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The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570.
The projection represents the poles as points, as they are on the sphere, but the meridians and continents are distorted. The equator and the prime meridian are the most accurate parts of the map, having no distortion at all, and the further away from those that one examines, the greater the distortion.
The projection is defined by:
:
where is the latitude, ''λ'' is the longitude, and ''λ'' is the longitude of the central meridian.
Scale is constant along the central 
Similar projections which wrap the east and west parts of the sinusoidal projection around the
"MODLAND Integerized Sinusoidal Grid"
/ref>
Pseudocylindrical ProjectionsTable of examples and properties of all common projections
from radicalcartography.net {{Authority control Map projections Equal-area projections
The sinusoidal projection is a pseudocylindrical equal-area map projection, sometimes called the Sanson–Flamsteed or the Mercator equal-area projection. Jean Cossin of Dieppe was one of the first mapmakers to use the sinusoidal, appearing in a world map of 1570.
The projection represents the poles as points, as they are on the sphere, but the meridians and continents are distorted. The equator and the prime meridian are the most accurate parts of the map, having no distortion at all, and the further away from those that one examines, the greater the distortion.
The projection is defined by:
:
where is the latitude, ''λ'' is the longitude, and ''λ'' is the longitude of the central meridian.
Scale is constant along 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 east–west scale is constant throughout the map. Therefore, the length of each parallel on the map is proportional to the cosine of the latitude, as it is on the globe. This makes the left and right bounding meridians of the map into half of a sine wave, each mirroring the other. Each meridian is half of a sine wave with only the amplitude differing, giving the projection its name. Each is shown on the map as longer than the central meridian, whereas on the globe all are the same length.
The true distance between two points on a meridian can be measured on the map as the vertical distance between the parallels that intersect the meridian at those points. With no distortion along the central meridian and the equator
The equator is a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can al ...
, distances along those lines are correct, as are the angles of intersection of other lines with those two lines. Distortion is lowest throughout the region of the map close to those lines.
Similar projections which wrap the east and west parts of the sinusoidal projection around the north pole
The North Pole, also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where the Earth's rotation, Earth's axis of rotation meets its surface. It is called the True North Pole to distingu ...
are the Werner Werner may refer to:
People
* Werner (name), origin of the name and people with this name as surname and given name
Fictional characters
* Werner (comics), a German comic book character
* Werner Von Croy, a fictional character in the ''Tomb Rai ...
and the intermediate Bonne
Bonne or Bonné can refer to:
People
; Given name
* Bonne of Armagnac (1399 – 1430/35), eldest daughter of Bernard VII, Count of Armagnac and of Bonne of Berry
* Bonne of Artois, (1396-1425), daughter of Philip of Artois, Count of Eu and of Mar ...
and Bottomley Bottomley and its homophone Bottomly are English surnames. They come from the placename formed by combining geographic terms "bottom" and " ley", and which refers to two small settlements each on opposite sides of a hill near Walsden and Halifax, We ...
projections.
The MODLAND Integerized Sinusoidal Grid, based on the sinusoidal projection, is a geodesic grid developed by the NASA's Moderate-Resolution Imaging Spectroradiometer ( MODIS) science team.NASA"MODLAND Integerized Sinusoidal Grid"
/ref>
See also
* List of map projections *Gerardus Mercator
Gerardus Mercator (; 5 March 1512 – 2 December 1594) was a 16th-century geographer, cosmographer and cartographer from the County of Flanders. He is most renowned for creating the 1569 world map based on a new projection which represented ...
, Nicolas Sanson
Nicolas Sanson (20 December 1600 – 7 July 1667) was a French cartographer who served under two kings in matters of geography. He has been called the "father of French cartography."
Life and work
He was born of an old Picard family of Sco ...
, and John Flamsteed – mathematicians who developed the technique.
References
External links
*Pseudocylindrical Projections
from radicalcartography.net {{Authority control Map projections Equal-area projections