Geodetic Toolbox

Toolbox for angle, coordinate and date conversions and transformations. Version 2.95.

Description

A collection of geodetic functions that solve a variety of problems in geodesy. Supports a wide range of common and user-defined reference ellipsoids. Most functions are vectorized. Functions include:

Angle Conversions
  deg2rad - Degrees to radians
  dms2deg - Degrees,minutes,seconds to degrees
  dms2rad - Degrees,minutes,seconds to radians
  rad2deg - Radians to degrees
  rad2dms - Radians to degrees,minutes,seconds
  rad2sec - Radians to seconds
  sec2rad - Seconds to radians
 
Coordinate Conversions
  ell2utm - Ellipsoidal (lat,long) to UTM (N,E) coordinates
  ell2xyz - Ellipsoidal (lat,long) to Cartesian (x,y,z) coodinates
  sph2xyz - Shperical (az,va,dist) to Cartesian (x,y,z) coordinates
  xyz2sph - Cartesian (x,y,z) to spherical (az,va,dist) coordinates
  xyz2ell - Cartesian (x,y,z) to ellipsoidal (lat,long,ht) coordinates
  xyz2ell2 - xyz2ell with Bowring height formula
  xyz2ell3 - xyz2ell using complete Bowring version
 
Coordinate Transformations
  refell - Reference ellipsoid definition
  ellradii - Various radii of curvature
  cct2clg - Conventional terrestrial to local geodetic cov. matrix
  clg2cct - Local geodetic to conventional terrestrial cov. matrix
  ct2lg - Conventional terrestrial (ECEF) to local geodetic (NEU)
  dg2lg - Differences in Geodetic (lat,lon) to local geodetic (NEU)
  lg2ct - Local geodetic (NEU) to conventional terrestrial (ECEF)
  lg2dg - Local geodetic (NEU) to differences in geodetic (lat,lon)
  direct - Direct geodetic problem (X1,Y1,Z1 + Az,VA,Dist to X2,Y2,Z2)
  inverse - Inverse geodetic problem (X1,Y1,Z1 + X2,Y2,Z2 to Az,VA,Dist)
  simil - Similarity transformation (translation,rotation,scale change)
 
Date Conversions
  cal2jd - Calendar date to Julian date
  dates - Converts between different date formats
  doy2jd - Year and day of year to Julian date
  gps2jd - GPS week & seconds of week to Julian date
  jd2cal - Julian date to calenar date
  jd2dow - Julian date to day of week
  jd2doy - Julian date to year & day of year
  jd2gps - Julian date to GPS week & seconds of week
  jd2mjd - Julian date to Modified Julian date
  jd2yr - Julian date to year & decimal year
  mjd2jd - Modified Julian date to Julian date
  yr2jd - Year & decimal year to Julian date
 
Error Ellipses
  errell2 - Computes error ellipse semi-axes and azimuth
  errell3 - Computes error ellipsoid semi-axes, azimuths, inclinations
  plterrel - Plots error ellipse for covariance matrix
 
Miscellaneous
  findfixed - Finds fixed station based on 3D covariance matrix
  pltnet - Plots network of points with labels
 
Example Scripts
  DirInv - Simple partial GUI script for direct and inverse problems
  DirProb - Example of direct problem
  Dist3D - Example to compute incremental 3D distances between points.
  InvProb - Example of inverse problem
  PltNetEl - Example plot of network error ellipses
  ToUTM - Example of conversion from latitude,longitude to UTM

The most recent version can be found at http://www.craymer.com/software/matlab/geodetic/.

• Acknowledgements: This submission has inspired the following:; Equinoxes and Solstices
• MATLAB release: MATLAB 7.9 (2009b)

[John D'Errico]

This seems pretty good from what I checked. There are many conversions in here.

A couple of minor points. I notice that there is no error checking. For example, in ellradii one must provide an axis length and eccentricity (squared). But there are no checks on the proper number of parameters or even on the sign of the eccentricity.

