0977: "Map Projections"

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Idhan
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Re: 0977: "Map Projections"

Postby Idhan » Fri Nov 25, 2011 6:03 am UTC

The idea of applying the Mollweide-to-Hammer transformation is interesting. I wonder what a "double-Hammer" map, with the Mollweide-to-Hammer transformation applied to a map that's already in Hammer, or a "double-Mollweide" map, with the Hammer-to-Mollweide transformation applied to a Mollweide map, would be like. The "double-Mollweide" would be especially interesting, I think -- it would be an equal area map where the parallels are actually further apart along the prime meridian and converge toward the boundary.

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Re: 0977: "Map Projections"

Postby Strebe » Fri Nov 25, 2011 10:19 am UTC

Idha wrote:I wonder what a "double-Hammer" map, with the Mollweide-to-Hammer transformation applied to a map that's already in Hammer, or a "double-Mollweide" map, with the Hammer-to-Mollweide transformation applied to a Mollweide map, would be like.


Hi, Idha. I posted images of the projections you suggested here:

Code: Select all

http://mapthematics.com/forums/viewtopic.php?f=8&t=223


Enjoy! And feel free to comment in that forum.

Regards,
— daan Strebe

Strebe
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Re: Strebe projection

Postby Strebe » Fri Nov 25, 2011 10:26 am UTC

PM 2Ring wrote:Thanks again. That "projection of a projection" technique is a neat idea; I guess it could be used to make vast numbers of variant projections. And you could do all sorts of weird & wonderful things if you use a different surface for the intermediate stage, rather than using a sphere. Reading your explanation in the above link reminded me of a projection technique that I read about a few years ago, which involved a couple of stereographic projections, but using a pseudosphere as the intermediate surface. But I can't for the life of me remember what the application was. :)

BTW, there seems to be a minor typo in your LaTeX. On line 2, you've used \phi_p instead of \varphi_p.


PM 2Ring, thanks for the kind comments and the correction. I have posted the corrected formulæ.

There are a lot of research papers that deal with stereographic projections on pseudospheres for various applications in physics, so it turned out to be a chore to track down the one you might have been referring to. Do let me know if you remember it!

Thanks & regards,
— daan Strebe

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Werner Cordiform fortune:

Postby homunq » Sat Nov 26, 2011 12:42 pm UTC

You worry about the quality of rationalist fanfic for My Little Pony.

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Re: 0977: "Map Projections"

Postby dmswart » Wed Nov 30, 2011 5:42 pm UTC

What projection would be a favorite for those who favor novelty? As in "You like They Might Be Giants, Wierd Al Yankovic and Sir Mix-a-lot. The best thing about Chess is it's many novel variations that come out every year. You wonder why they don't use gimmicky Statue of Liberty plays in the NFL more often."
--
David Swart

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Re: 0977: "Map Projections"

Postby dmswart » Wed Nov 30, 2011 5:48 pm UTC

Brett Dunbar wrote:
oelbert wrote:What happened to the Aitoff projection? I was disappointed to see it wasn't represented here...


The fairly similar Hammer projection gets more use in practice than Aitoff.


Brett, I'd say that depends. At my work, Aitoff plots are used almost exclusively to represent layouts of immersive displays from the observer's point of view.

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steve waterman
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Re: 0977: "Map Projections"

Postby steve waterman » Mon Feb 27, 2012 2:44 pm UTC

re - waterman projection

2012 satellite imaged versions now available
http://www.watermanpolyhedron.com/maps.html

A write-up upon the mathematics/derivation of this projection
http://www.watermanpolyhedron.com/methodp.html

and a "rebuttal" poster regarding the mathematical derivation
of numerous polyhedral projections
http://www.watermanpolyhedron.com/projectionAA.html
[ only low res shown...but use the magnifier to get better look ]

and what others have said about this projection/math
http://www.watermanpolyhedron.com/commentsall.html

helo darqness
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Re: 0977: "Map Projections"

Postby helo darqness » Thu Jul 05, 2012 9:50 pm UTC

This is old, I know. But new to me. There are still images of these maps, but the animation makes it better...

http://www.graflexdirections.com/projec ... index.html (wish this was a GIF)

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Re: 0977: "Map Projections"

Postby trapicki » Wed Feb 05, 2014 4:02 pm UTC

I miss my favourite projection: Azimuthal-equidistant.

Why I like it:
  • It's very handy for amateur radio operators: get real directions. And it shows easily why the transatlantic flights between Europe and North Amerika make this akward ark from Scottland to Canada.
  • It centers around my location. If you want a sensible map for your use, go and get your own.
  • It is not concerned with political incorrect scaling of different parts of the world. It's very simple: It's correct at the center and wrong everywhere else; the further away the more it's wrong. If you want something that is a little bit more 'correct', use Lambert azimuthal equal-area.
  • It realy looks awesome.
  • Have I said already that it only works well for one place? So you realy have to generate a separate map for every location. Nothing for the conformist 'one-fits-all' guys.
Of course you could use a gnomic projection, but azimuthal-equidistant has several advantages:
  • It covers the whole world.
  • The UN choose it for their logo.

