Use inverse formula directly, no rootfinding?

General discussion of map projections.
Atarimaster
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Re: Use backwards formula directly, no rootfinding?

Post by Atarimaster »

RogerOwens wrote:I meant to say what I meant clearly, completely and explicitly.
I didn’t mean to imply that you didn’t.
RogerOwens wrote: Well, I'll find out if/when I try it, if and when I have time to start that automated map-imaging project, something that would be completely unfamiliar and new to me, requiring a lot of time and work just to start in it.
I think that time would be much better spent by working yourself into the d3 scripts.
This way, the formula would at least be usable in other contexts than just your own image-generating process. If you want to avoid the problems with the root-finding thing, you might try FlexProjector, where generating own projections (based on existing ones) is a matter of dragging sliders and, maybe, entering a few numbers (which maybe are results of calculations you did on paper). It’d still be a lot of work, especially when you want to end up with a projections that’s equal-area.

And btw, since I now know that you’ve been talking of the inverse formula: Yes, d3 has them for each projection they support. But at least judging from the parts where I have taken a closer look, they don’t use them to generate the image.
RogerOwens
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Re: Use backwards formula directly, no rootfinding?

Post by RogerOwens »

Thanks for the suggestions, and especially for the map-images.

Well, if I start trying to deal with automated map-imaging, I'll probably just try it from scratch, even though that would be more difficult and time-consuming (and therefore less likely for feasibility and success). Then I'll find out, the hard way, exactly why the method that I described doesn't work. ...and then maybe try whatever more difficult method could work if done right (a big "if", for a beginner).

If it does turn out to require numerical root-finding, Bisection would be my first inclination, because it always converges at a rate that's useful enough if you don't need to accomplish too many thousands of solutions in a short amount of time. But if that map-imaging project requires sufficiently many thousands of root-finding solutions in a short time, then I realize that Bisection might be unfeasibly slow for the task.

So whether Bisection helps for that purpose depends on how many root-finding operations will be needed.

If Bisesction is prohibitively show for that job, then maybes I'd best find, copy, and use the popular, and elaborate, but presumably very fast, Brent method (which of course includes Bisection as a conditional fallback).

But that's getting way ahead of myself, at a time when I haven't even started trying to deal with automated map-imaging.

Thanks again for the map-images that you provided.

Michael Ossipoff
Last edited by RogerOwens on Wed Apr 19, 2017 10:35 am, edited 1 time in total.
daan
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Re: Use backwards formula directly, no rootfinding?

Post by daan »

RogerOwens wrote:But that eagerness to make a big issue about a term isn't new. As just one of several examples, in an earlier discussion, after I used the term "numerical methods", you used quotes ( " ") when you subsequently used the word, as if it, too, was incorrect.

So "backwards" formula isn't standard or most widely-used term for that meaning. Hardly an angry justifiably-contentious issue.
Stop twisting what is at issue. Your twisting is one of many reasons why engaging you is so vexing.

The issue is not that you misused a term. My first encounter with your coinage “backward formula” was simply one of confusion, and when I sorted out what you meant, I gave the proper term for what you meant without rancor or judgment. The same was true of your other inapt uses of terminology.

The immediate issue is your persistence in using a false term despite knowing it is false, for no reason anyone outside yourself would condone. You simply want to use it, despite that it contradicts the purpose of communication, which is to be understood. If you do not wish to be understood, then quit writing for others’ consumption.

Instead of learning something, which you seem highly resistant to, you:
  • ·Persist in your solipsistic blathering as if everyone else ought to adjust themselves to whatever your choices of meanings are for words, your choices of aesthetic preferences for map projections, your choices of significant traits for map projections, and your contrived terms for those traits;
    ·Wheedle people to do things for you;
    ·Fail to perform even the most rudimentary due diligence to confirm what you think or what words to use in order to convey what you think, but instead rely on contrivances, hazy recollections, and strained rhetorical arguments—using your own idiosyncratic terminology, to boot.
    ·Demonstrate little concern for or interest in what others who have earned their standing in the field have to say about any of these things, ranging from terminology, to the significance of traits, to the cognition of map projections.
Now, I’m sure psychologists have all sorts of things to say about robust contrarianism and the need to assert contrivances despite limited grasp of prior art. Not my domain, so I won’t elaborate, but at the larger scale, that characteristic contrarianism and the several ways it contribute to your mode of discourse, are what encourage me to respond in vexed tones.
In this instance, maybe it was anger about, and/or a desire for a noisy distraction from, the fact that, when he was going on about the great complicatedness of imaging a projection that lacks forward formulas, he’d neglected to mention the plain, straightforward direct use of the lat(y) and lon(x) formulas, that I described in the initial post that started this thread.
Yet another amusing example of ignorant and paranoid musings. Geocart uses this technique when appropriate, as you could infer if you’d bothered to have read my research papers.
I don't know why daan is so full of anger, or how he got to be like that.
Those who know daan, know that one of his passions is countering miseducation, willful ignorance, and quackery. Outside of that context, daan tends to be kind and helpful and has a robust sense of humor.

