Walter and Jacques,

I disagree with the 6-parameter suggestion.  I do not believe anything more than
a 3-parameter is reasonable to transform between a local archeological "Dig"
coordinate system and a geodetic system.

When I say 3 parameters, I mean a change in X coordinates, a change in Y
coordinates and a rotation.  For that sort of operation, Walter is correct in
that such a transformation can be done with a minimum of two points.  I would
like to suggest that more points be used as a check, but a unique solution is
satisfied with 2 points.  The 6-parameter solution offers 3 additional
parameters that should not be tolerated in such a survey.  A different scale in
each coordinate axis along with a factor for a non-orthogonal axis angle is
totally out of place.

Textbook for this sort of thing?  Good Grief!

   X =   X' cosine (theta) + Y'   sine (theta) + dX'

   Y = - X'   sine (theta) + Y' cosine (theta) + dY'

Presumably, the primed components are the "Dig" coordinates.  This is not rocket
science, it is High School Analytical Geometry.

This will be adequate for a "DIg" no larger than 1,000 acres or a linear feature
less than 5 miles long.  Bigger than that, and you should be working in a truly
Geodetic coordinate system that is a conformal (orthomorphic) Grid system with
corrections for azimuth, scale factor, and correction to mean sea level. 
However, something that big is probably going to have a surveyor associated with
the project and therefore they will take care of the details.

This can be extended into a local geodetic grid in itself if the geodetic
coordinates of the origin point is known along with a true meridian reference
(azimuth from true north).  With that accomodated, then the local "Dig"
coordinate system can be either an ellipsoidal polyhedric (similar to a
gnomonic), or can be an ellipsoidal azimuthal equidistant.  Both techniques have
been effectively used for islands and small countries in the 19th and 20th

Examples of the French used of the ellipsoidal Hatt Azimuthal Equidistant
projection for such "localized" surveys can be found in my "Grids and Datums"
column on the Republic of Gabon, published in the September, 1998 issue of
"Photogrammetric Engineering and Remote Sensing" and is downloadable from the
society's website at:

Note that the file is in Adobe Acrobat ".pdf" format.

In conclusion, use a 3-parameter transformation, and only a 3-parameter.


Clifford J. Mugnier ([EMAIL PROTECTED])
The Topographic Engineering Laboratory
Department of Civil and Environmental Engineering
New Orleans, Louisiana  70148

Voice and Facsimile: (504) 280-7095
Jacques Paris wrote:
> Walter,
> Have you considered using the AFFINE clause that could register any DXF in
> any "orthogonallly projected" or non-earth coordsys? The only delicate point
> is the calculation of the 6 parameters, difficulty residing essentially in
> the understanding of the direction of the change.
> I have detailled that question in chap 8 Registering a DXF map in "My Bag
> o'Tricks". I must have some Excel spreadsheet that would help in the
> computation of those parameters; if you think it could be of help, ask and
> I'll see what I can do.
> >
> > Hello mappers,
> > Are there some experts on coordsys transformations out there? In
> > the field Arheologists often work with a local coordsystem
> > (nonearth meters). During the gis analysis we want to place all
> > the information in an national non-earth(meters)coordsys.
> > Until now I used Rotator from the ftp-site. This works very
> > well, but I need to determine the angle of rotation and the
> > X, Y translation parameters. I think, it would be better to
> > digitize the excavation drawings directly in the
> > national nonearth coordsys by using control points from which
> > the national coordsys coordinates are used
> > (there are always points in the field from which both coordsys
> > coordinates are known).
> >
> > I would like to build a program (mbx) that asks the user- from
> > two points(is this enough?), both local and
> > national coordinates. The program then calculates the rotation
> > angle and the translation parameters. Then the user can give
> > a number of local coordinates and the program can calculate from
> > every local coordinates the national coordinates.
> > Is this possible with some simple goniometry and pythagoras?
> > Is there some information on this subject (books, internet)?
> >
> > Walter
> >
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