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candey edited this page Mar 17, 2015 · 7 revisions

CXFORM: Coordinate transformation package for IDL and C

Originally written by Ed Santiago (LANL) Extended by Ryan Boller

OVERVIEW

The CXFORM package contains a set of routines to convert spacecraft coordinates from one system to another, i.e., GSE-->GSM. It is written in C and can be used as either a C library (.so or .dll) or as an IDL function on most platforms (via its DLM -- Dynamically Loadable Module -- interface).

It has been tested under SunOS v5.7, Microsoft Windows 2000/XP, Mac OS X 10.3 & 10.4, and Linux kernel release 2.4.20. It has previously been tested under Solaris 2.6 and DEC OSF/1 V4.0.

It is largely based on Mike Hapgood's excellent introduction to coordinate transformations, along with Markus Fraenz' "Heliospheric Coordinate Systems" and Christopher Russell's "Geophysical Coordinate Transformations":

http://sspg1.bnsc.rl.ac.uk/Share/Coordinates/ct_home.htm 
http://www.space-plasma.qmul.ac.uk/heliocoords/ 
http://www-ssc.igpp.ucla.edu/personnel/russell/papers/gct1.html/

Note that since this follows much of Hapgood's formulae that are optimized for simplicity and efficiency, he specifies a level of precision of 0.001 degrees up to the year 2100 for each rotation angle, which has been deemed sufficient for space physics applications. The disclaimer applies that these should not be used for mission-critical flight applications due to their margin of error.

Formal testing has been completed as of 2004/12/01. The results can be found in the test_results directory. In general, they are within 1% of the results of SSCWeb's calculations (based on GEOPACK), and in many cases are within 0.01%.

If you find CXFORM to be useful (or have other comments), please let us know.
For one example of CXFORM in a production environment, visit the USGS EarthNow! Landsat Image Viewer http://earthnow.usgs.gov/. By converting satellite positions and velocities from GEI to GEO, the exact ground track can be computed, enabling city names and the track itself to be properly located.

DOWNLOAD / INSTALLATION

Source code: compile using instructions in install.txt. You will need the C compiler included in Xcode for MacOS X.

USAGE FROM IDL

The function prototype is

new_pos = CXFORM( pos, source_frame, dest_frame, time )

where: pos is a vector of length 3, containing the position in source_frame coordinates. It can also be a 2-D array of size [3, M], where M is the number of points to convert

source_frame    is an ASCII string naming the source coordinate system, e.g., 'GSE', 'J2000'.  See 
                "Coordinate Systems Implemented" below.

dest_frame      is also an ASCII string, naming the destination coordinate system.

time            is "ephemeris seconds past J2000 (1 Jan 2000 12:00)". The "date2es" function converts a 
                standard Gregorian time (mm,dd,yyyy) to Ephemeris Seconds past/before J2000. 
                See the included "date2es.pro" file for more details.

new_pos         is the position, in dest_frame coordinates.

Single-coordinate example:

IDL> es = date2es(9,30,1999,7,5,0)  ; Sep. 30, 1999 07:05:00 UTC
IDL> pos = cxform([1,0,0], 'GSE', 'GEO', es)
IDL> help,pos
POS             DOUBLE    = Array[3]
IDL> print,pos
       0.32034915      0.94616669    -0.046314350
IDL>

Multiple-coordinate example:

IDL> imp8GEI = fltarr(3, 5)
IDL> imp8Time = lonarr(5)
IDL>
IDL> help, imp8GEI
IMP8GEI        FLOAT        = Array[3, 5]
IDL> help, imp8Time
IMP8TIME    LONG        = Array[5]
IDL>
IDL>
IDL> imp8GEI[*,0] = [-32.562, 20.085, -10.471]
IDL> imp8GEI[*,1] = [-34.415, 4.229, -6.173]
...
IDL> print, imp8GEI
    -32.5620    20.0850        -10.4710
    -34.4150    4.22900        -6.17300
    -27.2210    -12.441        -0.34300
    -9.01000    -23.380         5.39300
     14.1890    -19.583         7.58900
IDL>
IDL> imp8Time = [-43200, 43200, 129600, 216000, 302400]
IDL>
IDL> imp8GEO = cxform(imp8GEI, 'GEI', 'GEO', imp8Time)
IDL>
IDL> print, imp8GEO
   25.418317       28.593709      -10.471000
   10.691414       32.984396      -6.1729999
  -6.5404276       29.205893     -0.34299999
  -20.772292       14.011294       5.3930001
  -22.419840      -9.0648980       7.5890002

Note that if your data is imported as [M, 3] instead of [3, M], you can transpose it using IDL's TRANSPOSE function:

IDL> correctArr = fltarr(3, M)
IDL> correctArr = TRANSPOSE(originalArr)

USAGE FROM C

See main.c included in this package for an example of using CXFORM in C. See install.txt for instructions on building it on your platform.

