# Rectified skew orthomorphic

## Description

The rectified skew orthomorphic, also known as the Hotine projection, is one version of the oblique Mercator projection derivations. It is used for conformal mapping of areas that are obliquely oriented and do not follow a north-south or east-west trend.

The projection's formulas were presented by Martin Hotine in 1946. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.0 and later.

## Projection properties

The subsections below describe the rectified skew orthomorphic projection properties.

### Graticule

Rectified skew orthomorphic is an oblique cylindric projection. In general, the meridians and parallels are projected as complex curves. Only two meridians, exactly 180° apart, can be projected as straight lines, crossing the poles. Both poles are presented as points inside the projection outline.

### Distortion

Rectified skew orthomorphic is a conformal map projection. It does not maintain true directions, but angles and shapes are maintained at infinitesimal scale. Distances are accurate along the central line if the scale factor is 1.0. If it is less than 1.0, there are two straight lines parallel to the central line with accurate scale. Area, distance, and scale distortions greatly increase with distance from the central line or from the two straight lines that are parallel to the central line.

## Usage

The rectified skew orthomorphic projection is appropriate for mapping large-scale or smaller areas with oblique orientation and do not follow a north-south or east-west predominant extent.

## Variants

There are two variants of projection available in ArcGIS:

• Rectified skew orthomorphic center has the coordinate origin at the latitude of the center along the central line. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.0 and later.
• Rectified skew orthomorphic natural origin has the coordinate origin of the projected coordinate system where the central line of the projection crosses the equator. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 9.0 and later.

## Limitations

The implementation of this projection in ArcGIS is limited such that approximately one degree of latitude and longitude around the antipodal point cannot be shown. When using ellipsoids, constant scale along the central line or along straight lines parallel to the central line is not maintained.

## Parameters

Rectified skew orthomorphic center parameters are as follows:

• False Easting
• False Northing
• Scale Factor
• Azimuth
• Longitude Of Center
• Latitude Of Center
• XY Plane Rotation

Rectified skew orthomorphic natural origin parameters are as follows:

• False Easting
• False Northing
• Scale Factor
• Azimuth
• Longitude Of Center
• Latitude Of Center
• XY Plane Rotation

### Particular parameter cases

If the azimuth is 0° or 180° the resulting projection appears as the transverse Mercator projection. If the latitude of the center is set on the equator and the azimuth parameter is either ±90°, the projection appears as the Mercator.

## 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.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.