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Re: 0977: "Map Projections"

Postby addams » Thu Feb 06, 2014 3:14 am UTC

helo darqness wrote:This is old, I know. But new to me. There are still images of these maps, but the animation makes it better...

http://www.graflexdirections.com/projec ... index.html (wish this was a GIF)

Thank you.
That is amazing.

I can't see them all.
The ones I can see, impress me.

Did a computer do it?

That is a sweet little program.
What else can it do?

Can the program fit the pieces together into an orb?
How big is the ball when the pieces are fit together?

It is fascinating.
I am easily amused.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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Re: 0977: "Map Projections"

Postby BrainMagMo » Sun Feb 09, 2014 6:17 pm UTC

Karilyn wrote:I tried tiling it, and while the effect was attractive, I was irritated the fact that it mirrored across the edges, causing some weird things, most notably showing two Australias next to each other.

Image


This is now my computer background.

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addams
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Re: 0977: "Map Projections"

Postby addams » Mon Feb 10, 2014 2:09 am UTC

I like this one.
http://www.nytimes.com/slideshow/2011/1 ... os-17.html

AfroCentric is Nice.
Sometimes I turn a Globe upside down.

Sometimes I turn it back over,
because it makes me dizzy.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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PM 2Ring
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Re: 0977: "Map Projections"

Postby PM 2Ring » Mon Feb 10, 2014 4:17 am UTC

addams wrote:I like this one.
http://www.nytimes.com/slideshow/2011/1 ... os-17.html

AfroCentric is Nice.
Sometimes I turn a Globe upside down.

Sometimes I turn it back over,
because it makes me dizzy.

:)

FWIW, Daan Strebe made a few posts earlier in this thread, eg viewtopic.php?f=7&t=76384&p=2818995#p2818995

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Copper Bezel
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Re: 0977: "Map Projections"

Postby Copper Bezel » Mon Feb 10, 2014 8:37 am UTC

Bumping this thread while not being Steve Waterman is a cruel tease.
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

she / her / her

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Jackpot777
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Re: 0977: "Map Projections"

Postby Jackpot777 » Tue Feb 11, 2014 3:32 pm UTC

Mapprehension wrote:(Concerning Peirce’s quincuncial:

Karilyn wrote:I tried tiling it, and while the effect was attractive, I was irritated the fact that it mirrored across the edges, causing some weird things, most notably showing two Australias next to each other.

Image

...

Ultimately there's no way to accurately tile this map, which is disappointing as it is a very visually attractive concept.


You tiled it accurately. The results are an accurate tile; if you follow that graticule lines you’ll see that nothing is actually placed improperly in a local sense. It’s just that the singularities at the corners cause abrupt bends, and so you get that annoying appearance of Australia too close to itself. You know those pesky singularities: Mathematical escape clause!


But that's not another Australia next to Australia. That's Antarctica. One is desert brown, the other is white.

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Flumble
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Re: 0977: "Map Projections"

Postby Flumble » Tue Feb 11, 2014 9:21 pm UTC

Jackpot777 wrote:But that's not another Australia next to Australia. That's Antarctica. One is desert brown, the other is white.

That's not what they're talking about. (At least I sincerely hope so) It's that some Australias are very close to eachother, contrary to Antarcticas which are evenly spaced.
Still, it's not only pairs of Australias that are close to eachother, but also Saudi-Arabias, Brazils and East-Africas. It's just that Australias are easier to spot because they're not part of a much larger landmass.

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Re: 0977: "Map Projections"

Postby antares » Mon Dec 15, 2014 8:34 am UTC

I recently got a big mercator projection map for my apartment wall. I like it because I can look it up when the news reports about country ABC or place XYZ. Plus my apartment looks more educated now :D But according to this comic, it seems I'm not really into maps and it makes me feel kinda stupid.

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Re: 0977: "Map Projections"

Postby addams » Mon Dec 15, 2014 8:57 am UTC

With one useful and well used map, You are not stupid.
Maps are useful and often beautiful.

Like what Einstein said about equations and flowers.
The equation describes the flower.
It is not the flower.

You could fill your apartment with maps and books about maps and still be lost.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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orthogon
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Re: 0977: "Map Projections"

Postby orthogon » Mon Dec 15, 2014 9:29 am UTC

addams wrote:Like what Einstein said about equations and flowers.
The equation describes the flower.
It is not the flower.

