Category Archives: Cartography

Declassified Military Satellite Imagery has Applications in a Wide Variety of Civilian Geospatial Studies

1. Overview of US military optical reconnaissance satellite programs

The National Reconnaissance Office (NRO) is responsible for developing and operating space reconnaissance systems and conducting intelligence-related activities for US national security.  NRO developed several generations of classified Keyhole (KH) military optical reconnaissance satellites that have been the primary sources of Earth imagery for the US Department of Defense (DoD) and intelligence agencies.  NRO’s website is here:

https://www.nro.gov

NRO’s early generations of Keyhole satellites were placed in low Earth orbits, acquired the desired photographic images on film during relatively short-duration missions, and then returned the film to Earth in small reentry capsules for airborne recovery. After recovery, the film was processed and analyzed.  The first US military optical reconnaissance satellite program, code named CORONA, pioneered the development and refinement of the technologies, equipment and systems needed to deploy an operational orbital optical reconnaissance capability. The first successful CORONA film recovery occurred on 19 August 1960.

Specially modified US Air Force C-119J aircraft recovers a
CORONA film canister in flight.  Source: US Air Force
First reconnaissance picture taken in orbit and successfully recovered on Earth;  taken on 18 August 1960 by a CORONA KH-1 satellite dubbed Discoverer 14.  Image shows the Mys Shmidta airfield in the Chukotka region of the Russian Arctic, with a resolution of about 40 feet (12.2 meters).  Source: Wikipedia

Keyhole satellites are identified by a code word and a “KH” designator, as summarized in the following table.

In 1976, NRO deployed its first electronic imaging optical reconnaissance satellite known as KENNEN KH-11 (renamed CRYSTAL in 1982), which eventually replaced the KH-9, and brought an end to reconnaissance satellite missions requiring film return.  The KH-11 flies long-duration missions and returns its digital images in near real time to ground stations for processing and analysis.  The KH-11, or an advanced version sometimes referred to as the KH-12, is operational today.

US film-return reconnaissance satellites from KH-1 to KH-9 shown to scale
with the KH-11 electronic imaging reconaissance satellite.  
Credit: Giuseppe De Chiara and The Space Review.

Geospatial intelligence, or GEOINT, is the exploitation and analysis of imagery and geospatial information to describe, assess and visually depict physical features and geographically referenced activities on the Earth. GEOINT consists of imagery, imagery intelligence and geospatial information.  Satellite imagery from Keyhole reconnaissance satellites is an important information source for national security-related GEOINT activities.

The National Geospatial-Intelligence Agency (NGA), which was formed in 2003, has the primary mission of collecting, analyzing, and distributing GEOINT in support of national security.  NGA’s predecessor agencies, with comparable missions, were:

  • National Imagery and Mapping Agency (NIMA), 1996 – 2003
  • National Photographic Interpretation Center (NPIC), a joint project of the Central Intelligence Agency (CIA) and DoD, 1961 – 1996

The NGA’s web homepage, at the following link: https://www.nga.mil/Pages/Default.aspx

The NGA’s webpage for declassified satellite imagery is here: https://www.nga.mil/ProductsServices/Pages/Imagery.aspx

2. The advent of the US civilian Earth observation programs

Collecting Earth imagery from orbit became an operational US military capability more than a decade before the start of the joint National Aeronautics & Space Administration (NASA) / US Geological Survey (USGS) civilian Landsat Earth observation program.  The first Landsat satellite was launched on 23 July 1972 with two electronic observing systems, both of which had a spatial resolution of about 80 meters (262 feet). 

Since 1972, Landsat satellites have continuously acquired low-to-moderate resolution digital images of the Earth’s land surface, providing long-term data about the status of natural resources and the environment. Resolution of the current generation multi-spectral scanner on Landsat 9 is 30 meters (98 feet) in visible light bands. 

