[Proj] Re: Discovery: libproj4 stmerc = French Gauss-Laborde projection

[Martin Vermeer]

On Wed, 2006-06-14 at 13:50 -0400, strebe at aol.com wrote:
> Hm. I didn't know about that web page. Obviously it's wrong -- for some 
> reason "p" appears in several different roles. I tend to think that's 
> an error in conversion to a web page. (I see that the entire blurb is a 
> single graphic, not HTML mark-up.) Certainly he's been pedantic and 
> precise in all his communications with me.
> 
> The p/2 exponent should read (e/2), where e is the eccentricity.

Yes, I agree.

> Use some other variable (perhaps p') in place of p in "Then, the 
> complex variable tan (p/2) can be obtained..." and "...yields the 
> argument p..."


Actually the argument p is simply the (ellipsoidal) co-latitude 
90d - phi.

The common expression in u and v corresponds to exp(psi), where psi is
the _isometric latitude_, i.e., essentially the "northing" in a
traditional (non-transverse) Mercator map plane.

Isometric latitude and longitude (psi, lambda) together as (x,y)
co-ordinates in a plane define a conformal mapping from the curved
Earth's surface. Using (psi, lambda) directly as rectangular
co-ordinates produces classical Mercator. Using

u + iv = exp(psi + i * lambda)

i.e., polar co-ordinates, produces the stereographic projection. This is
very much what Dr Wallis's formula looks like. Apparently for him it is
only a trick leading somewhere... but then I also get lost.

Regards Martin V

PS you may want to look at 

http://users.tkk.fi/~mvermeer/geom.pdf

pp 99-100 and around p. 90. Sorry it's in Fenno-ugrian formulese...


> Regards,
> -- daan Strebe
> 
> 
> -----Original Message-----
> From: Gerald I. Evenden <gerald.evenden at verizon.net>
> To: PROJ.4 and general Projections Discussions <proj at lists.maptools.org>
> Sent: Wed, 14 Jun 2006 11:42:40 -0400
> Subject:  Re: [Proj] Re: Discovery: libproj4 stmerc = French 
> Gauss-Laborde   projection
> 
>    On Wednesday 14 June 2006 1:12 am, Strebe at aol.com wrote:
> > You might contact Dr. David E. Wallis. He devised a much simpler 
> method
> > than Dozier's. I've implemented it for the full-ellipsoid. You can 
> see a
> > plot of an earth-like ellipsoid here:
> >
> > 
> http://mapthematics.com/Projection%20Images/Cylindrical/Transverse%20Merc
> at
> >or. GIF
> >
> > The method works for arbitrary eccentricities. Contact me privately if
> > you're interested. Since it is Dr. Wallis's invention, I'll put you in
> > contact with him.
> 
> Dr. Wells has a web page relating to the projection:
> 
> http://www.wallisphd.com/mercator.htm
> 
> that a Google search on his name will return.  Found this site several 
> years
> ago during a previous discussion about tmerc.  To me, the web page 
> appears
> unchanged and the "Publication Pending" notice at the top is certainly 
> taking
> a long time.
> 
> I should post him a letter for further information and follow up with a 
> phone
> call if no response.
> 
> The description of the equation present does not make much sense unless 
> what
> looks like p in the tan term is not the p described as colatitude.  
> Again,
> the first line says p,lambda is the colatitude and longitude yet the
> description following the formula talks about a p for the Elliptic 
> Integral
> of the second kind.
> 
> I must be missing something.
> 
> --
> Jerry and the low-riders: Daisy Mae and Joshua
> "Cogito cogito ergo cogito sum"
>    Ambrose Bierce, The Devil's Dictionary
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