Magritte said a similar thing about his picture of a pipe.
xtifr wrote:... and orthogon merely sounds undecided.

rmsgrey
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Re: 0977: "Map Projections"

Postby rmsgrey » Mon Dec 15, 2014 3:40 pm UTC

orthogon wrote:
addams wrote:Like what Einstein said about equations and flowers.
The equation describes the flower.
It is not the flower.

Magritte said a similar thing about his picture of a pipe.

And Joyce Kilmer about the limitations of poetry (particularly in regard to trees)

Kit.
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Re: 0977: "Map Projections"

Postby Kit. » Mon Dec 15, 2014 6:06 pm UTC

However, "sometimes a cigar is just a cigar."

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addams
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Re: 0977: "Map Projections"

Postby addams » Tue Dec 16, 2014 7:20 am UTC

rmsgrey wrote:
orthogon wrote:
addams wrote:Like what Einstein said about equations and flowers.
The equation describes the flower.
It is not the flower.

Magritte said a similar thing about his picture of a pipe.

And Joyce Kilmer about the limitations of poetry (particularly in regard to trees)

I love that Old Poem.
It's nice to have things like that Pop Up.
Thank you for that link.

oh, Some one said it directly.
https://en.wikipedia.org/wiki/Map–territory_relation
The Map is not The Territory.

Do you remember learning to read Maps?
What a funny experience.
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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orthogon
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Re: 0977: "Map Projections"

Postby orthogon » Tue Dec 16, 2014 1:12 pm UTC

rmsgrey wrote:
orthogon wrote:
addams wrote:Like what Einstein said about equations and flowers.
The equation describes the flower.
It is not the flower.

Magritte said a similar thing about his picture of a pipe.

And Joyce Kilmer about the limitations of poetry (particularly in regard to trees)

Feynman had a slightly different take on it. The equation may not be the flower, but fortunately we don't have to choose. There is beauty in the flower (or tree), and there is beauty in the equation; the latter "only adds" to the former.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 0977: "Map Projections"

Postby Copper Bezel » Wed Dec 17, 2014 5:10 am UTC

I don't think anyone meant to imply that there was a necessity to choose between maps and places to navigate with them.
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

she / her / her

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Re: 0977: "Map Projections"

Postby orthogon » Thu Dec 18, 2014 1:14 pm UTC

Copper Bezel wrote:I don't think anyone meant to imply that there was a necessity to choose between maps and places to navigate with them.

I didn't mean to imply that anyone meant to imply that. I'm not really sure what I did mean to imply. Perhaps that whether the equation is the rose, can be a substitute for the rose, complements or detracts from one's enjoyment of the rose are all different but overlapping questions. I was just musing, really.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 0977: "Map Projections"

Postby addams » Tue Dec 30, 2014 2:30 am UTC

orthogon wrote:
rmsgrey wrote:
orthogon wrote:
addams wrote:Like what Einstein said about equations and flowers.
The equation describes the flower.
It is not the flower.

Magritte said a similar thing about his picture of a pipe.

And Joyce Kilmer about the limitations of poetry (particularly in regard to trees)

Feynman had a slightly different take on it. The equation may not be the flower, but fortunately we don't have to choose. There is beauty in the flower (or tree), and there is beauty in the equation; the latter "only adds" to the former.

This Thread has been such a Joy to me.

Feynman and Einstein and Joyce Kilmer, a guy that was nearly overwhelmed by a tree,
along side trapicki's practical Azimuthal-equidistant.

It is all tangled up with so much beauty.
How we see The World.
How we show it to each other.

It's Great!
Life is, just, an exchange of electrons; It is up to us to give it meaning.

We are all in The Gutter.
Some of us see The Gutter.
Some of us see The Stars.
by mr. Oscar Wilde.

Those that want to Know; Know.
Those that do not Know; Don't tell them.
They do terrible things to people that Tell Them.

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orthogon
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Re: 0977: "Map Projections"

Postby orthogon » Thu Mar 05, 2015 4:24 pm UTC

Ooh, Mercator's 503rd birthday honoured by a Google Doodle. Too bad they missed the half-millennium. But then Google isn't really that into maps either.
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 0977: "Map Projections"

Postby Jack21222 » Mon Mar 20, 2017 12:54 am UTC

Necro-posting because now Randall has to hate Boston Public Schools:

http://www.wbur.org/edify/2017/03/16/wo ... ic-schools

Social studies teachers in the second, seventh and 11th grades in Boston schools will now have Peters projection maps to use in their classrooms.

The Peters projection map, also referred to as the Gall-Peters projection map, is considered an equal-area representation of the globe and was created as we know it in 1974
broken_escalator wrote:The Mako is powered by the rage of the physics it denies.

