INVERSE/FORWARD/INVERS3D/FORWRD3D Computation Utilities

INVERSE

Program INVERSE is the tool for computing the geodetic azimuth and ellipsoidal distance between two points given their latitudes and longitudes in degrees, minutes, and seconds. The user may select from a variety of reference ellipsoids, including GRS80(NAD 83) / WGS84 and Clarke 1866 (NAD 27), or may define their own reference ellipsoid in whatever units they prefer. The units for the listed ellipsoids are given in meters, and therefore the distances are also given in meters. Note that for the purpose of this application GRS80 and WGS84 are considered to be equivalent. The program reads input geodetic positions with the default hemispheres for the latitude and longitude set at North and West.

 The NGS program "INVERSE" uses the "Vincenty algorithm" (2, 3) to solve geodesic problems. It is an optimized version of Bessel's algorithm (1) for numerical computations by reducing the use of trigonometric functions. The INVERSE algorithm involves iteration to find the solution. In very rare instances, the results can fail to iterate properly when the two points are close to being anti-podal. For all other applications, this program has been shown to be fast, stable and accurate. There are other algorithms available, should INVERSE fail to meet your needs. Such algorithms include: Pittman, M. E. (1986) Precision direct and inverse solutions of the geodesic, Surveying and Mapping, Vol. 46, No. 1, pp. 47-54, March 1986 Sjoberg, L. E. and M. Shirazian (2012) Solving the direct and inverse geodetic problems on the ellipsoid by numerical integration, Journal of Surveying Engineering, Vol. 138, No. 1, pp. 9-16, February 2012 Karney, C. F. F. (2012) Algorithms for geodesics, J. Geodesy 87(1), 43-55 References: Bessel, F. W., (1826) On the computation of geographical longitude and latitude from geodetic measurements, Astronomische Nachrichten (Astronomical Notes), Band 4, No. 86, Spalten 241-254, Altona 1826 Vincenty, T., (1975) Direct and inverse solutions on the ellipsoid with application of nested equations, Survey Review, Vol. 23, No. 176, pp. 88-93. Vincenty, T., (1976) Correspondence: solutions of geodesics, survey Review, Vol. 23, No. 180, p. 294.

FORWARD

Program FORWARD is the tool for computing the geodetic position (latitude and longitude in degrees, minutes, and seconds) of a point given the geodetic position of a beginning point and the geodetic azimuth and ellipsoidal distance between the two points. The user may select from a variety of reference ellipsoids, including GRS80(NAD 83) / WGS84 and Clarke 1866 (NAD 27), or may define their own reference ellipsoid in whatever units they prefer. The units for the listed ellipsoids are given in meters, and therefore the distances should also be given in meters. Note that for the purpose of this application GRS80 and WGS84 are considered to be equivalent. The program reads input geodetic positions with the default hemispheres for the latitude and longitude set at North and West.

INVERS3D

Program INVERS3D is the three dimensional version of program INVERSE, and is the tool for computing not just the geodetic azimuth and ellipsoidal distance, but also the mark-to-mark distance, the ellipsoid height difference, the DX, DY, DZ (differential X, Y, Z used to express GPS vectors), and the DN, DE, DU (differential North, East, Up using the FROM station as the origin of the NEU-coordinate system). The program requires geodetic coordinates as input, expressed as either: 1) latitude and longitude in degrees, minutes, and seconds or decimal degrees along with the ellipsoid heights for both stations, or 2) rectangular coordinates (X, Y, Z in the Conventional Terrestrial Reference System) for each station. The program works exclusively on the GRS80 ellipsoid and the units are meters. Both types of coordinates may be used in the same computation. The program reads input geodetic positions with the default hemispheres for latitude and longitude set at North and West.

FORWRD3D

Program FORWRD3D is the tool for computing the 3D geodetic position for a point given the 3D geodetic position of a beginning point, along with one of the following four input options:

• DN, DE, DU (differential N, E, U using the FROM station as the origin of the NEU-coordinate system.)
• DX, DY, DZ (differential X, Y, Z used to express GPS vectors)
• delta height, forward azimuth, ellipsoidal distance
• delta height, forward azimuth, mark-to-mark distance
The program requires geodetic coordinates as input, expressed as either: 1) latitude and longitude in degrees, minutes, and seconds or decimal degrees along with the ellipsoid heights, or 2) rectangular coordinates (X, Y, Z in the Conventional Terrestrial Reference System). The program works exclusively on the GRS80 ellipsoid and the units are meters. The program reads input geodetic positions with the default hemispheres for latitude and longitude set at North and West.

For more information about these programs, see "Direct and Inverse Solutions Of Geodesics On The Ellipsoid With Application Of Nested Equations"