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<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>daan
wrote:</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT
face=Arial></FONT></SPAN> </DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009>> </SPAN>"Latitude of
center" seems even more problematic for the same reason:</DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009>> </SPAN>unless the
projection is vertically symmetrical, the "latitude of center" </DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009>> </SPAN>generally is
not at the center of the projection. </DIV>
<DIV dir=ltr align=left><FONT face=Arial></FONT> </DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>That's
true. If nothing else, the "latitude of center" can be far
</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>outside
the area of interest. </FONT></SPAN><SPAN class=840023108-25032009><FONT
face=Arial>(For example, the traditional </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>Swedish
Grid is based on a Transverse Mercator with </FONT></SPAN><SPAN
class=840023108-25032009><FONT face=Arial>origin </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>at the
equator, far from Sweden. I admit that "center" is not a
</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>very
good term </FONT></SPAN><SPAN class=840023108-25032009><FONT face=Arial>for
this point. I could argue that this projection </FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>in
theory </FONT></SPAN><SPAN class=840023108-25032009><FONT face=Arial>extends to
Antarctica, but on the other hand its associated</FONT></SPAN></DIV>
<DIV dir=ltr align=left><SPAN class=840023108-25032009><FONT face=Arial>datum
RT90 is not defined </FONT></SPAN><SPAN class=840023108-25032009><FONT
face=Arial>outside Sweden.) </FONT></SPAN></DIV>
<DIV><FONT face=Arial></FONT> </DIV>
<DIV>
<DIV><SPAN class=840023108-25032009>> </SPAN>Hence, if it is the latitude of
the projection's "center", then should we not call</DIV>
<DIV><SPAN class=840023108-25032009>> </SPAN>it the latitude of center (or
central latitude)? (In point of fact, since Hotine is </DIV>
<DIV><SPAN class=840023108-25032009>> </SPAN>infinite in extent there is no
mathematical "center", but at least symmetry allows</DIV>
<DIV><SPAN class=840023108-25032009>> </SPAN>a reasonable choice for a
center.) If it is the latitude at the origin, then should</DIV>
<DIV><SPAN class=840023108-25032009>> </SPAN>we not call it the latitude of
origin?</DIV>
<DIV> </DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>Well, that makes
sense. It could be both, of course, but I suppose
</FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>you prefer the term
"latitude of origin" in that case. It should be easy</FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>to </FONT></SPAN><SPAN
class=840023108-25032009><FONT face=Arial>determine whether a point
projects to the Cartesian origin. It seems </FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>harder to define
"center" in a formal way, so we could resort to the </FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>"center" term only when
necessary. If so, I know only two or three
projections</FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>where "center" would be
necessary: Krovak, Hotine Oblique Mercator (with</FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>origin at the natural
origin near the equator), and possibly EPSG's </FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>Polar Stereographic Variant
C, depending on which parameters </FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>that are used to define
it. Do you know any more examples? </FONT></SPAN></DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial></FONT></SPAN> </DIV>
<DIV><SPAN class=840023108-25032009><FONT face=Arial>Disclaimer: these are not
official opinions of Carmenta AB. But I can work on it.
</FONT></SPAN></DIV></DIV><!-- Converted from text/plain format -->
<P><FONT size=2>--<BR>Mikael Rittri<BR>Carmenta
AB<BR>SWEDEN<BR>www.carmenta.com</FONT> </P>
<DIV>
<HR tabIndex=-1>
<FONT face=Tahoma size=2><B>From:</B> proj-bounces@lists.maptools.org
[mailto:proj-bounces@lists.maptools.org] <B>On Behalf Of
</B>strebe<BR><B>Sent:</B> den 25 mars 2009 02:41<BR><B>To:</B> PROJ.4 and
general Projections Discussions<BR><B>Subject:</B> Re: [Proj] Cosmetic
latitudes...<BR></FONT><BR></DIV>
<DIV></DIV>
<DIV><BR>On Mar 24, 2009, at 2:19:09 AM, "Mikael Rittri"
<Mikael.Rittri@carmenta.com> wrote:<SPAN class=Apple-style-span
style="FONT-SIZE: 11px; FONT-FAMILY: -webkit-monospace; WHITE-SPACE: pre">
</SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre"><SPAN
class=Apple-style-span
style="BACKGROUND-COLOR: transparent"><BR></SPAN></SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre"><SPAN
class=Apple-style-span style="BACKGROUND-COLOR: transparent">>I just can't
see the logic.</SPAN></SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre"><BR></SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre">It is a mess, isn't
it?</SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre"><SPAN
class=Apple-style-span
style="BACKGROUND-COLOR: transparent"><BR></SPAN></SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre"><SPAN
class=Apple-style-span style="BACKGROUND-COLOR: transparent">>And aren't
there plenty of WKT flavours with different parameter names?</SPAN></SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre"><BR></SPAN></DIV>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre">Yes, presumably any
projection description is technically free to name its parameters whatever it
likes.</SPAN></DIV>
<DIV><PRE></PRE>
<DIV><SPAN class=Apple-style-span style="WHITE-SPACE: pre"><SPAN
class=Apple-style-span style="WHITE-SPACE: normal"><PRE><SPAN class=Apple-style-span style="FONT-FAMILY: Helvetica"><SPAN class=Apple-style-span style="BACKGROUND-COLOR: transparent">>If one prefers a single name for all versions of lat_0, then "latitude_of_origin"
>is not a good name, since it would be misleading for the Hotine Oblique Mercator
>(the origin is near the equator, not on the central latitude), and for the Krovak
>(the origin is at the oblique cone apex near Finland, not on the central latitude).