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Re: 0977: "Map Projections"

Postby pogrmman » Mon Mar 20, 2017 2:37 pm UTC

Jack21222 wrote:Necro-posting because now Randall has to hate Boston Public Schools:

http://www.wbur.org/edify/2017/03/16/wo ... ic-schools

Social studies teachers in the second, seventh and 11th grades in Boston schools will now have Peters projection maps to use in their classrooms.

The Peters projection map, also referred to as the Gall-Peters projection map, is considered an equal-area representation of the globe and was created as we know it in 1974



Why use such a bad projection?

I mean, it's not a bad projection, it just doesn't look good.

Just use something simple like Mollewide or whatever if you want to improve over a Mercator.

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Re: 0977: "Map Projections"

Postby Sableagle » Mon Mar 20, 2017 6:29 pm UTC

Open University assignment:
What you need to do
Take a grapefruit and draw a number of shapes on its peel with a pen (e.g. circles and squares). Make sure your shapes cover at least a third of the surface of the grapefruit. The shapes represent the land masses on Earth.
Carefully peel the grapefruit whilst trying to keep the skin in one piece.
Take your peel, and put some cuts in it at the edges with a knife or scissors so that it will lie completely flat on a table.
Do your shapes have exactly the same outlines?
Record your notes and observations of the distortions in the shapes of your peeled grapefruit in your lab notebook. You may also wish to take a photo and upload it to My Studio Work on OpenStudio.


How many years would it take to develop mapping software that can determine the outline of a shape on a grapefruit accurately enough to allow me to answer the question about whether or not the flattened shapes "have exactly the same outlines?"

For that matter, how long does it take to make so many cuts in a grapefruit skin "that it will lie completely flat on a table" without separating it into two or more parts?

I'm pretty sure this practical assignment can't actually be done.
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Re: 0977: "Map Projections"

Postby rmsgrey » Mon Mar 20, 2017 10:44 pm UTC

Sableagle wrote:Open University assignment:
What you need to do
Take a grapefruit and draw a number of shapes on its peel with a pen (e.g. circles and squares). Make sure your shapes cover at least a third of the surface of the grapefruit. The shapes represent the land masses on Earth.
Carefully peel the grapefruit whilst trying to keep the skin in one piece.
Take your peel, and put some cuts in it at the edges with a knife or scissors so that it will lie completely flat on a table.
Do your shapes have exactly the same outlines?
Record your notes and observations of the distortions in the shapes of your peeled grapefruit in your lab notebook. You may also wish to take a photo and upload it to My Studio Work on OpenStudio.


How many years would it take to develop mapping software that can determine the outline of a shape on a grapefruit accurately enough to allow me to answer the question about whether or not the flattened shapes "have exactly the same outlines?"

For that matter, how long does it take to make so many cuts in a grapefruit skin "that it will lie completely flat on a table" without separating it into two or more parts?

I'm pretty sure this practical assignment can't actually be done.


a) Grapefruit skin is mildly elastic so the number of cuts required is finite.
b) "Completely flat" presumably means "with upper surface parallel to the tabletop" rather than "with zero thickness", avoiding the need for singularities.

c) It's much easier to do with a balloon and some corkboard, though getting a perfect square after transformation may require an arbitrary number of pins...

Though, come to think of it, while a circle is still well defined even on the surface of a sphere, it's not immediately obvious what a "square" would be - I can make a case for a three-sided "square" covering 1/8 of the sphere's surface (a convex, equilateral shape with all corners right-angles).

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Re: 0977: "Map Projections"

Postby Sableagle » Tue Mar 21, 2017 8:24 pm UTC

Waxy grapefruit is a crap surface on which to try to draw with Sharpies and the results don't photograph well.

I'm supposed to cover one third on the grapefruit skin in ink. The only way I can think of to accurately do that is to mark out angles around the top or bottom and fill in between them, maybe 0-60 and 180-240 degrees or maybe 0-10, 30-40, 60-70, 90-100 and so on ... which is working backwards from a map projection, not forwards from my drawings.

My Sharpies are ruined. Damn wax.

Anyway, time to pick a cutting method.
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Re: 0977: "Map Projections"

Postby freezeblade » Tue Mar 21, 2017 9:02 pm UTC

That wax washes off with a soft cloth and warm water.
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Re: 0977: "Map Projections"

Postby Sableagle » Tue Mar 21, 2017 9:28 pm UTC

The Sharpie ink washes off with grapefruit juice ... and onto the cutting board, from which it does not wash off.

Maybe I should draw on inflated balloons, shoot them and send in the pieces.
Zohar wrote:You don't know what you're talking about. Please spare me your quote sniping and general obliviousness.

CorruptUser wrote:Just admit that you were wrong ... and your entire life, cyberspace and meatspace both, would be orders of magnitude more enjoyable for you and others around you.


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