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The sinusoidal projection is a pseudocylindrical equal-area 
Similar projections which wrap the east and west parts of the sinusoidal projection around the
"MODLAND Integerized Sinusoidal Grid"
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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
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 l ...
, 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, 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 also ...
, 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 axis of rotation meets its surface. It is called the True North Pole to distinguish from the Ma ...
are the Werner and the intermediate Bonne and Bottomley projections.
The MODLAND Integerized Sinusoidal Grid, based on the sinusoidal projection, is a geodesic grid
A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron.
Construction
A geodesic grid is a global Earth reference that uses triangular tiles based on the subdivision of a polyhedron (usually the icosahedron, a ...
developed by the NASA's Moderate-Resolution Imaging Spectroradiometer ( MODIS) science team.NASA"MODLAND Integerized Sinusoidal Grid"
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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, and John Flamsteed – mathematicians who developed the technique.
References
External links
*Pseudocylindrical Projections
from radicalcartography.net {{Authority control Map projections Equal-area projections