Adequately scaling maps
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Author:  marcelopaglia [ Wed Apr 13, 2011 3:22 pm ]
Post subject:  Adequately scaling maps

I want to use maps to compare the size of the U.S. economy vis-a-vis China's. Since the U.S.'s GDP adjusted by purchasing power parity is 60% larger than China's, I'm scaling the US map by 160%.
However, I'm not sure if the scaling is applied to the actual territory or to the box around the map. Moreover, in order to do it right, I think that both original maps would have the same size.
I greatly want to use your software to this extent but want to be sure that results are accurate and that I'm not misinterpreting them (one strange things is that when resizing by 160% the box of the US map grows more than two-fold).
I would appreciate your comments about how to use maps to compare indicators across countries, and the accuracy of results.
Marcelo Paglia

Author:  BeGraphic Team [ Thu Apr 14, 2011 5:13 pm ]
Post subject:  Re: Adequately scaling maps


If you rise the scale of a square from 100% to 200% (multiplied by 2) :
  • the width will increase by 2 times
  • the length will increase by 2 times
Therefore the surface area of your shape will increase by 4 times (= 2 x 2).

So if you want to make your freeform grow only twice, you have to make an increase of 1.414214

How do I know that 1.414214 X 1.414214 = 2 ?
Because the "square root" of 2 is 1.414214
Therefore to do what you want, use the Excel function "=SQRT(A1)" (better than A1)
... unless you want to cheat ;-)

More details here :

Author:  marcelopaglia [ Fri Apr 15, 2011 10:07 pm ]
Post subject:  Re: Adequately scaling maps


Thanks for your prompt and clear reply (you didn't include the link to more information... :)).

I'm still a bit dubious about safely resizing maps to compare characteristics (like GDP or population) across countries. If I get it right, the scaling applies to the frames around the maps and to the maps themselves –which is ok. However I still have the problem of countries having different shapes and therefore filling different areas within the frame.

Take for example Spain and Chile, which are both framed in a 4x4 square. Being pretty much square Spain would fill most of its frame (if it were totally square it would have an area of 16cm2 = 4x4), while being long and thin Chile would only fill a portion of its frame (let’s say 1cm wide x 4cm tall = 4 cm2). If Spain were three times Chile for a given indicator I would have to resize it by 1.732501 (sq. root of 3, according to excel ;) ), which would give me a frame for Spain of 48 cm2 (6.928203x6.928203).

If this is right, it would be ok to compare the sizes of the frames of the maps (48cm2 vs. 16cm2), but not the size of the maps themselves (48cm2 for Spain vs. 4cm2 for Chile).

Does this make sense to you?

Thanks and best wishes,

Author:  aldecis_begraphic [ Sat Apr 16, 2011 4:04 pm ]
Post subject:  Re: Adequately scaling maps

Dear BeGraphic user,

You ask very clever questions... that students get several months to study and understand.
I will try to give simple answers, and usable methods in several chapters.

Chapter 1 : What is a digital image?
There two types of images:
  • raster/bitmap images (made of millions of pixels/dots) like pictures in your newspaper or made by your camera, such as photos (e.g.: jpeg, gif...) that are made of millions of small colored dots
  • vector images (made of mathematical formulaes) that always exist in a rectangle shape, and that can be reduced or enlarged without loosing precision

More details:

With BeGraphic (or any other vector tool, such as Adobe Illustrator), when you change the scale of a country,
  • it's not its area that you exactly rule (select a freeform within Excel to catch the idea),
  • but its external rectangle's surface (e.g.: rectangular "marquee tool")

Therefore for any country having a large concav shape (border & coast) or with exclave, there will be a problem to workaround (see Chapter III)
Examples of concav states/countries or with exclave : Florida (USA), Italy (Europe), Greece (because of hundreds of islands), USA (but Guantanamo is only rented for USD 4,083... even if Cuba has always refused the check), UK with Gibraltar in Spain, France with Mayotte in Africa (nostalgic for its empire, France has made this former colony a 100% french department in 2011)...
Note : Concav definition
Note : Exclave definition :

Author:  aldecis_begraphic [ Sat Apr 16, 2011 4:28 pm ]
Post subject:  Re: Adequately scaling maps

Dear BeGraphic user,

You ask very clever questions... that students get several months to study and understand.
I will try to give simple answers, and usable methods in several chapters.

