The Cassini projection
is a map projection
described by César-François Cassini de Thury
in 1745Flattening the Earth: Two Thousand Years of Map Projections
, John P. Snyder, 1993, pp. 74-76, ISBN 0-226-76747-7.. It is the transverse
aspect of the equirectangular projection
, in that the globe is first rotated so the central meridian becomes the "equator", and then the normal equirectangular projection is applied. Composing these operations:
- <math>x = arcsin(cos(phi)sin(lambda)),</math>
- <math>y = arctanleft(fracright)</math>
where <math>lambda</math> is the longitude from the central meridian and <math>phi</math> is the latitude. When programming these equations, the inverse tangent
function used is actually the atan2
function, with the first argument <math>sin(phi)</math> and the second <math>cos(phi)cos(lambda)</math>.
The use of the Cassini projection has largely been superseded by the Transverse Mercator
projection, at least with central mapping agencies.
Things along the central meridian, and at right angles to it, are not distorted. Elsewhere, the distortion is largely in a north-south direction, and varies by the square of the central meridian. As such, the greater the longitudinal extent of the area, the worse the distortion becomes.
Due to this, the Cassini projection works best on long, narrow areas, and worst on wide... Read More