<html><body name="Mail Message Editor"><div><br></div><div>Mikael:</div><div><br></div><div>I think that sorts it out well, and I agree that "center" is harder to pinpoint, as well as having less precedence in the literature, and therefore less desirable when latitude of origin and latitude of center coincide.</div><div><br></div><div>I realized after I sent my last response that I had not addressed your original inquiry, which is the category term for what you have proposed "cosmetic latitudes". I have never seen such a term in the literature, so I don't think you would be causing trouble by inventing your own term. If I were to do it (which I might!), I would use something like "positioning latitude", in the sense that the latitude contributes to the graticule's position on the Cartesian plane, but nothing else.</div><div><br></div><div><span class="Apple-style-span" style="font-family: Arial; ">>Disclaimer: these are not official opinions of Carmenta AB. But I can work on it.</span><br></div><div><span class="Apple-style-span" style="font-family: Arial;"><br></span></div><div><span class="Apple-style-span" style="font-family: Arial;">(laugh)</span></div><div><span class="Apple-style-span" style="font-family: Arial;"><br></span></div>Regards,<div>— daan Strebe</div><div><br></div><div><br>On Mar 25, 2009, at 1:55:52 AM, "Mikael Rittri" <Mikael.Rittri@carmenta.com> wrote:<br><blockquote style="padding-left: 5px; margin-left: 5px; border-left-width: 2px; border-left-style: solid; border-left-color: blue; color: blue; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -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; "><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 class="Apple-converted-space"> </span></span>"Latitude of center" seems even more problematic for the same reason:</div><div dir="ltr" align="left"><span class="840023108-25032009">><span class="Apple-converted-space"> </span></span>unless the projection is vertically symmetrical, the "latitude of center"</div><div dir="ltr" align="left"><span class="840023108-25032009">><span class="Apple-converted-space"> </span></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. <span class="Apple-converted-space"> </span></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<span class="Apple-converted-space"> </span></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<span class="Apple-converted-space"> </span></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<span class="Apple-converted-space"> </span></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 class="Apple-converted-space"> </span></span>Hence, if it is the latitude of the projection's "center", then should we not call</div><div><span class="840023108-25032009">><span class="Apple-converted-space"> </span></span>it the latitude of center (or central latitude)? (In point of fact, since Hotine is</div><div><span class="840023108-25032009">><span class="Apple-converted-space"> </span></span>infinite in extent there is no mathematical "center", but at least symmetry allows</div><div><span class="840023108-25032009">><span class="Apple-converted-space"> </span></span>a reasonable choice for a center.) If it is the latitude at the origin, then should</div><div><span class="840023108-25032009">><span class="Apple-converted-space"> </span></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<span class="Apple-converted-space"> </span></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><p><font size="2">--<br>Mikael Rittri<br>Carmenta AB<br>SWEDEN<br>www.carmenta.com</font></p><div></div></span><br class="Apple-interchange-newline"></blockquote><br><div><br></div></div><div class="aol_ad_footer" id="u4A737B6795C140208E3678E7CF336E86"></div></body></html>