You’ll find more information on the Landsat program on the USGS website here: https://www.usgs.gov/land-resources/nli/landsat

3. Declassification of certain military reconnaissance satellite imagery

All military reconnaissance satellite imagery was highly classified until 1995, when some imagery from early defense reconnaissance satellite programs was declassified.  The USGS explains:

“The images were originally used for reconnaissance and to produce maps for U.S. intelligence agencies. In 1992, an Environmental Task Force evaluated the application of early satellite data for environmental studies. Since the CORONA, ARGON, and LANYARD data were no longer critical to national security and could be of historical value for global change research, the images were declassified by Executive Order 12951 in 1995”

You can read Executive Order 12951 here: https://www.govinfo.gov/content/pkg/WCPD-1995-02-27/pdf/WCPD-1995-02-27-Pg304.pdf

Additional sets of military reconnaissance satellite imagery were declassified in 2002 and 2011 based on extensions of Executive Order 12951.

The declassified imagery is held by the following two organizations:

  • The original film is held by the National Archives and Records Administration (NARA).
  • Duplicate film held in the USGS Earth Resources Observation and Science (EROS) Center archive is used to produce digital copies of the imagery for distribution to users.

The declassified military satellite imagery available in the EROS archive is summarized below:

USGS EROS Archive – Declassified Satellite Imagery – 1 (1960 to 1972)

  • This set of photos, declassified in 1995, consists of more than 860,000 images of the Earth’s surface from the CORONA, ARGON, and LANYARD satellite systems.
  • CORONA image resolution improved from 40 feet (12.2 meters) for the KH-1 to about 6 feet (1.8 meters) for the KH-4B.
  • KH-5 ARGON image resolution was about 460 feet (140 meters).
  • KH-6 LANYARD  image resolution was about 6 feet (1.8 meters).

USGS EROS Archive – Declassified Satellite Imagery – 2 (1963 to 1980)

  • This set of photos, declassified in 2002, consists of photographs from the KH-7 GAMBIT surveillance system and KH-9 HEXAGON mapping program.
  • KH-7 image resolution is 2 to 4 feet (0.6 to 1.2 meters).  About 18,000 black-and-white images and 230 color images are available.
  • The KH-9 mapping camera was designed to support mapping requirements and exact positioning of geographical points. Not all KH-9 satellite missions included a mapping camera.  Image resolution is 20 to 30 feet (6 to 9 meters); significantly better than the 98 feet (30 meter) resolution of LANDSAT imagery.  About 29,000 mapping images are available.

USGS EROS Archive – Declassified Satellite Imagery – 3 (1971 to 1984)

  • This set of photos, declassified in 2011, consists of more photographs from the KH-9 HEXAGON mapping program.  Image resolution is 20 to 30 feet (6 to 9 meters).

More information on the declassified imagery resources is available from the USGS EROS Archive – Products Overview webpage at the following link (see heading “Declassified Data”): https://www.usgs.gov/centers/eros/science/usgs-eros-archive-products-overview?qt-science_center_objects=0#qt-science_center_objects

4.  Example applications of declassified military reconnaissance satellite imagery

The declassified military reconnaissance satellite imagery provides views of the Earth starting in the early 1960s, more than a decade before civilian Earth observation satellites became operational.  The military reconnaissance satellite imagery, except from ARGON KH-5, is higher resolution than is available today from Landsat civilian earth observation satellites. The declassified imagery is an important supplement to other Earth imagery sources.  Several examples applications of the declassified imagery are described below.

Assessing Aral Sea depletion:

USGS reports: “The Aral Sea once covered about 68,000 square kilometers, a little bigger than the U.S. state of West Virginia. It was the 4th largest lake in the world. It is now only about 10% of the size it was in 1960…..In the 1990s, a dam was built to prevent North Aral water from flowing into the South Aral. It was rebuilt in 2005 and named the Kok-Aral Dam…..The North Aral has stabilized but the South Aral has continued to shrink and become saltier. Up until the 1960s, Aral Sea salinity was around 10 grams per liter, less than one-third the salinity of the ocean. The salinity level now exceeds 100 grams per liter in the South Aral, which is about three times saltier than the ocean.”

