Use inverse formula directly, no rootfinding?

[daan]

I think "shearing distortion" means tilting in some direction, as opposed to stretching.

I will write an article about this when I get time. It will all become clear.

— daan

[RogerOwens]

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 (then) 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.

We'll just have to agree to disagree about whether you said that.

You are relying, again, on your own distorted memory

No, daan, that isn't something that I'd come up with myself. That definition of map-shear wouldn't occur to me. You said it.

You said that a map is sheared if a cut globe can't be deformed into that map without shear.

I've admitted that maybe you said that conformal maps aren't sheared, by that definition, though I don't remember that.

, fabricating things and expecting other people to believe them

I didn't fabricate it. You said it.

in order to support your own delusional version of reality.

Again you're showing us your typical Internet flamewarrior namecalling behavior.

By your definition of shear, quoted above, if conformal maps aren't sheared, then all cylindrical maps likewise are not sheared.

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.

Incorrect. For one thing, you didn't say it somewhere elsewhere on the Internet, you said it at this forum.

"It exists and can be searched". Oh really?



Yes, a search at this forum could prove to you what you did or didn't say.
Of course it couldn't prove it to someone else.

You see, this forum has a nice feature called editing. Anyone can edit any of their posts at any time.

Need I say more?

Just pulling stuff out of your brain is not credible.

There's no way that that definition (the one that I quoted you on) would occur to me. You said it.

Where is your evidence?

If that statement is still in your post, then maybe a search could find it.

"Where is the evidence?" Maybe it isn't there anymore.

Why would you imagine anyone should take assertions like this seriously?

I can't speak for what someone else would conclude.

Though that definition (yours) isn't something that would occur to me, you can still claim that I'm lying.

But you, not I, are the one who insists on making issues of things like this. You're the one to whom these usage/definition issues are important.

If you cannot even manage to engage a simple matter of fact in a credible way...

See above.

..., why would you imagine people should trust your judgment in balancing your rhetorical arguments about the value of this or that map projection trait?

I don't ask people to trust or agree with my preferences. Their preferences are often different from mine. I tell why certain properties are useful. I tell why a property is unrealistic, and aesthetically a minus (A real skinny Africa might not bother you, but you can't call it an aesthetic plus). However I can't tell someone else which considerations are more important to them. Only they can decide that.

In discussions of preferences and map-merit, I tell of properties, and their advantages. I don't ask anyone to trust or agree with my "judgement" regarding which considerations are more important to them.

I can tell you lots of ways in which a Ford is better than a Chevy. Maybe they're all objectively true. They're all reasons why you should get a Ford instead of a Chevy.

Does that mean that you should "trust my judgement" and get a Ford instead of a Chevy? Of course not. ...because you can name ways in which a Chevy is better than a Ford. Those considerations are the ones that are more important to you, and that's why you prefer a Chevy to a Ford, and that's why you get a Chevy instead of a Ford.

My huge beef with your arguments has always been how imbalanced they are

.."imbalanced" if I don't value the various arguments, properties, and considerations in the same way you do.

, fixating

If you have a preference different from mine, and if you don't change it when you hear my arguments, then you must be "fixating" on what you like, because, if you were really open and fair, you'd change your preference to match mine. Is that how it goes?

...on highly specific characteristics and ignoring or arbitrarily discounting whatever traits do not pique your interest.

So, you're saying that I should value the various considerations, properties, pro-and-con arguments, with the same weights that you do. ...otherwise my judgement of the matter must be imbalanced, and I must be biased.

...and that I'm wrong if what piques your interest doesn't pique my interest.

Where's all that relativism of yours now?

Michael Ossipoff

[Atarimaster]

Incorrect. For one thing, you didn't say it somewhere elsewhere on the Internet, you said it at this forum.

"It exists and can be searched". Oh really?



Yes, a search at this forum could prove to you what you did or didn't say.
Of course it couldn't prove it to someone else.

You see, this forum has a nice feature called editing. Anyone can edit any of their posts at any time.

Need I say more?

On the page on which was talked about »shear« a lot, I see no difference in the version that’s stored here in the forum and the one that was captured by the wayback machine.

Instead, I see daan stating twice that shear is angular distortion.

The wayback machine isn’t under daan’s control and given the fact that this page was captured on 5 May 2016, daan must be a clairvoyant since obviously, he edited his posting sometime between January and May 2016, because he knew that we’ll come back to this matter a year later.
Wow.

daan, would you please tell me next week’s numbers on german lottery? Pleeeeeease!

