USER DOCUMENTATION
Programs : INVERSE, FORWARD, INVERS3D, FORWRD3D
Versions 2.0
Please note that the GRS80 and WGS84 are considered to be the same. Actually,
there is a very small difference in the flattening which results in the semi-minor
axis, b, being different by 0.0001 meters. There is no known application for
which this difference is significant.
The user is given the option of defining their own reference ellipsoid in whatever
units they prefer. (If, for example, the user wishes to define the semi-major
and semi-minor axes in miles, they may do so. The units for the geodetic distance
would then be given in miles also.) The units for all the listed reference ellipsoid
are given in meters, and therefore the distances are also in meters.
Programs INVERS3D and FORWRD3D work exclusively on the GRS80 ellipsoid and the
units are meters.
Note 1
Program FORWRD3D will do a conversion from mark-to-mark distance to ellipsoidal
distance, if a mark-to-mark distance is given as input. The first approximation
is computed using formulas given in the NOAA Technical Memorandum NOS NGS-10,
Use of Calibration Baselines, pages 26-27. These formulas are generally good
for distances less than 100 kilometers. The program will then do a forward computation
using the computed ellipsoidal distance. The mark-to-mark distance is then recomputed
from the resulting DX,DY,DZ. If the difference between the computed mark-to-mark
distance and the original mark-to-mark distance is greater than one millimeter,
then the difference is applied to the ellipsoidal distance and another forward
computation is performed. The program will continue iterating in this fashion
until convergence.
Note 2
All four programs read the input geodetic positions as real numbers (latitudes
are positive North, and longitudes are positive East), then convert them to
radians for internal computations. The conversion is done as follows:
radians = ( pi / 180 ) * (degrees + minutes/60 + seconds/3600)
The programs return the input values after :
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Nominal format: degrees, minutes & seconds ( hDD MM SS.sssss ) | ||||
<cr> |
(h default = N)
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0 00 00.00000 North
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0 |
"
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"
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0 0 0 |
"
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"
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0,0,0.0 |
"
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"
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0d 0m 0s |
"
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"
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00d 00m 00.000s |
"
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"
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10 0 1.00001 |
"
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10 00 01.00001 North
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10d 0m 1.00001s |
"
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10 00 01.00001 North
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+0 |
0 00 00.00000 North
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+0 0 0.0 |
0 00 00.00000 North
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+0,0,0.1 |
0 00 00.10000 North
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N0 |
0 00 00.00000 North
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N20 |
20 00 00.00000 North
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n20d20m22s |
20 20 22.00000 North
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n020d 20m 0022s |
20 20 22.00000 North
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n10 0 10.00001 |
10 00 10.00001 North
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-0 0 1.00001 |
00 00 01.00001 South
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-10 0 10.00001 |
10 00 10.00001 South
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S26 37 48.26371 |
26 37 48.26371 South
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Packed format: degrees-minutes-seconds (hDDMMSS.sssss) | ||||
N000000.000 |
0 00 00.00000 North
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N100010.00001 |
10 00 10.00001 North
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S263748.26371 |
26 37 48.26371 South
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Decimal format: degrees (hDD.dddddddd) | ||||
20.0 |
(h default = N)
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20 00 00.00000 North
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10.002777781 |
"
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10 00 10.00001 North
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s26.630073253 |
26 37 48.26371 South
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Some example longitude inputs are:
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Nominal format: degrees, minutes & seconds ( hDDD MM SS.sssss ) | ||||
<cr> |
(h default = W)
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0 00 00.00000 West
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0 |
"
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"
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0 0 0 |
"
