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Map Projections

Projection parameters

A map projection by itself isn't enough to define a projected coordinate system. You can state that a dataset is in Transverse Mercator, but that's not enough information. Where is the center of the projection? Was a scale factor used? Without knowing the exact values for the projection parameters, the dataset can't be reprojected.

You can also get some idea of the amount of distortion the projection has added to the data. If you're interested in Australia but you know that a dataset's projection is centered at 0,0the intersection of the equator and the Greenwich prime meridianyou might want to think about changing the center of the projection.

Each map projection has a set of parameters that you must define. The parameters specify the origin and customize a projection for your area of interest. Angular parameters use the geographic coordinate system units, while linear parameters use the projected coordinate system units.

Linear parameters

False easting is a linear value applied to the origin of the x coordinates. False northing is a linear value applied to the origin of the y coordinates.

False easting and northing values are usually applied to ensure that all x and y values are positive. You can also use the false easting and northing parameters to reduce the range of the x or y coordinate values. For example, if you know all y values are greater than 5,000,000 meters, you could apply a false northing of -5,000,000.

Height defines the point of perspective above the surface of the sphere or spheroid for the Vertical Near-Side Perspective projection.

Angular parameters

Azimuth defines the center line of a projection. The rotation angle measures east from north. Used with the Azimuth cases of the Hotine Oblique Mercator projection.

Central Meridian defines the origin of the x coordinates.

Longitude of Origin defines the origin of the x coordinates. The central meridian and longitude of origin parameters are synonymous.

Central Parallel defines the origin of the y coordinates.

Latitude of Origin defines the origin of the y coordinates. This parameter may not be located at the center of the projection. In particular, Conic projections use this parameter to set the origin of the y coordinates below the area of interest. In that instance, you don't need to set a false northing parameter to ensure that all y coordinates are positive.

Longitude of Center is used with the Hotine Oblique Mercator Center (both Two-Point and Azimuth) cases to define the origin of the x coordinates. Usually synonymous with the longitude of origin and central meridian parameters.

Latitude of Center is used with the Hotine Oblique Mercator Center (both Two-Point and Azimuth) cases to define the origin of the y coordinates. It is almost always the center of the projection.

Standard Parallel 1 and Standard Parallel 2 are used with Conic projections to define the latitude lines where the scale is 1.0. When defining a Lambert Conformal Conic projection with one standard parallel, the first standard parallel defines the origin of the y coordinates.

For other conic cases, the y coordinate origin is defined by the latitude of origin parameter.

  • Longitude of first point
  • Latitude of first point
  • Longitude of second point
  • Latitude of second point

The four parameters above are used with the Two-Point Equidistant and Hotine Oblique Mercator projections. They specify two geographic points that define the center axis of a projection.

Pseudo standard parallel 1 is used in the Krovak projection to define the oblique cone’s standard parallel. The x, y plane rotation defines the orientation of the Krovak projection along with the x scale and y scale parameters.

Unitless parameters

Scale factor is a unitless value applied to the center point or line of a map projection.

The scale factor is usually slightly less than one. The UTM coordinate system, which uses the Transverse Mercator projection, has a scale factor of 0.9996. Rather than 1.0, the scale along the central meridian of the projection is 0.9996. This creates two almost parallel lines approximately 180 kilometers, or about 1°, away where the scale is 1.0. The scale factor reduces the overall distortion of the projection in the area of interest.

x and y scales are used in the Krovak projection to orient the axes.

Option is used in the Cube and Fuller projections. In the Cube projection, option defines the location of the polar facets. An option of 0 in the Fuller projection will result in all 20 facets. Specifying an option value between 1–20 will create a single facet.

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