth ( bearing as measured relative to true north). Navigation on a fixed course (i.e., s ...

s (rhumb lines) from one chosen central point (the intersection of the central meridian and central

latitude In geography, latitude is a geographic coordinate system, geographic 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 t ...

) are shown straight lines, correct in

azimuth An azimuth (; from ) is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system. Mathematically, the relative position vector from an observer ( origin) to a point ...

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 equivalent, authalic, or equal-area projection is a map projection that preserves relative area measure between any and all map regions. Equivalent projections are widely used for thematic maps showing scenario distribution su ...

nor conformal.

Description

A loxodrome on the surface of the Earth is a curve of constant bearing: it meets every

parallel of latitude A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth (ignoring elevation) at a given latitude coordinate line. Circles of latitude are often called parallels becaus ...

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.

References

External links

Loximuthal projection
{{Map projections Map projections

Description

See also

References

External links