In dms2deg, I noticed one interesting feature. Converting from 32 degrees, 12 minutes, -3 seconds, results in a degree prediction of:

dms2deg([32 12 -3])
ans =
      -32.201

Overall, its still pretty good.

[Nice Work]

Nice work

[Ali Ebrahimi]

 

[Jagkrich A.warangkul]

Thanks

[Ray Borough]

Very Useful

[Gene Newton]

Thank you.

[jaime torres]

gracias

[Christopher]

under matlab which file do i put this in so that it is being used?

[Sebastian Hölz]

There is a potential bug in function ell2UTM, which may lead to wrong results in the calculated northing, if the funciton is called with a vector containing coordinates from both southern and northern hemisphere. Change lines 23-27, which read ...

if lat>=0
  No=0;
else
  No=10000000;
end

to ...

No(size(lat))=0; % False northing (north)
No(lat<0) = 1e7; % False northing (south)

Sebastian

[Mike Craymer]

I corrected the bug for vector and array input to function ell2utm per Sebastian Holz's comments and posted a new version 2.91. Unfortunately, the fix only worked for row vectors. I've corrected it again in version 2.92 and tested it this time to make sure it works. Sorry for any problems this may have caused. In addition to error checking, I'll consider adding array input to all functions in the next major release (this Summer I hope).

[Sepideh]

Thanks for that, very useful

[Jonathan]

Hello,

Thank you for such a useful toolbox! I have a question, however, regarding transforming lat,lon on the WGS84 ellipsoid to local North East Up. If I use the same lat,lon coordinate as both my point to convert and my origin, why would I get a -21.5 km local North value? Shouldn't North and East both be zero?

Thanks again,
Jon

<SNIP>

>> [a,b,e2,finv] = refell('WGS84'); %get ellipsoid params
rlat = deg2rad(40); rlon = deg2rad(-108); %lat,lon
[Xec Yec Zec] = ell2xyz(rlat,rlon,0,a,e2) %convert to ECEF xyz
[N E Up] = ct2lg(Xec,Yec,Zec,rlat,rlon) %convert to local NEU

Xec =
  -1.5119e+06
Yec =
  -4.6532e+06
Zec =
   4.0780e+06

N =
  -2.1054e+04
E =
     0
Up =
   6.3693e+06

</SNIP>

[Mike Craymer]

Dear Jonathon,

I just saw your question about transforming lat,lon to N,E,U. The ct2lg function in your last step requires as input the X,Y,Z coordinate *differences* between the two points. In your example, you entered the X,Y,Z coordinates for just one point. ct2lg would have interpreted this as very large X,Y,Z coordinate differences. The correct conversion for your example is given below (you need to enter the X,Y,Z differences in ct2lg as Xec-Xec, Yec-Yec, Zec-Zec).

Thanks for your comments!
-Mike

>> [a,b,e2,finv] = refell('WGS84'); %get ellipsoid params
rlat = deg2rad(40); rlon = deg2rad(-108); %lat,lon
[Xec Yec Zec] = ell2xyz(rlat,rlon,0,a,e2) %convert to ECEF xyz
[N E Up] = ct2lg(Xec-Xec,Yec-Yec,Zec-Zec,rlat,rlon) %convert to local NEU

Xec =

  -1.5119e+06

Yec =

  -4.6532e+06

Zec =

   4.0780e+06

N =

     0

E =

     0

Up =

     0

[Bryce]

dates.m does a 'clear all' at the beginning of its loop. Not cool!

It would be much better to clear the actual names of variables that you use in the script. Resetting people's workspace variables is not nice.

Looks like a good toolbox, though. Thanks!

[Ram Acharya]

It is a good tool. However, I couldn't make its use while I wanted to convert lat longs to UTM, for lats [26.4546 -- 30.4485 degrees North ] and longs [80.074 -- 88.23319 degrees East]. The UTM zone is 45R . However your tool splits it into 44R and 45R. Could you review your code for that particular region. Thanks.