— daan
RogerOwens
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Re: Use backwards formula directly, no rootfinding?

Post by RogerOwens »

daan wrote: The issue is not that you misused a term. My first encounter with your coinage “backward formula” was simply one of confusion, and when I sorted out what you meant, I gave the proper term for what you meant without rancor or judgment. The same was true of your other inapt uses of terminology.

The immediate issue is your persistence in using a false term despite knowing it is false, for no reason anyone outside yourself would condone.
"Condone". A strong word, implying wrongdoing.
You simply want to use it, despite that it contradicts the purpose of communication, which is to be understood. If you do not wish to be understood, then quit writing for others’ consumption.
I admit that it didn't occur to me that backwards isn't the opposite of forward. I certainly didn't know about the great importance of saying "inverse", or that it was an issue that would cause such anger.



...you persist in your solipsistic blathering as if everyone else ought to adjust themselves to whatever your choices of meanings
are for words
No, I never made or intended an issue about word-meanings.
, your choices of aesthetic preferences for map projections, your choices of significant traits for map projections
I''ll remind you that projection-preference was the subject-line topic of a thread in which I was expressing preferences and stating properties.
, and your contrived terms for those traits;
Not quite sure what terms you're referring to. As for "linear", I said that a map is linear if x-distance is proportional to longitude-difference, and y distance is proportional to latitude-difference. If you're saying that there was already a different term for that property, you didn't say what it was.

Have I used nonstandard meanings for "equal-area", "conformality", "pseudocylincrical" ? ...what then?

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 it in a way that's obviously different from the way that everyone else uses it. Now, I prefer to just speak of non-perpendicular intersection of meridians and parallels.
·Wheedle people to do things for you;
Tobias suggested that, talking so much about PF8.32, it would be good if I provided an image of it. Then he set about imaging Linear PF8.32, from the formulas that I posted for it. I then requested images for versions it with two different conformality-compromise-configurations--a lat 30 standard parallel, and my 45/0 compromise. And I requested images of cylindrical projections with those two compromises.

Tobias initially volunteered to image PF8.32, and then, yes, I requested a few additional images. ... a few more instances of something that Tobias had indicated interest and willingness to do, and that I didn't know how to do. My requests were always expressed as questions using the word "could". If I was asking too much, Tobias would have said so, and/or not provided the images.

For some reason that upsets daan very much.
·Fail to perform even the most rudimentary due diligence to confirm what you think
Meaningless without well-supported specifics. Of course if I made incorrect statements regarding objective facts, you should have felt free to specify what they were. ...instead of your usual vague generalizations and angry-noises.
or what words to use in order to convey what you think
Already answered, above.
and strained rhetorical arguments
Again, vague generalization. You're unclear what you mean by "rhetorical, or how you justify its use. I've been stating preferences, and reasons for them. I've been stating arguably-desirable properties, and telling what I claim is desirable about them. Most of that discussion was in a thread whose subject-line title was a question about people's preferences.

daan seems to be espousing an extreme relativism that would ban expression of preferences, and reasons for them. My criticism wasn't entirely negative or un-constructive, because I proposed projections that do well by a combination of some possible desiderata that I spoke favorably of.
·Demonstrate little concern for or interest in what others who have earned their standing in the field have to say about any of these thing (namely daan?), ranging from terminology, to the significance of traits, to the cognition of map projections.
daan should have felt free to specify particular instances in which a statement of mine, regarding objective fact, is contrary to what is said by authorities.

