## Description

The Miller cylindrical projection is a compromise cylindrical map projection. The projection is a modification of the Mercator projection, thus they are almost identical near the equator. Although the Miller projection does not project poles to infinity, distortion is still severe at the poles.

The Miller cylindrical projection was developed by Osborn M. Miller in 1942. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.

## Projection properties

The subsections below describe the Miller cylindrical projection properties.

### Graticule

Miller is a cylindric projection. The meridians are equally spaced straight lines. The parallels and both poles are straight lines, perpendicular to meridians and the same length as the equator. The spacing between parallels grows away from the equator, but it does not increase as much as it does on the Mercator projection. The graticule is symmetric across the equator and the central meridian. The height-to-width ratio of the whole map is 0.73.

### Distortion

This projection is neither conformal nor equal-area. Shapes, areas, distances, directions, and angles are all generally distorted. There is no distortion at the equator. Distortion increases away from the equator and becomes severe in polar areas. Distortion values are symmetric across the equator and the central meridian.

## Usage

This projection can be used for general world maps not requiring accurate areas, and whose phenomena change with longitude. But its use is not recommended due to extreme distortion in polar regions.

## Variants

There are two variants of this projection available in ArcGIS. Neither variant supports the ellipsoid.

- Miller is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later. This variant uses the semimajor axis for the radius and equations for a sphere.
- Miller auxiliary sphere is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.3 and later. This variant uses sphere-based equations with a sphere specified by the Auxiliary Sphere Type parameter.

## Limitations

This projection is supported on spheres only. Some distortion properties are not maintained when an ellipsoid is used.

## Parameters

Miller parameters are as follows:

- False Easting
- False Northing
- Central Meridian

Miller auxiliary sphere parameters are as follows:

- False Easting
- False Northing
- Central Meridian
- Auxiliary Sphere Type, with values as follows:
- 0 = use semimajor axis of the geographic coordinate system
- 1 = use semiminor axis
- 2 = calculate and use authalic radius
- 3 = use authalic radius and convert geodetic latitudes to authalic latitudes

##### Note:

If the geographic coordinate system uses a sphere, the Auxiliary Sphere Type uses the radius of the sphere in all four cases.

## Sources

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.