[daan]

"It exists and can be searched". Oh really?



Yes, a search at this forum could prove to you what you did or didn't say.
Of course it couldn't prove it to someone else.

You see, this forum has a nice feature called editing. Anyone can edit any of their posts at any time.

Need I say more?

You are on notice.

You can use the Wayback Machine or other mechanisms to search old material, even if the currently accessible copy is edited. Perhaps you did not know that, but that only exacerbates your malevolence: You exploited your ignorant belief that your slanderous insinuations could not be substantiated in order to cast doubt on whatever contrary evidence other people might turn up. You are vile.

You are lying, over and over, and you are doing it to support your delusions. I donʼt care if you think “delusions” is name-calling, a matter you seem much more concerned with than with the truth. The term and my use of it are factual. What you claim as infallible memories, and hold to fanatically, can be objectively refuted.

• delusional | də'lōōZH(ə)nəl | adj.
  ·characterized by or holding idiosyncratic beliefs or impressions that are contradicted by reality or rational argument, typically as a symptom of mental disorder.
  ·based on or having faulty judgment; mistaken.
  — New Oxford American Dictionary

It is startling and disturbing that you evidence such belief in the infallibility of your own memories, and that they ought to be taken as evidence. Healthy humans have the capacity to doubt themselves. Your assertions and memories are garbage. They are useless. They are not evidence for anyone else; nor ought they be evidence to you. I donʼt trust my own memory. I substantiate my claims. Any reasonable person does.

If you ever again stubbornly press disputed claims about forum members using only your own memory as evidence, I will delete your account.

It is pathetic that it comes to this. I advocate robust debate and I loathe censorship, but what you’re doing meets no standards of truth; nor does it have anything to do with the purpose of this forum.

— daan

[RogerOwens]

I'd never heard of the WayBack Machine before Tobias and daan mentioned it, in the two most recent posts to this thread.

Not to change the subject, but:

If all conformal maps are un-sheared,

...and if Mercator can be deformed into any cylindrical map without shearing,

...then all cylindrical maps are un-sheared.


...Because, when an un-sheared map is deformed into another map, without shearing, then in what meaningful sense can the new map be said to be sheared?

------------------------------------------------------------------------------

I've been using some terms, coined by me, that are rather wordy. Here's how I'm going to say them more briefly:

1. NS/EW scale-disproportion:

II'll call that "compression"

(The compression could be NS or EW)

2. Nonperpendicularity of meridian and parallel:

I'll call that "slant"

(...as I began to do previously)

-----------------
Edit-added comment:

What I say about slant here is in reference to maps in equatorial aspect.
----------------

I still don't know what the official cartographic definition of map-shear is, so I can't say whether or not it's the same thing as slant, and the tilt that Piotr referred to.

But if all conformal maps are un-sheared, and if, as that implies (see above), conformal maps and cylindrical maps are the ones that don't have slant, and are also the ones that don't have shear...

Whatever it is that "shear" might mean, it occurs in maps that have slant, and is absent in maps that don't have slant. Maybe I should revise my guess? Maybe "shear" is slant. Maybe "shear" is just a word for slant.

But what about maps not in equatorial aspect. Is Cassini (Transverse Cylindrical-Equidistant) un-sheared, like standard Cylindrical-Equidistant?

Sure. Mercator is conformal regardless of aspect, and a Transverse Mercator can be deformed, without shear, into a Cassini with the same equator. So the argument above follows for transverse and oblique cylindrical projections too.

What about slant? If it's taken literally, Cassini has slant. But I don't know if it's meaningful and useful to define slant for oblique or tranverse maps.

So, for now at least, my term "slant" is defined only for projections in equatorial aspect (Their equator coincides with the Earth's equator).

Michael Ossipoff

[RogerOwens]

Just as a map is conformal if and only if it's conformal everywhere (except maybe for one, two, or a few points, as Lagrange), a map is unslanted or slant-free if and only if it has no slant anywhere.

I just wanted to add that clarification of what I mean by unslanted or slant-free.

Michael Ossipoff

[RogerOwens]

Tobias--

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.

Why have two words for the same thing?

Anyway, the problem with that is that cylindrical projections have no shear, though they do have angular-distortion.

(as described in one of the later posts of mine in this thread)

At first I thought that maybe slant and shear might be the same thing, until it occurred to me that I've only been speaking of the slant of maps in equatorial aspect, and shear might even not be a useful term to define for non-equatorial-aspect maps.

So, my first guess for what shear means is the my current guess.

Michael Ossipoff