So, for example, do authoritative experts say that it doesn't look unnatural, unrealistic or implausible for a large continent at the center of the map to have significant NS/EW scale-disproportion--something that wouldn't be seen in a photo of a globe?

Oops, there I go again with my non-standard terminology (NS/EW scale-disproportion) If there's a better (and shorter) standard word for that--which means the same thing--then I should adopt it.

Sometimes I use terms like "NS/EW scale-disproportion", or "non-perpendicular intersection of parallels", because I don't know of an official (and safe from being contested) standard word, or a way to better say what I mean. I use those terms to refer two main kinds of shape-distortion on maps.
...that characteristic contrarianism and the several ways it contribute to your mode of discourse, are what encourage me to respond in vexed tones.
In at least some instances, you're using "contrarianism" to mean "not agreeing with daan's positions regarding comparisons of aesthetics or merit.

For one thing, you seem to feel that, comparison of merits is meaningless because different people like different things. Fine, individuals can still be permitted to state preferences and reasons for them, and suggest some measures of merit.

In particular, much of my map-projection-preference has to do with usefulness. Ways in which maps can be useful are matters of objective fact. I've been stating some objective facts about kinds of usefulness that some maps have, and some don't have (and maps that have lots of them, and maps that don't have any of them).

Are those objective-fact statements about usefulness contradicted by your experts?

As for aethetics, the main thing that I've been criticizing all along can be described in the way that I've recently been describing it: Significant or extreme NS/EW scale-disproportion in the center of the map, aesthetically-objectionable because it's quite absent from a photo of a globe. I've admitted that some maps that I like have that fault, but that they thereby gain an otherwise-unattainable combination of usefulness-properties in return for it.

Do your experts say otherwise?
In this instance, maybe it was anger about, and/or a desire for a noisy distraction from, the fact that, when he was going on about the great complicatedness of imaging a projection that lacks forward formulas, he’d neglected to mention the plain, straightforward direct use of the lat(y) and lon(x,y) formulas, that I described in the initial post that started this thread.
Refering to the obvious method I described, for direct use of lat(y) and lon(x,y) formulas for constructing a pseudocylindrical map on a projection that doesn't have a set of forward formulas:
Geocart uses this technique when appropriate.
Fine. I can't claim to be the inventor of something so obvious as that.

I just meant that you might have felt chagrined because you hadn't mentioned it when you were telling me how very difficult and complicated it would be to make an image of a projection that doesn't have a set of forward formulas, and that it's necessarily a numerical root-finding problem.
, as you could infer if you’d bothered to have read my research papers.
...and as I'd have known if you'd said so, when you were going on about the great complexities and difficulties of imaging a map on a projection that doesn't have a set of forwards formulas, and saying that it's necessarily a numerical root-finding problem.

Michael Ossipoff
daan
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Re: Use backwards formula directly, no rootfinding?

Post by daan »

RogerOwens wrote:
daan wrote:The issue is not that you misused a term. My first encounter with your coinage “backward formula” was simply one of confusion, and when I sorted out what you meant, I gave the proper term for what you meant without rancor or judgment. The same was true of your other inapt uses of terminology.

The immediate issue is your persistence in using a false term despite knowing it is false, for no reason anyone outside yourself would condone.
"Condone". A strong word, implying wrongdoing.
« laugh » Wow. Here you yet again fail to address the actual problem, the actual problem being why you insist on using your invented term in place of the pervasive, informative, unmistakable, easily searched upon, serviceable, accepted term, and giving no reasons whatsoever for this insistence. Instead, despite evidently not caring what words mean to anyone else, now want to quibble about one connotation of a word unrelated to map projections, a connotation that I may or may not have even meant. Brilliant.
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.
« 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 (and where anyone can see yet more misuse and misunderstanding of terms, leading you to draw false conclusions). You invented non-existent statements from cartographers (with some hand-waving about Deetz & Adams and Raisz) about how the term is used, and failed to come up with a single reference (see my complaint about never doing due diligence and relying on hazy memory). 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. The episode about shear powerfully illustrates my points for me. Thanks for bringing it up. Brilliant.
·Wheedle people to do things for you;
Tobias suggested that, talking so much about PF8.32, it would be good if I provided an image of it. Then he set about imaging Linear PF8.32, from the formulas that I posted for it. I then requested images for versions it with two different conformality-compromise-configurations--a lat 30 standard parallel, and my 45/0 compromise. And I requested images of cylindrical projections with those two compromises.