On the USGS website, the “Earthshots: Satellite Images of Environmental Change” webpages show the visible changes at many locations on Earth over a 50+ year time period.  The table of contents to the Earthshots webpages is shown below and is at the following link: http:// https://earthshots.usgs.gov/earthshots/

USGS Earthshots Table of Contents

For the Aral Sea region, the Earthshots photo sequences start with ARGON KH-5 photos taken in 1964.  Below are three screenshots  of the USGS Earthshots pages showing the KH-5 images for the whole the Aral Sea, the North Aral Sea region and the South Aral Sea region. You can explore the Aral Sea Earthshots photo sequences at the following link: https://earthshots.usgs.gov/earthshots/node/91#ad-image-0-0

Assessing Antarctic ice shelf condition:

In a 7 June 2016 article entitled, ”Spy satellites reveal early start to Antarctic ice shelf collapse,” Thomas Sumner reported:

“Analyzing declassified images from spy satellites, researchers discovered that the downhill flow of ice on Antarctica’s Larsen B ice shelf was already accelerating as early as the 1960s and ’70s. By the late 1980s, the average ice velocity at the front of the shelf was around 20 percent faster than in the preceding decades,….”

You can read the complete article on the ScienceNews website here: https://www.sciencenews.org/article/spy-satellites-reveal-early-start-antarctic-ice-shelf-collapse

Satellite images taken by the ARGON KH-5 satellite have revealed how the accelerated movement that triggered the collapse of the Larsen B ice shelf on the east side of the Antarctic Peninsula began in the 1960s. The declassified images taken by the satellite on 29 August 1963 and 1 September 1963 are pictured right.  
Source: Daily Mail, 10 June 2016

Assessing Himalayan glacier condition:  

In a 19 June 2019 paper “Acceleration of ice loss across the Himalayas over the past 40 years,” the authors, reported on the use of HEXAGON KH-9 mapping camera imagery to improve their understanding of trends affecting the Himalayan glaciers from 1975 to 2016:

“Himalayan glaciers supply meltwater to densely populated catchments in South Asia, and regional observations of glacier change over multiple decades are needed to understand climate drivers and assess resulting impacts on glacier-fed rivers. Here, we quantify changes in ice thickness during the intervals 1975–2000 and 2000–2016 across the Himalayas, using a set of digital elevation models derived from cold war–era spy satellite film and modern stereo satellite imagery.”

“The majority of the KH-9 images here were acquired within a 3-year interval (1973–1976), and we processed a total of 42 images to provide sufficient spatial coverage.”

“We observe consistent ice loss along the entire 2000-km transect for both intervals and find a doubling of the average loss rate during 2000–2016.”

“Our compilation includes glaciers comprising approximately 34% of the total glacierized area in the region, which represents roughly 55% of the total ice volume based on recent ice thickness estimates.”

You can read the complete paper by J. M. Maurer, et al., on the Science Advances website here: https://advances.sciencemag.org/content/5/6/eaav7266

3-D image of the Himalayas derived from HEXAGON KH-9 satellite mapping photographs taken on December 20, 1975. Source:  J. M. Maurer/LDEO

Discovering archaeological sites:

The Center for Advanced Spatial Technologies, a University of Arkansas / U.S. Geological Survey collaboration, has undertaken the CORONA Atlas Project using military reconnaissance satellite imagery to create the “CORONA Atlas & Referencing System”. The current Atlas focuses on the Middle East and a small area of Peru, and is derived from 1,024 CORONA images taken on 50 missions. The Atlas contains 833 archaeological sites.

“In regions like the Middle East, CORONA imagery is particularly important for archaeology because urban development, agricultural intensification, and reservoir construction over the past several decades have obscured or destroyed countless archaeological sites and other ancient features such as roads and canals. These sites are often clearly visible on CORONA imagery, enabling researchers to map sites that have been lost and to discover many that have never before been documented. However, the unique imaging geometry of the CORONA satellite cameras, which produced long, narrow film strips, makes correcting spatial distortions in the images very challenging and has therefore limited their use by researchers.”

Screenshot of the CORONA Atlas showing regions in the Middle East
with data available.

CAST reports that they have “developed methods for efficient 

orthorectification of CORONA imagery and now provides free public access to our imagery database for non-commercial use. Images can be viewed online and full resolution images can be downloaded in NITF format.”  