TEST RESULTS

The bulk of the testing used SSCWeb's Locator Tabulator (http://sscweb.gsfc.nasa.gov/cgi-bin/sscweb/Locator.cgi) as the data source. As stated in the introduction, this service uses GEOPACK for its calculations. An included file, tester.c, was used to read in data from SSCWeb and compare it to the results of CXFORM. In addition, one data point was used from the HelioCoords transformation package (http://www.space-plasma.qmul.ac.uk/heliocoords/) documentation as a sanity check and also as a test for the heliospheric systems that are not present in SSCWeb.

ACE data, year 2000, ~40k data points (cxform/test_results/ACE_2000_results.pdf) Geotail data, year 1993, ~40k data points (cxform/test_results/Geotail_1993_results.pdf) IMP-8 data, year 2003, ~40k data points (cxform/test_results/HelioCoord_Comparison.pdf) Geocentric S/C Position from HelioCoords documentation, 1 data point (cxform/test_results/HelioCoord_Comparison.pdf)

COORDINATE SYSTEMS IMPLEMENTED

GEI Geocentric Equatorial Inertial, also known as True Equator and True Equinox of Date, True of Date (TOD), ECI, or GCI J2000 Geocentric Equatorial Inertial for epoch J2000.0 (GEI2000), also known as Mean Equator and Mean Equinox of J2000.0 GEO Geographic, also known as Greenwich Rotating Coordinates (GRC), or Earth-fixed Greenwich (EFG) MAG Geomagnetic GSE Geocentric Solar Ecliptic GSM Geocentric Solar Magnetospheric SM Solar Magnetic RTN* Radial Tangential Normal (Earth-centered) GSEQ Geocentric Solar Equatorial HEE Heliocentric Earth Ecliptic HAE Heliocentric Aries Ecliptic HEEQ Heliocentric Earth Equatorial

  • = this system has not been implemented/tested and should be treated as such

ADDING NEW COORDINATE SYSTEMS

This package has been designed to allow for easy additions of new coordinate systems. All you need to do is define one transformation between the new system and any of the existing ones. Once you do that, the Perl script will generate code to convert to all others. This, of course, means that a working copy of Perl must be installed. You will need the IxHash module if it is not already installed. It can be found at http://search.cpan.org/dist/Tie-IxHash/

Here's what you do:

  1. Edit the file cxform-manual.c and add a new function, xxxx_twixt_yyyy, where xxxx' is any existing coordinate frame, and yyyy' is the new one.

  2. Run "perl gen_cxform_auto.pl cxform-manual.c" from the prompt. This will create a new cxform-auto.c with support for your new coordinate system.

  3. Build and install a new CXFORM library as described in install.txt.

  4. Run and test it in IDL/C. That's it!

If it works, please send in your code.

VERSION HISTORY

2000/06/21 v0.2 Ed Santiago: Last released version from Ed. 2003/09/12 v0.3 Ryan Boller: First modified version from Ryan. Added RTN and GSEQ systems, IGRF model, slightly different time manipulation, Windows support, additional documentation, and standalone C functionality. 2004/03/19 v0.4 Ryan Boller: Updated Makefile to auto-detect platform and to build under Mac OS X. HEEQ system now implemented by Kristi Keller. 2004/05/21 v0.5 Ryan Boller: Fixed small discrepancy in calculation of T0 and lambda0. Results now match those of SSCWeb's (GEOPACK- based) when the mag pole lat/lon is fixed to their values, as they haven't updated their IGRF coefficients. 2004/12/01 v0.6 Ryan Boller: Finished comprehensive testing, posted results. Updated IGRF to Revision 9 (http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html).
Moved cxRound, date2es, and gregorian_calendar_to_jd to cxform-manual.c so it is included in the shared library. 2006/10/19 v0.7 Ryan Boller: Updated IGRF coefficients to 10th generation. Fixed IDL DLM interface under Windows XP & IDL 6.0+. Updated installation documentation. 2009/11/25 v0.71 Ryan Boller: Updated Mac compiler flags to compile 32- and 64-bit versions on Intel- and PPC-based CPUs. Fixed memory pointer problem on 64-bit machines (now using IDL_MEMINT instead of IDL_LONG in cxform-dlm.c).

KNOWN ISSUES / TODOs

  • Mac shared object does not link with C objects. May need to convert to a dylib. The shared object does work with the IDL DLM interface, though.
  • RTN System needs to be tested for accuracy.
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