daan:
The reason why I didn’t immediately stop saying “backwards formulas” was because, in spite of what you said, I believed it to be a valid word for “inverse formulas”. That was because, as I said, someone at the proj.4 mailing-list once asked me for the forward and backwards formulas of a projection that I’d suggested.
It isn’t unreasonable, or heinous, to assume that a term used by one of the cartographers at the proj.4 forum was a valid term.
But, my own Internet search (before you described your Internet search) found that “inverse formulas” is more often used (I, too, found it in that manual, by the author of Flattening The Earth.).
Also, I noticed how terribly “backwards formulas” was upsetting you.
And so, note that, in my previous post in this discussion, I didn’t use the term “backwards formulas”, except in quotes, referring to the term itself, rather than to inverse formulas.
Get over it, daan.
I’d said:
Earlier, when I used the term "shear" (which I now avoid unless someone else uses it), you said that all flat maps have it, You defined in a way that's obviously different from the way that everyone else uses it.
Your answer:
« laugh » Wow. No, it only differs from how •you• use it. It would be amusing how far into the ludicrous you are willing to go, if it weren’t so tragic. I never said all flat maps have shear; you fabricated that. Conformal maps have no shear, which I pointed out at the time
Suppose that a globe’s surface, made from an easily deformable material, were cut along one of its meridians (from pole to pole). I’ll call that that globe’s surface a “cut globe”. You said, at that time, that a flat map has shear if deforming a cut globe surface into that flat map requires shearing of the material of that globe surface.
Now you say that you said that conformal maps are an exception to that statement that all maps have "shear", as you defined it, quoted directly above.
What I can assure you of is that you defined map-shear as the need for shearing of a cut-globe’s surface, in order to deform it into a map.
When I use “shear” with that meaning, I’ll put it in quotes, and will say “shear” by your definition.
Though I don’t remember you saying that, by your definition, conformal maps don’t have “shear”, of course I can’t say absolutely for sure that you didn’t say it.
But is it true that conformal maps don’t have “shear”, by your definition that I quoted above?
Vertical (north-south) deformation of a cylindrical projection, uniform along a parallel, doesn’t shear any part of the map’s surface. You could deform a Cylindrical-Equidistant map into a Mercator map, or vice-versa, without any shear of the map’s surface.
That means that, if you could deform a cut-globe surface into a Mercator projection without shear, and then deform that into a Cylindrical-Equidistant, without shear, you’d thereby deform the cut-globe into Cylindrical-Equidistant without shear.
So, if you could deform a cut-globe into a Mercator map, without shear, then you could deform a cut-globe into a Cylindrical-Equidistant map without shear..
So, if that’s so, can you say that conformal maps don’ t have “shear”, as you defined it, and that Cylindrical-Equidistant maps do?
If all maps have “shear”, then “shear” wouldn’t be a very useful attribute for distinguishing among maps.
If all non-conformal maps have “shear”, and all conformal maps don’t have “shear”, then “shear” is just another word for non-conformality.
I couldn’t find a definition of shear, as a map-distorition, on the Internet. You have an Internet article in which you define shear as a bending or twisting. That didn’t seem real helpful.
So you’re quite right: I can’t say what the word “shear” really means, as a map-distortion.
That’s why I instead speak of non-perpendicularity of meridian-parallel intersections. (without claiming that it’s what the word “shear” refers to).
At first I wanted to call that “slant”, because that name is a lot shorter. But you made an angry issue about my coining a term, and so now I speak of non-perpendicularity of meridian-parallel intersections.
But I emphasize that I don't claim that that is the cartographic definition of shear-distortion.
As I said, I avoid the word “shear”, unless someone else uses it.
I’m not going to hazard a guess about what “shear” really means, as a map distortion. Well, ok, I will:
If I had to guess, I’d say that a map is sheared if it isn’t conformal, and can’t be deformed into a conformal map without shear. By that definition, Sinusoidal, Winkel-Tripel, and the pseudocylindricals are sheared, but cylindrical maps are not sheared.
That seems best to fit how I’ve heard the term “shear” used, but I make no claim that that is what “shear” means. I make no claim to know what “shear” officially means, when it denotes a map distortion.
