The Mercator projection is a map projection that was widely used for navigation since loxodromes are straight lines (although great circles are curved). The following equations place the x-axis of the projection on the equator and the y-axis at longitude , where is the longitude and is the latitude.
(1)
| |||
(2)
| |||
(3)
| |||
(4)
| |||
(5)
| |||
(6)
|
The inverse formulas are
(7)
| |||
(8)
| |||
(9)
| |||
(10)
|
where is the Gudermannian.
An oblique form of the Mercator projection is illustrated above. It has equations
(11)
| |||
(12)
| |||
(13)
|
where
(14)
| |||
(15)
| |||
(16)
|
The inverse formulas are
(17)
| |||
(18)
|
There is also a transverse form of the Mercator projection, illustrated above (Deetz and Adams 1934, Snyder 1987). It is given by the equations
(19)
| |||
(20)
| |||
(21)
| |||
(22)
| |||
(23)
|
where
(24)
| |||
(25)
|
Finally, the "universal transverse Mercator projection" is a map projection which maps the sphere into 60 zones of each, with each zone mapped by a transverse Mercator projection with central meridian in the center of the zone. The zones extend from S to N (Dana).