</SPAN></SPAN></PRE>
<DIV>If the latitude of origin and the central meridian do not, in fact, project
to the Cartesian origin, then the term really ought not apply. It is unfortunate
that Snyder has used the same symbology (Φ₀) to denote the latitude of the map
center in the Hotine as he has elsewhere to denote the latitude of origin. But
that is a conflation of symbology, not terminology. His annotations for that
projection call Φ₀ the latitude at the center of the map. I can't
speak about the Krovac, since I have never studied it.</DIV>
<DIV><BR></DIV>
<DIV>"Latitude of center" seems even more problematic for the same reason:
unless the projection is vertically symmetrical, the "latitude of center"
generally is not at the center of the projection. There are two different
principles at play here: a latitude of origin and a latitude of center. They
should be distinguished by terminology. It is unfortunate that we must live with
legacy conflations and confusions of terminology and symbology, but I do not
think the situation would be helped by simply adopting a single term for
distinct things.</DIV>
<DIV><BR></DIV>
<DIV>Hence, if it is the latitude of the projection's "center", then
should we not call it the latitude of center (or central latitude)? (In point of
fact, since Hotine is infinite in extent there is no mathematical "center", but
at least symmetry allows a reasonable choice for a center.) If it is the
latitude at the origin, then should we not call it the latitude of origin?</DIV>
<DIV><SPAN class=Apple-style-span
style="WHITE-SPACE: pre"><BR></SPAN></DIV></SPAN></SPAN></DIV></DIV>
<DIV><SPAN class=Apple-style-span
style="BACKGROUND-COLOR: transparent">Regards,</SPAN></DIV>
<DIV>— daan Strebe</DIV>
<DIV><BR></DIV><BR>On Mar 24, 2009, at 2:19:09 AM, "Mikael Rittri"
<Mikael.Rittri@carmenta.com> wrote:<BR>
<BLOCKQUOTE
style="PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: blue 2px solid; COLOR: blue"><SPAN
class=Apple-style-span
style="WORD-SPACING: 0px; FONT: 11px -webkit-monospace; TEXT-TRANSFORM: none; COLOR: rgb(0,0,0); TEXT-INDENT: 0px; WHITE-SPACE: normal; LETTER-SPACING: normal; BORDER-COLLAPSE: separate; orphans: 2; widows: 2; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0"><PRE>> Mikael wrote:
>
> > [-- text deleted --]
> >
> > "Latitude of origin" sounds fine, but I am not too fond of using
> > many different names for what is called lat_0 in Proj.4. The
> > EPSG Guidance Note 7.2 has gone too far in this direction, I
think.
> > I like "central latitude" as the only name.
>
> Please note also that "Latitude of origin" is the name in the Well
Known Text
> format specification.
> E.g.,
>
> PARAMETER["latitude_of_origin",49],
>
> Regards,
> - daan Strebe
For some projections, yes. Perhaps for the majority. But for some
projections,
it is "latitude_of_center".
And some projections have "central_meridian", while others have
"longitude_of_center" instead.
I have tried to figure out the reasons why, by looking at the OGC WKT
names
at http://www.remotesensing.org/geotiff/proj_list , and first I thought
that
"central_meridian" is used if and only if the central meridian appears
as a straight vertical line. When the meridian is curved, it seems that
"longitude_of_center" is used instead, and the "center" suffix spills
over
and renames "latitude_of_origin" to "latitude_of_center", even when
there
is no particular reason that it should spill over.
However, things aren't that simple. The central meridian of Krovak
appears
as a straight vertical line, but it is called "longitude_of_center"
anyway.
And the central meridian of the New Zealand Map Grid is called
"central_meridian",
even though it appears as a curved line.
I just can't see the logic. And aren't there plenty of WKT flavours
with different
parameter names?
If one prefers a single name for all versions of lat_0, then
"latitude_of_origin"
is not a good name, since it would be misleading for the Hotine Oblique
Mercator
(the origin is near the equator, not on the central latitude), and for
the Krovak
(the origin is at the oblique cone apex near Finland, not on the central
latitude).
Regards,
--
Mikael Rittri
Carmenta AB
SWEDEN
www.carmenta.com</PRE></SPAN></BLOCKQUOTE><BR>
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