Tobias initially volunteered to image PF8.32, and then, yes, I requested a few additional images. ... a few more instances of something that Tobias had indicated interest and willingness to do, and that I didn't know how to do. My requests were always expressed as questions using the word "could". If I was asking too much, Tobias would have said so, and/or not provided the images.

For some reason that upsets daan very much.
« laugh » Wow. Somehow you have forgotten that you also requested that I make images for your PF8.32 projection, twice, as well as speculated that I ought to be able to easily implement your projections in Geocart and thereby fulfill your request for images. You’ve requested images from me in the past for other whims, several of which I went ahead and provided because sometimes I’m nice that way. And of course, you completely left out that Tobias had kindly set up a substantial infrastructure for you so that you could draw your own maps, but rather than learn to push a couple of buttons, you whined some more until Tobias just did it for you. This illustrates your pattern of selecting snippets and portraying them as the whole. Brilliant.
·Fail to perform even the most rudimentary due diligence to confirm what you think
Meaningless without well-supported specifics.
Oh, you already did that for me. See above concerning the “shear” episode. I mean, no, I’m not going to go through and document every episode again. The history is here for all to see.

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.

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.
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.

It’s amusing. This entire waste of words and negativity could have been averted by normal, reasonable human behavior. “Oh, it’s called inverse formulas? Didn’t know that. Thanks.” And then maybe looking it up if he were skeptical. And then adopting it in order to foster understanding. But no.

Pity.

— daan
Piotr
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Re: Use inverse formula directly, no rootfinding?

Post by Piotr »

I think "shearing distortion" means tilting in some direction, as opposed to stretching.
RogerOwens
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Re: Use backwards formula directly, no rootfinding?

Post by RogerOwens »

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
Atarimaster
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Re: Use backwards formula directly, no rootfinding?

Post by Atarimaster »

Just a single point which lepas into my eye:
RogerOwens wrote: 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.
(…)
If all non-conformal maps have “shear”, and all conformal maps don’t have “shear”, then “shear” is just another word for non-conformality.
Well, that’s just exactly what daan said, in the thread he linked to above:
Shear normally refers to angular distortion.
And since conformal maps are the only ones having no angular distortion – so yes, »shear« is another word for non-conformality.
RogerOwens
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Re: Use inverse formula directly, no rootfinding?

Post by RogerOwens »

Piotr wrote:I think "shearing distortion" means tilting in some direction, as opposed to stretching.
Yes, that's consistent with my guess about what shear means. By my guessed definition, conformal maps and cylindrical maps are the maps that aren't sheared.

In fact, maybe perpendicularity of parallel-meridian intersections is possessed by maps that fit that guessed definition, and only by those maps.

Your definition, quoted above, sounds like my definition of "slant"--nonperpendicularity of meridian-parallel intersections.

So yes, I think we're talking about the same map-attribute.

Michael Ossipoff
daan
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Re: Use backwards formula directly, no rootfinding?

Post by daan »

RogerOwens wrote:daan:
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.
Ossipoff, really, seriously? Seriously? Do you not grasp how toxic your modes of discourse end up being? I never said any such thing. You are relying, again, on your own distorted memory, fabricating things and expecting other people to believe them in order to support your own delusional version of reality.

Where is the due diligence here? If I ever wrote such a thing in a form that you could consume it, then it exists on the Internet and can be searched. Just pulling stuff out of your brain is not credible. How is it that you do not understand this simple, basic truth? How can you imagine that this is a useful way to approach a conversation, let alone a dispute? Where is your evidence? Why would you imagine anyone should take assertions like this seriously?

If you cannot even manage to engage a simple matter of fact in a credible way, why would you imagine people should trust your judgment in balancing your rhetorical arguments about the value of this or that map projection trait? My huge beef with your arguments has always been how imbalanced they are, fixating on highly specific characteristics and ignoring or arbitrarily discounting whatever traits do not pique your interest. Those are subjective matters. Now we're dealing with facts, where there is no bias left to contend with, and yet this is what you come up with for a convincing argument?

— daan
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