Chapter 2 : What is the right map?
You ask the crucial question that during centuries no cartographer has a found a perfect reply to.
How should we show a country on a map, that is to say how to transform a globe into a sheet of paper.

Why choosing the right map projection is important for building a cartogram (meaningful area):

This question is the key problem of what is the right map: Map projection

In "map projection", you have to decide between
  • showing the right direction/shape of all countries (coast & border)... but then the north and south poles (small points) become as large as the equator line (the largest part of the earth)
  • showing the right surface... but then the shape of all countries far from the equator line won't have meaningful shapes (not usable coast & border for sailors). By the way, the method to distord a map to get plausible surface is called Cartogram.
  • preserving distance our shortest way or...
  • a mix of previous choices (each country has its own balanced solution, mainly optimized for itself)

If USA has chosen ellipsoid & WGS84 (for GPS), French have another way to make maps (Lambert conformal conic projection):

More explanation about cartograms:

Author:  aldecis_begraphic [ Sat Apr 16, 2011 5:56 pm ]
Post subject:  Re: Adequately scaling maps

Dear BeGraphic user,

You ask very clever questions... that students get several months to study and understand.
I will try to give simple answers, and usable methods in several chapters.

Chapter 3 : How to do a Cartogram with BeGraphic?
First of all, you understand that no human being is able to quantify the surface of a country on a map, especially when the shape is not a rectangle or a circle.
  • So if you decrease smoothly the country (very little change), nobody will notice the gap... unless you keep the shadow of the former shape
  • If you increase the country's size, the frontline countries might be hidden
  • If you move the adjacent countries, the all map will become ridiculous and difficult to understand.

There are very few clever ways to show quantities on a map
  • best way : by using BeGraphic, put a sub-dashboard (e.g.: micro-chart/sparkline on top of each country on the map)
  • alternative solution : 1) transform your indicator into a ratio (actual vs past), 2) round the numbers (in statisitics, it's called "discretization"), 3) then transform the categories into a scale of colors to build a choropleth maps by using BeGraphic

If you really insist to do a cartogram, BeGraphic can rule the only usable one, called "non-contiguous cartogram" where the reader sees both positions (current and past).
Even if the best case is when the change is always a decrease :

If you want other types of cartograms (quite complex to benchmark two status, usually unusable to give a rational insight... and not in Microsoft Office), go to
Usually the Cartogram don't begin by using authalic maps (equal-area or equiareal projection). Even if these maps are especially designed to preserve equivalent area for all countries, cartogram don't like them because
  • at first users don't recognize countries on these maps (as it's nonconventional maps, the audience thinks there is a dirty trick... even if it's the full opposite)
  • the change between the map and the cartogram is not spectacular enough, because areas are beginning at the right size

Example of a authalic map (preserving comparable areas. Proof: small size of Greenland):

Author:  Belickaya [ Sat Nov 23, 2013 4:00 am ]
Post subject:  Adequately scaling maps

We will post links to our maps soon. We are still working on some of them.
And yeah, Magis, maybe we can play on the VM server or something. I still get pretty bag ping there over 170 but if UT comp is on, it makes it a bit better. Well keep in touch.

Author:  faundA [ Sat Jun 25, 2022 10:55 pm ]
Post subject:  -

Would Love to see MWCM add Bisnarck and Minas Tirith to the map list That would be WOW

ps All the new maps are GREAT GREAT JOB STEEL

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