Ah, if I had remembered about this situation, I could have checked a few months ago, when I retrieved all my books. Yes, it seems Dr. Böhm has a problem in his formulations. I am happy I did not release this bad version in Geocart “into the wild”! I will correct it.
Thank you, Tobias.
— daan
Wagner VIII and Hufnagel projections
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Atarimaster
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- Joined: Fri Nov 07, 2014 2:43 am
Re: Wagner VIII and Hufnagel projections
Hello,
this post will end up with an proposal for Geocart, so maybe I should’ve put it to the "Wish list" board. However we started talking about the Wagner variants here, so I thought it might be appropriate to post it here.
Recently I realized something I didn’t see before. Mostly because at that time, I had no access to Dr. Böhm’s original article he presented in Kartographische Nachrichten. But now the article can be downloaded from
http://www.boehmwanderkarten.de/archiv/ ... mplete.pdf
It’s in German but I hope the formulae and images will give you some clues even if you don’t understand German.
Moreover, I’ve read "A new pseudocylindrical equal-area projection for adaptive composite map projections" by Bojan Savric and Bernhard Jenny, available at
http://cartography.oregonstate.edu/pdf/ ... ection.pdf
Let’s talk about Dr. Böhm first:
He is pointing out that Wagner VII and VIII are essentially special cases of a formula system that provides a lot of possible map projections. He presents 5 configuration parameters that are used to describe each of this possible projections, e.g. 65-60-60-0-200 are the values that generate Wagner VII.
And now I saw that Savric and Jenny are doing the same thing but they restrict themselves to the first two of Dr. Böhm’s parameters, the first one being bounding parallel, the second one the bounding meridian.
If you compare page 7 of Savric/Jenny to page 8 of Dr. Böhm, you’ll see that they show similar or even the same results.
Dr. Böhm’s 3rd and 4th parameters set the areal distortion:
It’s the latitude up to which the areal distortion in controlled (60° on Wagner VIII) and the degree of areal distortion that is reached at the aforementioned latitude. Setting this value to 1 results in an equal-area projection (Wagner VII), a value of 1.2 (= 20% areal distortion at 60° N/S) generates Wagner VIII. And No. 5 is the ratio of equator length to the length of the central meridian. Dr. Böhm decided to use percental values for 4 and 5, thus Wagner VIII reads in his notation 65-60-60-20-200.
So, what’s interesting about it?
As Böhm show on his website (again, German only)
http://www.boehmwanderkarten.de/kartogr ... rld_3.html
his four Wagner variations as well as Canters’ optimized versions of Wagner VII/VIII can be described using the five parameters. And of course, it also works with the pseudocylindrical projection that is proposed by Savric and Jenny.
So, here’s my proposal:
Wouldn’t it be nice if a new projection was added to Geocart (maybe called "Generic Wagner" or something like that) which offers the five parameters in Geocart’s Parameters dialog?
Kind regards,
Tobias
this post will end up with an proposal for Geocart, so maybe I should’ve put it to the "Wish list" board. However we started talking about the Wagner variants here, so I thought it might be appropriate to post it here.
Recently I realized something I didn’t see before. Mostly because at that time, I had no access to Dr. Böhm’s original article he presented in Kartographische Nachrichten. But now the article can be downloaded from
http://www.boehmwanderkarten.de/archiv/ ... mplete.pdf
It’s in German but I hope the formulae and images will give you some clues even if you don’t understand German.
Moreover, I’ve read "A new pseudocylindrical equal-area projection for adaptive composite map projections" by Bojan Savric and Bernhard Jenny, available at
http://cartography.oregonstate.edu/pdf/ ... ection.pdf
Let’s talk about Dr. Böhm first:
He is pointing out that Wagner VII and VIII are essentially special cases of a formula system that provides a lot of possible map projections. He presents 5 configuration parameters that are used to describe each of this possible projections, e.g. 65-60-60-0-200 are the values that generate Wagner VII.
And now I saw that Savric and Jenny are doing the same thing but they restrict themselves to the first two of Dr. Böhm’s parameters, the first one being bounding parallel, the second one the bounding meridian.
If you compare page 7 of Savric/Jenny to page 8 of Dr. Böhm, you’ll see that they show similar or even the same results.
