Sinusoidal projection
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 is defined by:
where φ is the latitude, λ is the longitude, and λ0 is the central meridian.[1]
The north-south scale is the same throughout the central meridian, and the east-west scale is identical throughout the map. So, on the map, as in reality, the length of each parallel is proportional to the cosine of the latitude, and the shape of the map for the whole earth is the area between two symmetric rotated cosine curves. However all the other meridians are longer than the central meridian on the map (while in reality of course they are all the same length).
To obtain the distance along a meridian, you project the line segment onto the central meridian and measure it there - or to put it another way - you use the vertical distance between the parallels that intersect the meridian at those points (shorter than the distance between the points themselves). There is no distortion at all along the central meridian or along the equator - angles of intersection with those lines are also accurately measured.
Similar projections which wrap the east and west parts of the sinusoidal projection around the north pole are the Werner and the intermediate Bonne and Bottomley 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.[2]
References
- ^ Map Projections—A Working Manual, USGS Professional Paper 1395, John P. Snyder, 1987, pp. 243–248
- ^ NASA: "MODLAND Integerized Sinusoidal Grid"
External links
- Cybergeo article
- Table of examples and properties of all common projections, from radicalcartography.net