The can explore the CORONA Atlas & Referencing System here: https://corona.cast.uark.edu

Conducting commercial geospatial analytics over a broader period of time:

The firm Orbital Insight, founded in 2013, is an example of commercial firms that are mining geospatial data and developing valuable information products for a wide range of customers. Orbital Insight reports:

“Orbital Insight turns millions of images into a big-picture understanding of Earth. Not only does this create unprecedented transparency, but it also empowers business and policy decision makers with new insights and unbiased knowledge of socio-economic trends. As the number of Earth-observing devices grows and their data output expands, Orbital Insight’s geospatial analytics platform finds observational truth in an interconnected world. We map out and quantify the world’s complexities so that organizations can make more informed decisions.”

“By applying artificial intelligence to satellite, UAV, and other geospatial data sources, we seek to discover and quantify societal and economic trends on Earth that are indistinguishable to the human eye. Combining this information with terrestrial data, such as mobile and location-based data, unlocks new sources of intelligence.”

The Orbital Insight website is here: https://orbitalinsight.com/company/

5. Additional reading related to US optical reconnaissance satellites

You’ll find more information on the NRO’s film-return, optical reconnaissance satellites (KH-1 to KH-9) at the following links:

  • Robert Perry, “A History of Satellite Reconnaissance,” Volumes I to V, National Reconnaissance Office (NRO), various dates 1973 – 1974; released under FOIA and available for download on the NASA Spaceflight.com website, here: https://forum.nasaspaceflight.com/index.php?topic=20232.0

You’ll find details on NRO’s electronic optical reconnaissance satellites (KH-11, KH-12) at the following links:

6. Additional reading related to civilian use of declassified spy satellite imagery

General:

Assessing Aral Sea depletion:

Assessing Antarctic ice sheet condition:

Assessing Himalayan glacier condition:

Discovering archaeological sites:

What’s been happening in your neighborhood for the past 750 million years?

A 15 February 2019 article by Meilan Solly in the Smithsonian online magazine describes a recently released interactive map of the world that shows how the Earth’s continents have moved since 750 million years ago.   With your cursor, you can zoom in and rotate the globe in any direction. Using a pull-down menu at the top center of the screen, you can see the relative positioning of the landmasses at the point in time you selected.  A similar selection box in the upper right corner of the screen allows you to select a particular geological or evolutionary milestone (i.e., first land animals) in Earths’ development.  Even better, you can enter an address in the text box in the upper-left corner of the screen and then see how your selected location has migrated as you explore through the ages.

You can read the Smithsonian article here:

https://www.smithsonianmag.com/smart-news/map-lets-you-plug-your-address-see-how-neighborhood-has-changed-over-past-750-million-years-180971507/?utm_source=smithsoniandaily&utm_medium=email&utm_campaign=20190215-daily-responsive&spMailingID=38891027&spUserID=ODE1MzYyNTI5NjM5S0&spJobID=1461358228&spReportId=MTQ2MTM1ODIyOAS2

You can directly access the interactive globe here:

http://dinosaurpictures.org/ancient-earth#0

Following are screenshots showing what’s happened to the Lyncean Group’s meeting site in San Diego during the past 750 million years.

I hope you enjoy the interactive globe, with visualization created and maintained by Ian Webster, plate tectonic and paleogeographic maps by C.R. Scotese, and the address search tool by LocationIQ.

Current world map
20 million years ago
66 million years ago – dinosaur extinction
105 million years ago
240 million years ago – Pangea supercontinent
400 million years ago – first land animals.  Looks like the first land animals couldn’t have emerged from the sea in San Diego.
600 million years ago – Pannotia supercontinent
750 million years ago

Polyhedral Projections Improve the Accurately of Mapping the Earth on a 2D Surface

Representing the Earth’s 3-dimensional surface on a 2-dimensional map is a problem that has vexed cartographers through the ages. The difficulties in creating a 2D map of the world include maintaining continental shapes, distances, areas, and relative positions so the 2D map is useful for its intended purpose.

Old world mapWorld map circa 1630. Source: World Maps Online

In this article, we’ll look at selected classical projection schemes for creating a 2D world map followed by polyhedral projection schemes, the newest of which, the AuthaGraph World Map, may yield the most accurate maps of the world.

