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<pre style="font-size: 9pt;"><tt><tt>>The only context that I use the term "interruption" in discussing<br>
>cartographic projections are in cases like Goode's world maps or<br>
>"orange peal" charts often using the sinusoidal projection. Please<br>
>define what *you* mean by interruptions.<br>
</tt></tt></pre>
<div><font face="Arial, Helvetica, sans-serif">An interruption is any location where two points of infinitesimal separation on the globe are mapped to two points having finite separation on the plane. This happens somewhere on all projections. All along an interruption, the projection formulæ are no longer a function; they are multivalue.<br>
<br>
Regards,<br>
-- daan Strebe<br>
<br>
<br>
</font></div>
-----Original Message-----<br>
From: Gerald I. Evenden <geraldi.evenden@gmail.com><br>
To: strebe <strebe@aol.com><br>
Cc: proj@lists.maptools.org<br>
Sent: Thu, 28 Aug 2008 8:46 am<br>
Subject: Re: Global Gauss-Kruger and libproj4---the final story<br>
<br>
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<pre style="font-size: 9pt;"><tt>On Thursday 28 August 2008 12:37:36 am strebe wrote:<br>
> On Aug 27, 2008, at 5:32:33 PM, "Gerald I. Evenden"<br>
> <<a href="mailto:geraldi.evenden@gmail.com">geraldi.evenden@gmail.com</a>> wrote:<br>
><br>
> ________<br>
><br>
> Yes, you run into them every 10 to 20 years.<br>
><br>
> ________<br>
><br>
> No, I run into=2
0them commonly. Perhaps you run into them every ten or twenty<br>
> years.<br>
<br>
Perhaps you would like to present an example. <br>
______<br>
><br>
> No other projection has a requirement that the user needs to know an<br>
> arcane formula to manipulate graphical usage to interpret the results.<br>
> There is currently no means for libproj4 to return such information.<br>
><br>
> ________<br>
><br>
> I do not understand that utterance. The problem has nothing to with<br>
> "graphical usage", whatever that means. It has to do with the results of<br>
> the projection at a single point. Many world projections do not come with a<br>
> 90°N/S, 180° E/W natural boundary that the client software can treat as<br>
> some fixed convention, and all projections have interruptions. An<br>
> interruption automatically means the projection formulæ are not a function,<br>
> which renders this utterance invalid:<br>
<br>
The only context that I use the term "interruption" in discussing cartographic <br>
projections are in cases like Goode's world maps or "orange peal" charts <br>
often using the sinusoidal projection. Please define what *you* mean by <br>
interruptions.<br>
> ________<br>
><br>
> I am tired of repeating, libproj4 is *NOT* a graphic routine any more than <br>
> sine or tangent. In the case of making maps it is merely the process that <br>
> transforms information from one coordinate system to another!<br>
<br>
Amen!<br>
> ________<br>
><br>0A> Sine and tangent are functions. A projection is not.<br>
<br>
Let us stop here for a moment. From an online dictionary: "function (math) A <br>
quantity so connected with another quantity that if any alteration be made in <br>
the latter there will be a consequential alteration in the former." In this <br>
case lat,lon <=>x,y. Change lat,lon and you change x,y and vice versa. The <br>
mechanism that determines the functional relationship is the cartographic <br>
transformation---a procedure that defines the relationship between two <br>
coordinate systems. In the case of computing Z=f(K), f is a function.<br>
<br>
> It is generating <br>
> formulæ that are (usually) a function over the range of the map except at<br>
> boundaries, where they are multivalued. You have chosen, for your own<br>
> convenience, to ignore the the possible multiple results of the projecting<br>
> formulæ. That is fine, but it does not make your rant correct; it only<br>
> makes your decision convenient for you. In any case, if you're tired of<br>
> repeating yourself, then quit repeating yourself. I suspect everyone else<br>
> is tired of it, too — particularly because it's a straw man.<br>
> Would you like a list of world projections whose boundaries differ from the<br>
> boundaries of finite cylindric projections?<br>
<br>
I am aware of some, especially those I call cartoon projections (I do not mean <br>
that in a pejorative way) like those that plot the world on a cube o
r some <br>
other solid or ones with very odd boundary system. These are usually very <br>
interrupted projections requiring difficult geographic clipping functions <br>
that (other than longitude range reduction) is *not* a function of libproj4. <br>
We have already covered the +-180 problem and flat pole maps. Let's see, <br>
cylindricals, pseudocylindricals, conics, globulars, ... . Even general <br>
oblique projections are no problem other than odd boundaries. I managed to <br>
make plots of the above with libproj4 as it now stands. See manual.<br>
<br>
Please list a few provided there is a url to a picture of the listed <br>
projection.<br>
<br>
> And if there are many <br>
> projections with other kinds of boundaries, would you explain again how it<br>
> is that the ellipsoidal transverse Mercator is somehow unique in that<br>
> regard?<br>
><br>
> I don't care if you don't implement a global ellipsoidal transverse<br>
> Mercator. If you don't want to implement it, then don't implement it.<br>
> Surely no one can begrudge that — no one's paying you to, as far as I know.<br>
> I just don't see the point of rationalizing that decision with sophistry,<br>
> or why you'd expect your audience to swallow the rationalizations. I<br>
> suggest just stating that you're not convinced of the value of the work, or<br>
> that you hate the ellipsoidal transverse Mercator, or that you're tired,<br>
> and be done with it. Which reminds me: once again, I am tired of the
se<br>
> sorts of conversations, and am done with this one.<br>
<br>
Oh gee. But this is so much fun! Please don't go.<br>
<br>
> Regards,<br>
> -- daan Strebe<br>
...<br>
-- <br>
The whole religious complexion of the modern world is due<br>
to the absence from Jerusalem of a lunatic asylum.<br>
-- Havelock Ellis (1859-1939) British psychologist<br>
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