OGDI Projection Reference Manual

i. Introduction

Various mathematical formulas exist which are used to project the earth's spherical surface onto a flat, two-dimensional surface. Each coordinate system used to display geographic data is based on a particular map projection. A map projection is represented by a projection descriptor. The projection descriptor must include enough information to define such things as the shape of the earth being assumed (spherical or type of ellipsoid), units of measure to be used, and so on. Since any representation of the earth's surface in two dimensions distorts shape, area, distance, or direction, and since different projections produce different distortions, care should be taken when combining map layers from different data sources and projections. 

Changing from one projection system to another may produce extreme distortion, and combining data from various projections may produce inaccurate data results. The characteristics of each projection make them useful for some applications and not useful for others, particularly as the degree of distortion inherent to them may vary for different regions of the earth.   

1. The Projection Descriptor

All possible arguments and parameters are listed in the following. This list may appear long but most of the arguments and parameters are optional. 

+proj=acronym is required for the selection of the cartographic projection and the name is an acronym for the desired projection. 

+ellps=acronym selects standard, predefined ellipsoid figures. For spherical-only projections, the major axis is used as the radius. 

+units=acronym allows you to select the unit of measurement to which the Cartesian coordinates will be converted. 

+azimuth=degree is an angle 0 and 360 degrees measured clockwise from the north. Allows the rotation of all objects that belong to a coverage. 

+R=R specifies that the projection should be computed as a spherical Earth with a radius corresponding to the numeric value you enter in this field. 

+a=a defines an elliptical Earth's major axis. 

+es=e defines an elliptical Earth's squared eccentricity. Optionally, +b=b, +e=e, +rf=1/f or +f=f can be used where b, e and f are minor axes, representing eccentricity and flattening, respectively. 

+R_A must be used with elliptical Earth parameters. It specifies that spherical computations be used with the radius of a sphere that has a surface area equivalent to the selected ellipsoid. 

+R_V can be used in a similar manner to calculate the sphere radius of an ellipse of equivalent volume. 

+R_a must be used with elliptical Earth parameters. The spherical radius of the arithmetic mean of the major and the minor axes is used. +R_g and +R_h can be used for the equivalent geometric or harmonic mean of the major and minor axes. 

+R_lat_a=o must be used with elliptical Earth parameters. The spherical radius of the arithmetic mean of the principal radii of the ellipsoid at latitude o is used. 

R_lat_g=o can be used for equivalent geometric means of the principle radii. 

+x_0=x specifies false easting; the value entered is added to the x value of the Cartesian coordinate. This is used in grid systems to avoid negative grid coordinates. 

+y_0=y specifies false northing; the value entered is added to the y value of the Cartesian coordinate. This is used in grid systems to avoid negative grid coordinates. 

+lon_0=degree specifies the central meridian. Along with +lat_0=degree, it normally determines the geographic origin of the projection. 

+lat_0=degree specifies the central parallel. See +lon_0=degree. 

+geoc when this option is selected, it specifies that geographic data coordinates are to be treated as geocentric. 

+over inhibits the reduction of input longitude to a range between -180 degrees and +180 degrees of the central meridian. 

+zone=n is used for UTM and MTM zone selection. 

+lon_1=degree is the longitude of the first point defining geodetic. 

+lat_1=degree is the latitude of the first point defining geodetic. 

+lon_2=degree is the longitude of the second point defining geodetic. 

+lat_2= degree is the latitude of the second point defining geodetic. 

+lat_ts=degree is the latitude of true scale. Polar aspect only. 

+lat_b=degree is the minimum error within the small or great circle defined by the angular distance, from the tangency point of the plane. Default 90. 

+k=scale is the scale factor. 

+h=height is the height of the perspective point. 

+ns is used for non-skewed cartesian coordinates. 

+south is used for Southern hemisphere applications. 

+W=value is a real value that determines the normal Hammer projection. 

+lsat=number is the LANDSAT satellite number, must be in the range 1-5. 

+path=number is the path number; must be in ranges 1-251 for lsat=1,2,3 or 1-233 for n = 3,4. 

+azi=degree is an angle measured clockwise from the north. Used only with Laborde projection of Madagascar. 

+no_cut is used to limit the extent of the projection to the hemisphere. 

+k_0=scale is the scale factor to adjust the equator scale. 

+lon_ts=degree is a longitude of true scale. 

+alpha=value determines the method to be used; the cartesian coordinates are rotated by the value of alpha. 

+lonc=degree is the longitude of the point of origin. 

+phi_0=degree is the latitude of the point of origin. 

+no_rot is used for no rotation of the coordinates. 

+no_uoff is used to suppress the offset in the pre-rotated axis. 

+rot_conv is used for the rotation of the coordinates by the origin convergence angle.

2. Examples

The following examples are valid projection definitions: 

+proj=longlat 

+proj=lcc +ellps=GRS80 +lat_0=44 +lat_1=44 +lat_2=60 +lon_0=-68.5 

+proj=utm +zone=11 +ellps=clrk66

3. References

Evenden, G.I., 1993. Cartographic Projection Procedures, Release 4, Interim Report, USGS, September 17, 40 p. 

Evenden, G.I., 1995. Cartographic Projection Procedures, Release 4, Second Interim Report, USGS, September 24, 21 p. 

LAS Inc., 1996. Open Geographic Datastore Interface (OGDI), Version 1.0: Programmer's Reference, 145p.