Dr. Böhm’s 3rd and 4th parameters set the areal distortion:
It’s the latitude up to which the areal distortion in controlled (60° on Wagner VIII) and the degree of areal distortion that is reached at the aforementioned latitude. Setting this value to 1 results in an equal-area projection (Wagner VII), a value of 1.2 (= 20% areal distortion at 60° N/S) generates Wagner VIII. And No. 5 is the ratio of equator length to the length of the central meridian. Dr. Böhm decided to use percental values for 4 and 5, thus Wagner VIII reads in his notation 65-60-60-20-200.
So, what’s interesting about it?
As Böhm show on his website (again, German only)
http://www.boehmwanderkarten.de/kartogr ... rld_3.html
his four Wagner variations as well as Canters’ optimized versions of Wagner VII/VIII can be described using the five parameters. And of course, it also works with the pseudocylindrical projection that is proposed by Savric and Jenny.
So, here’s my proposal:
Wouldn’t it be nice if a new projection was added to Geocart (maybe called "Generic Wagner" or something like that) which offers the five parameters in Geocart’s Parameters dialog?
Kind regards,
Tobias
Re: Wagner VIII and Hufnagel projections
Thanks for the suggestion, Tobias.
You may not be shocked to know that I already did this work back when you directed me to Dr. Böhm’s article. The full generalized Wagner (which is what I call it in the UI) will be in the next Geocart release. Given your explanation of the parameters, I may augment the UI’s description of the parameters somewhat. I already state, as a rule unattached to any particular projection, For an equal-area projection, m₂ must be 1 and a∙b∙m∙n must equal 1. I’ll see if there is enough room to provide a brief description of some of the other parameters.
Cheers!
— daan
You may not be shocked to know that I already did this work back when you directed me to Dr. Böhm’s article. The full generalized Wagner (which is what I call it in the UI) will be in the next Geocart release. Given your explanation of the parameters, I may augment the UI’s description of the parameters somewhat. I already state, as a rule unattached to any particular projection, For an equal-area projection, m₂ must be 1 and a∙b∙m∙n must equal 1. I’ll see if there is enough room to provide a brief description of some of the other parameters.
Cheers!
— daan
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Atarimaster
- Posts: 446
- Joined: Fri Nov 07, 2014 2:43 am
Re: Wagner VIII and Hufnagel projections
No, I’m not shocked.daan wrote: You may not be shocked to know that I already did this work back when you directed me to Dr. Böhm’s article.
That’s great news, thanks already!daan wrote:The full generalized Wagner (which is what I call it in the UI) will be in the next Geocart release.
I’m curious what it’ll be… I probably couldn’t come up with an description that’ll fit into the UI without overwhelming the user.daan wrote:Given your explanation of the parameters, I may augment the UI’s description of the parameters somewhat. (…)
Kind regards,
Tobias
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Atarimaster
- Posts: 446
- Joined: Fri Nov 07, 2014 2:43 am
Re: Wagner VIII and Hufnagel projections
Well, I couldn’t hold my breath any longer, I was too anxious to play with Wagner variations.daan wrote:The full generalized Wagner (which is what I call it in the UI) will be in the next Geocart release.
And since I had everything that I needed right there…
I just released the Wagner Variations Generator (I failed to come up with a better name). You can enter parameters as noted by Dr. Böhm and, by using the d3.js scripts, a SVG rendering of the corresponding projection will be generated. Admittedly, I stole the idea from your Hufnagel interactive tool, although my WVG is not as sleek since it doesn’t update the projection on-the-fly.
So, in case anybody wants to give it a shot:
http://map-projections.net/make-my-wagner/
(The mobile version still needs a bit of work but it should work fine in any desktop browser that can handle SVG.)
The downside is that it didn’t quite help to satisfy my curiosity.
Because now, I’d really like to create decent maps using Geocart’s full generalized Wagner instead of the schematic images that the d3 scripts can render.
Kind regards,
Tobias
Re: Wagner VIII and Hufnagel projections
I’ve been so bad. I really need to push out the new version. Soooo many new projections… I’ll chat with you privately about a beta test.Atarimaster wrote:Because now, I’d really like to create decent maps using Geocart’s full generalized Wagner instead of the schematic images that the d3 scripts can render.
— daan