1. Classical Projections

To get an appreciation for the large number of classical projection schemes that have been developed to create 2D world maps, I suggest that you start with a visit to the Radical Cartography website at the following link, where you’ll find descriptions of 31 classical projections (and 2 polyhedral projections).

http://www.radicalcartography.net/?projectionref

Now let’s take a look at the following classical projection schemes.

  • 1569 Mercator projection
  • 1855 Gail equal-area projection & 1967 Gail-Peters equal-area projection
  • 1805 Mollweide equal-area projection
  • 1923 Goode homolosine projection

Mercator projection

The Mercator world map is a cylindrical projection that is created as shown in the following diagram.

Cylindrical projection

Source: adapted from http://images.slideplayer.com/15/4659006/slides/slide_17.jpg

Mercator map

Source:https://tripinbrooklyn.files.wordpress.com/2008/04/new_world60_small.gif?w=450

Important characteristics of a Mercator map are:

  • It represents a line of constant course (rhumb line) as a straight line segments with a constant angle to the meridians on the map. Therefore, Mercator maps became the standard map projection for nautical purposes.
  • The linear scale of a Mercator map increases with latitude. This means that geographical objects further from the equator appear disproportionately larger than objects near the equator. You can see this in the relative size comparison of Greenland and Africa, below.

Greenland & Africa

 

 

 

 

 

 

 

 

The size distortion on Mercator maps has led to significant criticism of this projection, primarily because it conveys a distorted perception of the overall geometry of the planet.

Gail equal-area projection & Gail-Peters equal-area projection

James Gail developed a cylindrical “equal area” projection that attempted to rectify the significant area distortions in Mercator projections. There are several similar cylindrical “equal-area” projection schemes that differ mainly in the scaling factor (standard parallel) used.

In 1967, German filmmaker Arno Peters “re-invented” the century old Gail equal-area projection and claimed that it better represented the interests of the many small nations in the equatorial region that were marginalized (at least in terms of area) in the Mercator projection.   Arno’s focus was on the social stigma of this marginalization. UNESCO favors the Gail-Peters projection.

Gall–Peters_projection_SWSource: By Strebe – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=16115242

Mollweide equal-area projection

The key strength of this projection is in the accuracy of land areas, but with compromises in angle and shape. The central meridian is perpendicular to the equator and one-half the length of the equator.  The whole earth is depicted in a proportional 2:1 ellipse

This projection is popular in maps depicting global distributions. Astronomers also use the Mollweide equal-area projection for maps of the night sky.

Mollweide_projection_SW

Source: Wikimedia Commons

An interrupted Mollweide map addresses the issue of shape distortion, while preserving the relative accuracy of land areas.

Interrupted Mollweide

Source: http://www.progonos.com/furuti/MapProj/Normal/ProjInt/ProjIntC/projIntC.html

Goode homolosine projection

This projection is a combination of sinusoidal (to mid latitudes) and Mollweide at higher latitudes. It has no distortion along the equator or the vertical meridians in the middle latitudes. It was developed as a teaching replacement for Mercator maps. It is used by the U.S. Geologic Service (USGS) and also is found in many school atlases. The version shown below includes extensions repeating a few portions in order to show Greenland and eastern Russia uninterrupted.

Goode Homolosine Projection

Source: http://www.progonos.com/furuti/MapProj/Normal/ProjInt/ProjIntC/projIntC.html

2. Polyhedral Projections

In his 1525 book, Underweysung der Messung (Painter’s Manual), German printmaker Abrecht Durer presented the earliest known examples of how a sphere could be represented by a polyhedron that could be unfolded to lie flat for printing. The polyhedral shapes he described included the icosahedron and the cuboctahedron.

While Durer did not apply these ideas at the time to cartography, his work laid the foundation for the use of complex polyhedral shapes to create 2D maps of the globe. Several examples are shown in the following diagram.

