The most common projections for cylinders are listed below.

## Cassini

Though not used commonly today, Cassini was once the standard for a number of European nations, including England and France. Developed in 1745 by C. F. Cassini de Thury for the first major survey of France. This projection is neither equal-area nor conformal. Most meridians and parallels are complex curves, except for the central meridian, the Equator and each meridian 90 degrees from the central meridian.

## Danish System 1934/1945

These two systems convert Europe 1950 based UTM coordinates to the desired local systems. The transformations, which are bi-variant polynomials, not only convert from one Cartesian coordinate system to another, but also from one datum to another. This represents a departure from the normal method of performing a datum shift. This projection was implemented by using the Transverse Mercator projection and then added the polynomial on as a post-processor. Thus, the standard Transverse Mercator project converts internal geographic coordinates to UTM coordinates, and then uses the polynomial post-processor to generate the required results in the local region of interest.

The projection requires a single parameter that is a zone number. The values are:

This parameter specifies most of the other parameters with the exception of units and paper scale.

## Danish System 34/45 with KMS 1999 Polynomials

The Danish System 34/45 with KMS 1999 Polynomials is a variation of the Danish System 34/45 that conforms to the standards of KMS (Kort & Matrikelstyrelsen) and uses the polynomial transform KMS developed for this transform. Computations using this variation closely match the results required by KMS. This projection has three zones, indicated by the zone number parameter.

- 1 S34 Jylland
- 2 S34 Sjælland
- 3 S45 Bornholm

## Eckert 4 (Eckert IV)

This projection and the similar Eckert 6 are only used for maps of the entire world. Part of a set of six projections presented by Max Eckert in 1906 of Germany, but only IV and VI have been used to any great extent. It is usually found on thematic maps showing world climate conditions or population distribution.

This projection is supported in the spherical form only.

In each of the six projections, the pole lines are half the length of the Equator. In Eckert 4, the parallels are not equally spaced apart but all are straight lines. The central meridian is straight, the outer meridians, at 180 degrees, are semi-circles. The rest are elliptical arcs, spaced equally apart. It is an equal-area projection.

## Eckert 6 (Eckert VI)

The Eckert 6 is an equal-area projection. The meridians are sinusoidal curves, except for the central meridian which is a straight line. Like Eckert 4, all parallels are unequally spaced straight lines. The Equator is twice as long as the lines at the poles.

## Equidistant Cylindrical

One of the oldest projections known, probably developed by Eratosthenes around 200 BC, its use is limited today. It is neither conformal nor equal-area, meridians and parallels are equally spaced straight lines.

## Gauss-Kruger

Gauss-Kruger is identical to a Transverse Mercator, except that the parameter scale reduction factor is always

1.0. Scale reduction factor does not appear as a parameter for this projection. This coordinate system exists to allow users who are used to the Gauss-Kruger projection terminology.

## Mercator

The most well known map projection, it is conformal. Meridians are equally spaced straight lines. Parallels are straight lines, but not spaced equally. The Flemish cartographer Gerardus Mercator is generally accepted as the man who developed this projection around 1569. It is used mostly for navigation and has been the U.S. navigation standard since 1910.

## Mercator with Scale Reduction

Identical to Mercator projection except that it uses a user specified standard latitude instead of scale reduction factor to determine latitude(s) which are tangent to the cylinder.

## Miller Cylindrical

This projection is not conformal or equal-area. Parallels and meridians are straight lines, at right angles. Meridians are spaced equally, parallels get wider as you move away from the equator. First presented in the

U.S. in 1942 by O. M. Miller and is used mainly for world maps.

This projection is supported in the spherical form only.

## Mollweide

A cylindrical projection also used as the mid-latitude to polar regions of the Homolsine projection.

## New Zealand

A form of the Oblique Mercator designed specifically for the official grid maps of New Zealand. This projection is a conformal projection.

## Normal Equal Area Cylindrical

Created by Lambert in 1772, Normal Equal Area Cylindrical is also called Lambert Equal Area Cylindrical. It is hardly used by anyone in its original form. Modified versions are more common. In the original, meridians are equally spaced straight lines, parallels cross them at right angles. The parallels are straight lines which get closer together as you near the pole.

## Oblique Mercator Projection

The Oblique Mercator is also known as the Hotine Oblique Mercator. This is a conformal projection. It is suitable for areas which stretch along a line that is oblique to meridians. Most commonly seen on grid maps of the Alaska panhandle (Zone 1) and single maps of countries encompassing areas as far apart as Switzerland, Madagascar and Borneo.

