[Proj] Re: Linear projections reply
mikeo2106 at msn.com
Mon Jun 30 19:03:34 EDT 2008
> Assuming you had some reason for posting your work, I briefly noted how your work fits in with standard definitions and mathematical formulations.
Yes, and I appreciated your comments. I meant no criticism or complaint about them.
I later found that I could display the mathematical part of your posting if I read the posting from the archives, instead of from the batch-digest.
> Whether it "goes without saying" that there is no limit to the number of "linear" projections depends upon the reader. Perhaps it goes without saying for you.
As you said, pseudocylindrical projections are linear. Clearly, no matter how such a map's rightmost and leftmost meridians are curved, each parallel can be uniformly divided, giving the X position a linear relationship to longitude. And the parallels can be evenly spaced. No matter how the leftmost and rightmost meridians are curved. So it's at least intuitively clear that there can be infinitely many linear projections, because there are infinitely many ways that the leftmost and rightmost meridians can be curved. I don't call that a mathematical proof, but just an intuitive justification for what I said.
> In general I do not see the benefit of explaining that you already know something unless someone clearly implies that you do not.
Ok, neither do I.
Alright, I was a bit defensive, reading into your comment an implication that I believed that I had listed all the possible linear projections. To tell the truth, I perceived, right after sending that e-mail, that my reply was unnecessarily defensive.
Quite possibly all or nearly all of the facts that I've stated in my postings here have been things that you and other list members already know. (but maybe someone browsing the list at some future time won't know one of those facts). So I would certainly not complain or criticize if someone said something that I already know. I said "It goes without saying..." only to assert that I hadn't meant otherwise.
It was not my intention to cross the politeness-line.
> Cylindric projections are a specialization of pseudocylindric. Whether it is incorrect to call a cylindric projection "pseudocylindric" is something best left to > those of uselessly pedantic temperment.
Oh come on now, you're saying that no one should ever say anything about the merits of a term. No one can deny that saying that a cylindrical projection is "pseudocylindrical" has something of a self-contradictory sound. How about generalized-cylindrical, or cylindricalish, or something like that? Maybe some would say that "generalized-cylindrical" is too long, and that "cylindricalish" is too colloquial-sounding. But the -ish, -isch, -isk, -ic suffix has a lot of historical validity. Maybe it acquired its colloquial popularity because of its brevity, but that shouldn't deny us the use of that brevity.
More information about the Proj