You invented non-existent statements from cartographers
So you say, and your support for that statement follows, immediately below:
(with some hand-waving about Deetz & Adams and Raisz)
You’re misusing the term “handwaving”. “Handwaving” doesn’t mean “quoting”.
about how the term is used
Presumably “the term” refers to “shear”.
No, I didn’t quote Deetz and Adams, or Raisz about the definition of “shear”, or how it’s used.
What I said was that some well-known cartographer(s) said, in a book of theirs, that, of all the equal-area world maps, the one with the least angular-distortion is the Cylindrical-Equal-Area. I said that the author(s) might have been Adams and Deetz, or Raisz.
, and failed to come up with a single reference (see my complaint about never doing due diligence and relying on hazy memory).
As I said at the time, it was a long time ago. I’d say it was around 1971 to 1975. And yes, for some reason I neglected to write down the names of the author(s) :^)
Meanwhile I explained in detail how and why your notion of shear was broken. You simply ignored that explanation, and evidently suppressed the memory of it, or something.
Not at all. You said that a map is “sheared” if a cut globe can’t be deformed into that map without shearing.
That was your definition of “shear”.
I don’t claim to know the official correct cartographic definition of “shear distortion”. That’s why I avoid using that term.
The episode about shear powerfully illustrates my points for me.
Well, it powerfully illustrates
something.
« laugh » Wow. Somehow you have forgotten that you also requested that I make images for your PF8.32 projection, twice
Oh yes. What could be more heinous :^)
Did I ask twice? If you’d answered “No” the first time, then I wouldn’t have asked a 2nd time (quite a bit later, it seems to me). I assumed that you didn’t notice the first request.
The request won't be repeated, and the ease or difficulty for you, of making that map, won't be mentioned by me either.
Get over it.
, as well as speculated that I ought to be able to easily implement your projections in Geocart and thereby fulfill your request for images.
Incorrect. When I said that you said that you can easily make a map from its formula in Geocart, I said that in reference to someone else’s statement that they couldn’t find PF8.32 in Geocart.
Maybe it was incorrect to say that you couldn’t easily make PF8.32 from its formula, in Geocart, but maybe it wasn’t incorrect.
You recently said that, in Geocart, you sometimes image a map by the straightforward direct use of its inverse formulas, in the manner that I described in this thread’s initial post. PF8.32 is pseudocylindrical, and so it’s at least possible that you might be able to image Equal-Area PF8.32 in that manner.
It doesn’t matter. If it were easy, you still wouldn’t do it. And what you do or don’t do is entirely your business.
Obviously I won’t make the request, or mention anything about it, again.
But it wasn’t in connection with my own request that I said that you could easily accomplish that.
daan continues:
Here we have an outright lie:
daan seems to be espousing an extreme relativism that would ban expression of preferences, and reasons for them.
Of course this is false; otherwise I would have chided other contributors for their expression of preferences and the reasons they give for them. What really happens is that you cyclically get so enthusiastic over your labored, selective arguments that you start telling people that they ought to prefer what you prefer. This happened again just recently, which at the time I gave specific quotes for, but of course you want to make others think I’m just being mean and so you’ve lied about my actual criticisms.
This issue of daan’s, about advocacy, can only be adequately answered in a separate posting. Let’s dispose of that issue once and for all. That will follow this posting, tomorrow, or maybe later today.
daan continues:
Yet another lie:
...that characteristic contrarianism and the several ways it contribute to your mode of discourse, are what encourage me to respond in vexed tones.
I
In at least some instances, you're using "contrarianism" to mean "not agreeing with daan's positions regarding comparisons of aesthetics or merit.
You, dear reader, can perform a search on this site as well as I can. You will discover that I have used the term “contrarian” in exactly two situations:
•Ossipoff rejects “inverse formulas” in favor of his own contrivance “backward formulas”, giving only the most cursory excuse and refusing to adopt real words for existing things.
•The text of a talk I gave that has nothing to do with Ossipoff or anyone disagreeing with me.
Stop lying, Ossipoff.
Well, that’s good, if now daan is only saying that I was contratian about the “backwards formulas” term.
However, daan referred to “[my] characteristic contrarianism”, suggesting that he meant it in a more general way.
And, daan, you say that that characteristic contrarianism’s contribution to my mode of discourse is the whole reason for your vexed tone. So it would seem that you weren’t only referring, by that term, to “backwards formulas.”
No matter.
Michael Ossipoff