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Gerald I. Evenden <gerald.evenden@verizon.net> writes:<BR>
<BR>
I wrote:<BR>
<BLOCKQUOTE CITE STYLE="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE"></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">> Because the finite nature of the ellipsoidal transverse Mercator is so<BR>
> rarely known, and because no numeric solutions have ever been<BR>
> published, and because there is no geodetic need for such a<BR>
> projection, it is entirely likely that I have produced the only images<BR>
> of the projection ever made. I would be happy to make some available<BR>
> if anyone is interested.<BR>
</BLOCKQUOTE></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
<BLOCKQUOTE CITE STYLE="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE"></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">It is difficult for me to refrain from becoming a bit sarcastic here<BR>
as your story sounds like a tabloid exposure. I will remain a<BR>
sceptic until I see peer review publication.<BR>
</BLOCKQUOTE></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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.<BR>
<BR>
Here is one reference; I imagine there are more, probably in Lee's and Thompson's papers:<BR>
<BR>
"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</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">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."<BR>
<BR>
-- J.P. Snyder, "Calculating Map Projections for the Ellipsoid", The American Cartographer, Vol. 6, No. 1, April 1979.<BR>
</FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
<BLOCKQUOTE CITE STYLE="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE"></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">As for conformity, its application is limited to large-scale<BR>
cadastral mapping. Conformity is a concept which only<BR>
applies to the infinitesimal region about a point. At a distance<BR>
distortion is quickly apparent and eventually becomes extreme.<BR>
Conformal projection for global presentations is most useful to<BR>
demonstrate the limitation of conformal projections.<BR>
</BLOCKQUOTE></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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.<BR>
<BR>
<BLOCKQUOTE CITE STYLE="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE"></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">As for the Peter's projection (a perverse use of the well known<BR>
cylindrical equal area) it has been severely criticized by well<BR>
know cartographers.<BR>
</BLOCKQUOTE></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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.<BR>
<BR>
<BLOCKQUOTE CITE STYLE="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE"></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">In some<BR>
cases it would be very difficult to provide an analytic function<BR>
defining the projection boundary and the nature of this function<BR>
will mathematically. Even if the function is known, the determination<BR>
of the intersect with the limiting function and the vector is just<BR>
about as complicated as determining the intersection by using the<BR>
projection itself.<BR>
</BLOCKQUOTE></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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.<BR>
<BR>
<BLOCKQUOTE CITE STYLE="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px" TYPE="CITE"></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2">Lastly, like the cadastral people supply their addenda to meet their<BR>
need, the datum conversion group add their addenda, then why shouldn't<BR>
the graphic types do the same.<BR>
</BLOCKQUOTE></FONT><FONT COLOR="#000000" FACE="Palatino" FAMILY="SERIF" SIZE="2"><BR>
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.<BR>
<BR>
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.<BR>
<BR>
Regards,<BR>
<BR>
daan Strebe<BR>
Geocart author<BR>
http://www.mapthematics.com/<BR>
<BR>
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