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"
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0,0,0.0 |
"
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"
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0d 0m 0s |
"
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"
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00d 00m 00.000s |
"
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"
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10 0 1.00001 |
"
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10 00 01.00001 West
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10d 0m 1.00001s |
"
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10 00 01.00001 West
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-1 |
1 00 00.00000 West
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-0 0 1.00001 |
0 00 01.00001 West
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-10 0 10.00001 |
10 00 10.00001 West
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W0 |
0 00 00.00000 West
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W20 |
20 00 00.00000 West
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w20d20m22s |
20 20 22.00000 West
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w020d 20m 0022s |
20 20 22.00000 West
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w10 0 10.00001 |
10 00 10.00001 West
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+0 |
0 00 00.00000 East
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+0 0 0.0 |
0 00 00.00000 East
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+0,0,0.1 |
0 00 00.10000 East
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E26 37 48.26371 |
26 37 48.26371 East
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Packed format: degrees-minutes-seconds (hDDDMMSS.sssss) | ||||
W0000000.000 |
0 0 0.00000 West
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W0100010.00001 |
10 0 10.00001 West
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E0263748.26371 |
26 37 48.26371 East
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Decimal format: degrees (hDDD.dddddddd) | ||||
20.0 |
(h default = W)
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20 00 00.00000 West
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10.002777781 |
"
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10 00 10.00001 West
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-10.002777781 |
10 00 10.00001 West
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+10.002777781 |
10 00 10.00001 East
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e26.630073253 |
26 37 48.26371 East
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LAT = | 34 | 00 | 12.12345 | North |
LON = | 111 | 00 | 12.12345 | West |
LAT = | 33 | 22 | 11.54321 | North |
LON = | 112 | 55 | 44.33333 | West |
Forward azimuth | FAZ = | 249 | 3 | 16.4237 | From North |
Back azimuth | BAZ = | 67 | 59 | 11.1619 | From North |
Ellipsoidal distance | S = | 191872.1190 | m |
LAT = | 45 | 00 | 12.00000 | North |
LON = | 68 | 00 | 0.00000 | West |
LAT = | 44 | 33 | 0.00000 | North |
LON = | 70 | 12 | 34.78900 | West |
Forward azimuth | FAZ = | 254 | 42 | 44.6439 | From North |
Back azimuth | BAZ = | 73 | 9 | 21.3315 | From North |
Ellipsoidal distance | S = | 182009.1679 | m |
Sample Outputs From Programs INVERS3D and FORWRD3D
Example 3 (FORWRD3D):
For Sample Input:
FROM: bill
LAT: 34,00,00.0
LON: 111 00 00.0
EHT: 76.0
dh: -22.0
FAZ: 245,00,34.7
S: 123456.7891
TO: george
Sample Output:
X = | -1896956.7156 m | LAT = |
34 00 00.00000 | North | |
Y = | -4941741.1960 m | LON = |
111 00 00.00000 | West | |
Z = | 3546489.0623 m |
EHT = |
76.0000 | meters |
X = | -2011507.3910 m | LAT = | 33 31 25.93490 | North | |
Y = | -4927927.6718 m | LON = | 112 12 16.40986 | West | |
Z = | 3502571.6004 m | EHT = | 54.0000 | meters |
Forward azimuth | FAZ = | 245 | 00 | 34.7000 | From North |
Back azimuth | BAZ = | 64 | 20 | 24.6862 | From North |
Ellipsoidal distance | S = | 123456.7891 | m | ||
Delta Height | dh = | -22.0000 | m | ||
Mark-to-mark distance | D = | 123456.1224 | m |
DX = | -114550.6754 m | DN = | -52153.4448 m | |
DY = | 13813.5242 m | DE = | -111892.5928 m | |
DZ = | -43917.4619 m | DU = | -1216.5690 m |
Zenith (mk-to-mk) | ZD = | 90 33 52.62 |
Apparent zenith distance | = | 90 29 07.10 |
For Sample Input:
FROM: MOUNT WHITNEY, CA
LAT: 36,34,42.89133
LON: 118 17 31.18182
EHT: 4395.832
TO: BAD WATER (DEATH VALLEY), CA
LAT: 36 1 37
LON: 116,49,32
EHT: -101.868
Sample Output:
X = | -2432166.7206 m | LAT = | 36 34 42.89133 | North | |
Y = | -4518536.0565 m | LON = | 118 17 31.18182 | West | |
Z = | 3782560.2447 m | EHT = | 4395.8320 | Meters |
X = | -2330458.8019 m | LAT = | 36 01 37.00000 | North | |
Y = | -4608415.6501 m | LON = | 116 49 32.00000 | West | |
Z = | 3730550.0939 m | EHT = | -101.8680 | Meters |
Forward azimuth | FAZ = | 114 | 29 | 26.9586 | From North |
Back azimuth | BAZ = | 295 | 21 | 32.6566 | From North |
Ellipsoidal distance | S = | 145239.0603 | m | ||
Delta Height | dh = | -4497.7000 | m | ||
Mark-to-mark distance | D = | 145354.3872 | m |
DX = | 101707.9187 m | DN = | -60202.3026 m | |
DY = | -89879.5936 m | DE = | 132158.0537 m | |
DZ = | -52010.1508 m | DU = | -6150.5675 m |
Zenith (mk-to-mk) | ZD = | 92 25 30.56 |
Apparent zenith distance | = | 92 19 55.21 |