[Geotiff] Mercator_2sp

[Laurence R Moore]

Complete equations are also in Snyder's USGS Professional Paper 1395, 
available in several formats at http://pubs.er.usgs.gov/usgspubs/pp/pp1395
.  The Mercator is on pages 38-47 (hard copy page numbers; PDF pages are 
47-56).  See the last section on page 47 (PDF 56) for the 2SP case.

-----------------------------
Larry Moore
USGS, Rolla MO
15S XC 1032 0144
lmoore at usgs.gov


geotiff-bounces at lists.maptools.org wrote on 03/17/2009 09:41:34 AM:
> to: geotiff
> 03/17/2009 09:51 AM
> From: "Russell Ron" <Ron.Russell at UKHO.gov.uk>
> To:<geotiff at lists.maptools.org>
> 
> Frank,
> 
> Calculating the scale factor at the equator given 'latitude of true
> scale' is no problem - see
> 
> http://www.remotesensing.org/geotiff/proj_list/mercator_2sp.html
> 
> however several pieces of viewing software refuse to accept a floating
> point value for the Scale at Natural origin (in particular ArcGis). I
> can't remember whether GDAL did or not (I must admit it is at the end of
> my list!). ListGeo and Proj4 are happy with the keys I have suggested.
> 
> Before dealing with Geotiffs, I don't think I had ever come across any
> real Mercator projection that did not use the Mercator_2sp model!
> 
> It is all a bit frustrating.
> 
> I will see if I can cope with raising a ticket.
> 
> Thanks,
> 
> (BTW, thanks for your effort in supporting libgeotiff and also proj4)
> 
> Ron Russell
> 
> IT Specialist - Digital Mapping & Charting
> 
> United Kingdom Hydrographic Office
> 
> Tel: +44 (0) 1823 337900 ext 3798 
> 
> www.ukho.gov.uk
> 
> The United Kingdom Hydrographic Office
> 
> P please consider the environment before printing this email 
> 
> 
> > -----Original Message-----
> > From: Frank Warmerdam [mailto:warmerdam at pobox.com]
> > Sent: 17 March 2009 14:10
> > To: Russell Ron
> > Cc: geotiff at lists.maptools.org
> > Subject: Re: [Geotiff] :Mercator_2sp
> > 
> > Russell Ron wrote:
> > > Good Morning,
> > >
> > > Can anyone give any guidance as to the keys that should be used when
> > specifying the Mercator_2sp projection? What we used to do, and was
> > apparently accepted by ArcGis 9.2 no longer works with ArcGis 9.3. It
> > seems impossible to satisfy all software!
> > >
> > > My current 'best attempt' is (for example)
> > >
> > >       ProjCoordTransGeoKey (Short,1): CT_Mercator
> > >       ProjLinearUnitsGeoKey (Short,1): Linear_Meter
> > >       ProjNatOriginLongGeoKey (Double,1): xxxx
> > >       ProjNatOriginLatGeoKey (Double,1): yyyy
> > >       ProjFalseEastingGeoKey (Double,1): 0
> > >       ProjFalseNorthingGeoKey (Double,1): 0
> > >       ProjScaleAtNatOriginGeoKey (Double,1): 1
> > >       ProjStdParallel1GeoKey (Double,1): yyyy
> > >
> > > Where yyyy is what I would call 'Latitude of true scale'.
> > >
> > > This does not seem a true definition of Mercator where I think the
> > Latitude origin is always the equator!
> > >
> > > However these keys seem to do what we want with most software that
> we
> > use (but not GDAL!)
> > 
> > Ron,
> > 
> > There is only one Mercator formulation in GDAL (and in the libgeotiff
> > "normalize" code), and it assumes it is provided a scale at the origin
> > which is normally on the equator.
> > 
> > If you have a standard parallel at which the scale is 1, I guess it is
> > expected that you will somehow use it to compute the scale at the
> origin
> > and provide that instead.
> > 
> > The GDAL/libgeotiff handling of Mercator is pretty much defined by
> > 
> >    http://www.remotesensing.org/geotiff/proj_list/mercator_1sp.html
> > 
> > I must confess I don't know a good way of computing the scale at the
> > equator if given a latitude of true scale.  I suppose you could
> establish
> > two points at that latitude that are truly one meter apart (using some
> > non-mercator projection with this as a latitude of true scale) and
> then
> > see how far those points are apart in mercator to establish the
> scaling
> > needed to return it to a distance of one meter in mercator.
> > 
> > I would be open to adding proper support for Mercator_2SP if someone
> > can provide me with some guidance.  It is annoying that there is only
> > one CT_Mercator in libgeotiff, so it is going to be very messy to
> > normalize this projection in libgeotiff into a single set of
> parameters.
> > 
> > A ticket would be helpful to track this.
> > 
> > Best regards,
> > --
> >
> ---------------------------------------+--------------------------------
> --
> > ----
> > I set the clouds in motion - turn up   | Frank Warmerdam,
> > warmerdam at pobox.com
> > light and sound - activate the windows | http://pobox.com/~warmerdam
> > and watch the world go round - Rush    | Geospatial Programmer for
> Rent
> 
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