# Oblique Mercator Azimuth Projection

The Oblique Mercator projection is a cylindrical, conformal map projection. It is similar to the Mercator projection, except that the cylinder is wrapped around the ellipsoid so that it touches the surface along the great circle path chosen for the central line, instead of along the earth's equator. Scale becomes infinite 90 degrees from the central line and is true along a chosen central line, along two straight lines parallel to the central line, or along a great circle at an oblique angle. The Oblique Mercator projection is used for geographic regions that are centered along lines that are neither meridians nor parallels, but that may be taken as great circle routes passing through the region, such as the Alaskan panhandle. In this variation of the Oblique Mercator projection, a point and an azimuth define the central line where the cylinder touches the ellipsoid.

The planar points determined by this projection may be left “unrectified” (often these are referred to as the u, v coordinates in published formula) or they may be “rectified” (often these are referred to as the x, y coordinates in published formula). Rectification consists of rotating the coordinates by a certain angle. This implementation of the Oblique Mercator projection allows for a flag to be set to determine if the points should be rectified, or not. By default, the points will be rectified. If an unrectified version of the projection is desired, the “Unrectified Flag” parameter should be set to 1.

In the case where the points are rectified, the angle of rotation may be one of three values. Most commonly, it may be a user-specified rotation, or a rotation such that the y-axis will be parallel to the meridian through the center of the projection (the angle used in this case is often referred to in published formula as alpha). Less commonly, it may be a rotation such that the y-axis will be parallel to the meridian through the natural origin of the projection (the angle used in this case is often referred to in published formula as gamma). If the “Rotation Angle” parameter is a non-zero number, it will be used in the rectification. If the “Rotation Angle” is zero, the default behavior will be to rectify so that the y-axis will be parallel to the meridian through the center of the projection. If it is desired that the rectification cause the y-axis to be parallel to the meridian through the natural origin of the projection, the “Use Gamma Flag” parameter should be set to 1.

By default, the planer coordinates will be provided in terms of the natural origin of the projection. Alternately, they may be shifted based on the center of the projection. If it is desired that the coordinates be shifted, the “Center Flag” parameter should be set to 1. Note that this is only an option in the Oblique Mercator Azimuth projection, and is not currently supported in the Two Point case.

By default, the “Azimuth” parameter provided is assumed to be the angle at the center of the projection (alpha). However, there may be times when you want instead to specify the angle at the natural origin of the projection (gamma). Since each angle may be computed based on the other, either one can be specified when define the projection. If the “Azimuth Is Gamma” flag is set, it is assumed that the value passed in via the “Azimuth” parameter is the angle at the natural origin of the projection (gamma). Otherwise, it is assumed that the value passed in via the “Azimuth” parameter is the angle at the center of the projection (alpha).

The "ObliqueMercatorAzimuth" Projection has the following Parameters:

 Parameter Name Parameter String Units Longitude at the Center of the Projection central_meridian AngularValue Latitude of the Origin of the Projection latitude_of_origin AngularValue Azimuth of the Central Line azimuth AngularValue Scale Factor at the Center of the Projection scale_factor double False Easting false_easting LinearValue False Northing false_northing LinearValue Rotation Angle (Defaults to 0) rotation_angle AngularValue Unrectified Flag (Defaults to 0) unrectified_flag Long Use Gamma Flag (Defaults to 0) use_gamma_flag Long Center Flag (Defaults to 0) center_flag Long Azimuth is Gamma (Defaults to 0) azimuth_is_gamma Long