Most of the meridians and all of the parallels are complex curves. However, the two meridians which are 180 degrees apart are straight lines.

## Oblique 1 Point and Oblique 2 Points

The Oblique 1 point and the Oblique 2 points are variant projections. For large regions of the earth, the Oblique 1 Point is chosen. For smaller areas, the Oblique 2 Point may be better.

## Hotine Oblique Mercator 1 point (rectified)

Defined by a single point and an azimuth, the projection produces rectified X and Y coordinates with the origin at the intersection of the central geodesic with the equator of the aposphere. This is the variation which produces the correct results for Zone 1 of the Alaska state plane system.

## Hotine Oblique Mercator 1 point (unrectified)

Defined by a single point and an azimuth, the projection produces unrectified UV coordinates with the origin at the intersection of the central geodesic with the equator of the aposphere. Not a very useful projection but preserved for historical reasons.

## Hotine Oblique Mercator 2 point (rectified)

Defined by two points, the projection produces rectified XY coordinates with the origin at the intersection of the central geodesic with the equator of the aposphere. This variation uses the azimuth of the central line at the projection origin (i.e., the single point) as the rotation angle in the rectification process. Not a very useful projection but preserved for historical reasons.

## Hotine Oblique Mercator 2 point (unrectified)

Defined by two points, the projection produces unrectified UV coordinates with the origin at the intersection of the central geodesic with the equator of the aposphere. Not a very useful projection but preserved for historical reasons.

## Rectified Skew Orthomorphic Projection (Oblique Mercator) Origin at Intersection

Defined by a single point and an azimuth. This projection produces rectified XY coordinates with the origin at the intersection of the central geodesic and the equator of the aposphere. This is the variation which produces the results most users expect from a Rectified Skew Orthomorphic projection.

The rectification technique is the one commonly used in places other than Alaska.

## Origin at Center

Defined by a single point and an azimuth. This projection produces rectified XY coordinates with the origin at the central point (i.e., the single defining point). This is the variation which would be most useful to a cartographer defining their own coordinate system.

The rectification technique is the one commonly used in places other than Alaska.

## Swiss Oblique Cylindrical Projection

An orthographic projection. There are two singularity points - either pole on the oblique sphere.

## Hungarian EOV Projection

An orthographic project that accepts the following parameters: • origin longitude - Longitude of central meridian • origin latitude

- � normal latitude - Normal Parallel determines Gaussian sphere radius
- � scale reduction factor

The Swiss Oblique Cylindrical Projection and the Hungarian EOV are considered to be variations of the same projection, however, the Hungarian EOV is the more generalized of the two.

## Transverse Equal Area Cylindrical

This is the transverse of the Normal Equal Area Cylindrical projection, proposed by Lambert in 1772. The central meridian is a straight line.

Meridians 90 degrees from the central meridian are also straight lines. The Equator is a straight line. All other parallels and meridians are complex curves.

The longitude of true scale is the central meridian or along two lines of longitude equally spaced from the central meridian.

Area is not distorted anywhere on this projection.

## Transverse Mercator (TM)

A conformal projection, first presented by Lambert in 1772. Sometimes known as Gauss Kruger or simply Gauss (when scale reduction factor is 1.0). In its ellipsoidal form is one of the most widely used projections in the world. It is used for official topographic mapping in many countries. In the United States, it is used with the State Plane Coordinate System for States with a north-south extent.

With the Transverse Mercator projection, most meridians and parallels are complex curves. The central meridian and meridians ninety degrees from the central meridian, as well as the Equator are straight lines.

The well known Universal Transverse Mercator (UTM) is a specific use of the Transverse Mercator with the specification of central meridians and a scale reduction factor of 0.9996 (a 1:2500 reduction).

## Transverse Mercator with Affine Post-processor

Similar to Transverse Mercator Projection but also allows as affine transform to take place after the projection has taken place.

## South Orientated Transverse Mercator (South Africa)

This projection is a variation of Transverse Mercator. When the SOTRM parameter "quadrant=3", SOTRM produced the same results as TM. This projection exists so that users expecting to see a separate system for South Africa will find one. See **Transverse Mercator (TM)** for technical specifications and sample output.

As applied to virtually all CAD drawing systems, X continues to be an easting value and easting values increase towards the east. Similarly, Y continues to be a northing value and increases towards the north.

## Ordinance Survey 2002 (OST02)

The Ordinance Survey 2002 (Great Britain) is Transverse Mercator with its specific affine post processor applied to the transformed coordinates. At the time of release, this version of OST02 is still unofficial. Bentley advises against using it as a standard until it is made official.