[Ist]

That's seems to be very useful package. Thank You!

[Mike Craymer]

Dear Bryce,
You are right! The "clear all" in dates.m is not cool. I've replaced it with clearing the specific variables used in the script. A new version 2.95 of the toolbox will be posted shortly fixing this in dates.m as well as other affected example scripts. In the meantime, users should remove any "clear" or "clear all" when using the examples. Thank you for bringing this to my attention!
-Mike

[Mike Craymer]

Dear Ram,
By default, the ell2utm function uses the standard UTM zone definition where the earth is divided into 60 zones each 6 deg of longitude in width. Zone 1 is bounded by longtiudes 180 deg E and 186 deg E.

<http://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system>;

By this definition, Zone 44 is bounded by longitudes 78 deg E and 84 deg E, while Zone 45 is bounded by 84 deg E and 90 deg E. That is, Zone 44 starts at 180+(44-1)*6-360=78. The boundary between Zones 44 and 45 therefore bisects what you call Zone 45R. You can verify this with the on-line version of GeoConvert at

<http://geographiclib.sourceforge.net/cgi-bin/GeoConvert>;

In any case, the ell2utm function allows you to specify the central meridian for any non-standard zone definitions. See help ell2utm for more information.

-Mike

[Mike Craymer]

Sorry the URL's in my previous comment did not format correctly. They should have been specified as:

http://en.wikipedia.org/wiki/Universal_Transverse_Mercator_coordinate_system

http://geographiclib.sourceforge.net/cgi-bin/GeoConvert

[Mike Craymer]

A new version 2.95 of the Geodetic Toolbox is now available. Unfortunately, I am unable upload it to the MATLAB Central File Exchange (keep getting an error). Until the Mathworks resolves the problem, you can find the new version at <http://www.craymer.com/software/matlab/geodetic/>;.

Updates include:

- Added new jd2mjd & mjd2jd functions for modified Julian date conversions.
- Modified ct2lg & lg2ct functions to optionally use different lat,lon for each point.
- Corrected use of ell2utm function in ToUTM example script.
- Removed "clear all" in example scripts to avoid clearing user's workspace.
- Modified functions to use GRS80 reference ellipsoid by default.

See Content.m for the full list of changes.

[Mike Craymer]

Sorry again! I keep forgetting that the MATLAB File Exchange doesn't like the use of the standard angle brackets enclosing URLs. Here is the clickable URL sans brackets:

http://www.craymer.com/software/matlab/geodetic/

[Vihang bhatt]

It is really a good toolbox. Thank you for making my life little easy. One suggestion for the author on Julian dates. In the function jd2cal, jd has to be positive. jd can be negitive (if they exist), following modification needed to the code

if(a==0)
   dy = c - e - fix(30.6001*f) + rem((jd+0.5),max(a,1));
else
 dy = c - e - fix(30.6001*f) + rem((jd+0.5),a);
end

In above case you are able to get 1st gragorian date for zeroth julian day. otherwise greogrian calander start from 2nd jan.

Dr. Vihang Bhatt

[joo tan]

mike..
if i wnat to set the central meridian, like zon 50, where can i get the central meridian value??

[Shien Kwun Leong]

Very useful! Thank you very much.

[Mike Craymer]

Re: 23 Jul 2011 post by muhammad faiz pa'suya

Dear Muhammad: The ell2utm function will automatically determine and output the standard UTM zone in which your input coordinates fall. To also have it output the central meridian for the zone(s), change the first line of the ell2utm.m function from

     function [N,E,Zone]=ell2utm(lat,lon,a,e2,lcm)
to
     function [N,E,Zone,lcm]=ell2utm(lat,lon,a,e2,lcm)

This will be implemented in the next version of the Toolbox. To understand how the zones are determined, see the Wikipedia entry for UTM.