[OSRS-PROJ] Re: Concerning calumny and the ellipsoidal transverse Mercator

[Strebe at aol.com]

Gerald I. Evenden <gerald.evenden at verizon.net> writes:

   I wrote:
> > Because the finite nature of the ellipsoidal transverse Mercator is so
> > rarely known, and because no numeric solutions have ever been
> > published, and because there is no geodetic need for such a
> > projection, it is entirely likely that I have produced the only images
> > of the projection ever made. I would be happy to make some available
> > if anyone is interested.
> 
> It is difficult for me to refrain from becoming a bit sarcastic here
> as your story sounds like a tabloid exposure.  I will remain a
> sceptic until I see peer review publication.
> 
So, I offered to supply the mathematics of the scenario, which is the final 
authority. However, you prefer to see an annotation in a peer-reviewed journal. 
Presumably that is because you do not feel qualified to analyze the 
mathematics. If that is so then it seems odd that you feel qualified to dispense 
skepticism, not to mention ridicule.

Here is one reference; I imagine there are more, probably in Lee's and 
Thompson's papers:

"The transverse Mercator projection is one of the most extensively used in 
large scale topographic mapping. Closed equations of chiefly academic  interest 
are given here, rearranged from Lee's and Thompson's work with the Gauss-Kr
üger ellipsoidal adaptation of Lambert's original work. In this version, the map 
is conformal everywhere, and the central meridian is standard. The entire map 
is finite, unlike the spherical version which extends to infinity."

-- J.P. Snyder, "Calculating Map Projections for the Ellipsoid", The American 
Cartographer, Vol. 6, No. 1, April 1979.


> As for conformity, its application is limited to large-scale
> cadastral mapping.  Conformity is a concept which only
> applies to the infinitesimal region about a point.  At a distance
> distortion is quickly apparent and eventually becomes extreme.
> Conformal projection for global presentations is most useful to
> demonstrate the limitation of conformal projections.
> 
Not so. Conformal maps of any extent are useful for showing accurate shapes 
over short distances. The shapes of (for example) small islands, short 
coastline segments, or provincial boundaries are correct on any conformal map. That is 
a valuable property. It is also true that local directions are correct once 
north has been established. I encourage you to loosen up your thinking a bit. 
Rigidity is not rigor.

> As for the Peter's projection (a perverse use of the well known
> cylindrical equal area) it has been severely criticized by well
> know cartographers.
> 
Peters made all sorts of ridiculous claims concerning "his" projection. On 
the other hand, cylindrical equal-area projections do have reasonable, if 
limited, uses. For instance, if you need a single, basic projection whose central 
meridian must be able to move freely without changing the shapes of mapped 
objects, then you are restricted to cylindrical projections. You yourself recommend 
equal-area projections; hence Peters must be useful. Yes, that's a limited 
use, but any small-scale projection is limited in use.

> In some
> cases it would be very difficult to provide an analytic function
> defining the projection boundary and the nature of this function
> will mathematically.  Even if the function is known, the determination
> of the intersect with the limiting function and the vector is just
> about as complicated as determining the intersection by using the
> projection itself.
> 
As I indicated in my original post, it is not necessary to provide an 
analytic function defining the projection boundary. It is only necessary to supply a 
parametric function that provides spherical coordinates defining boundary 
segments. Yes; it's a bit of work, but it's also impossible to draw boundaries 
without it. If that is not PROJ's purview, then fine, but you cannot dismiss the 
need for such facility amongst perfectly reasonable clients of software 
packages such as PROJ.

> Lastly, like the cadastral people supply their addenda to meet their
> need, the datum conversion group add their addenda, then why shouldn't
> the graphic types do the same.
> 
Because the job of describing the outer boundary is that of the projection's, 
not the client's. It's the projection which knows, or ought to know, its own 
boundary. If the client must supply the boundary definition for any arbitrary 
projection then the client might as well just implement the projection 
transformations as well. The two are not separable. If your position is that PROJ is 
not for graphical clients then your position seems tenable to me; otherwise it 
does not.

My intent is not to criticize PROJ. My intent is to discuss matters relevant 
to those who use   it. A particular graphical user has run into a problem, one 
he probably considered to be minor. Far from minor, the problem is 
fundamental to the graphical display of map projections. It's not to be taken lightly. 
In any case, I am finished discussing these topics with Mr. Evenden publicly. 
If anyone needs further information on these topics feel free to contact me 
directly or on the list if it merits public attention.

Regards,

daan Strebe
Geocart author
http://www.mapthematics.com/


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