Polygom globes & mapsSource: J.J. van Wijk, “Unfolding the Earth: Myriahedral Projections”

Now we’ll take a look at the following polyhedral maps:

  • 1909 Bernard J. S. Cahill’s butterfly map
  • 1943 & 1954 R. Buckminster Fuller’s Dymaxion globe & map
  • 1975 Cahill-Keyes World Map
  • 1996 Waterman polyhedron projections
  • 2008 Jarke J. van Wijk myriahedral projection
  • 2016 AuthaGraph World Map

Bernard J. S. Cahill’s Butterfly Map

Cahill was the inventor of the “butterfly map,” which is comprised of eight symmetrical triangular lobes. The basic geometry of Cahill’s process for unfolding a globe into eight symmetrical octants and producing a butterfly map is shown in the following diagram made by Cahill in his original 1909 article on this mapping process.

Cahill mapping process

The octants were arrayed four above and four below the equator. As shown below, the octant starting point in longitude (meridian) was strategically selected so all continents would be uninterrupted on the 2D map surface. This type of projection offered a 2D world map with much better fidelity to the globe than a Mercator projection.

Cahill butterfly mapCahill’s 1909 map. Source: genekeys.com

You can read Cahill’s original 1909 article in the Scottish Geographical Magazine at the following link:

http://www.genekeyes.com/CAHILL-1909/Cahill-1909.html

R. Buckminster Fuller’s Dymaxion Globe & Map

In the 1940s, R. Buckminster Fuller developed his approach for mapping the spherical globe onto a polyhedron. He first used a 14-sided cuboctahedron (8 triangular faces and 6 square faces), with each edge of the polyhedron representing a partial great circle on the globe. For each polyhedral face, Fuller developed his own projection of the corresponding surface of the globe. Fuller first published this map in Life magazine on 1 March 1943 along with cut-outs and instructions for assembling a polygonal globe.

Dymaxion map 1943Fuller’s 1943 Dymaxion map. Source: Life magazine

RBF 1st Dymaxion globeFuller’s 1943 cuboctahedron Dymaxion globe.  Source: Life magazine

You can see the complete Life magazine article, “R. Buckminster Fuller’s Dymaxion World,” at the following link:

https://books.google.co.uk/books?id=WlEEAAAAMBAJ&pg=PA41&source=gbs_toc_r&redir_esc=y&hl=en#v=onepage&q&f=false

A later, improved version, known as the Airocean World Map, was published in 1954. This version of Fuller’s Dymaxion map, shown below, was based on a regular icosahedron, which has 20 triangular faces with each edge representing a partial great circle on a globe.

Dymaxion mapSource: http://www.genekeyes.com/FULLER/1972-BF-BNS-.25-.95.1-Sc-1.jpg

You can see in the diagram below that there are relatively modest variations between the icosahedron’s 20 surfaces and the surface of a sphere.

Sphere vs icosahedron

Source: https://sciencevspseudoscience.files.wordpress.com/2013/09/embedded_icosahedron.png

Dymaxion globe2

Fuller’s icosahedron Dymaxion globe.   Source: http://workingknowledge.com/blog/wp-content/uploads/2012/03/DymaxionPic.jpg

You can watch an animation of a spherical globe transforming into an icosahedron and then unfolding into a 2D map at the following link:

https://upload.wikimedia.org/wikipedia/commons/b/bb/Dymaxion_2003_animation_small1.gif

Cahill-Keyes World Map

The Cahill–Keyes World Map developed in 1975 is an adaptation of the 1909 Cahill butterfly map. The Cahill-Keyes World map also is a polyhedral map comprised of eight symmetrical octants with a compromise treatment for Antarctica. Desirable characteristics include symmetry of component maps (octants) and scalability, which allows the map to continue to work well even at high resolution.

Cahill-KeyesSource: http://imgur.com/GICCYmz

Waterman polyhedron projection maps

The Waterman polyhedron projection is another variation of the “butterfly” projection that is created by unfolding the globe into eight symmetric, truncated octahedrons plus a separate eight-sided piece for Antarctica.  The Atlantic-centered projection and the comparable Pacific-centered projection are shown below.

Waterman Atlantic

Waterman Pacific

Source, two maps: watermanpolyhedron.com

The Waterman home page is at the following link:

http://watermanpolyhedron.com/deploy/

Here the developers make the following claims:

“Shows the equator clearly, as well as continental shapes, distances (within 10 %), areas (within 10 %) angular distortions (within 20 degrees), and relative positions, as a compromise: statistically better than all other World maps.”

Myriahedral projection maps

A myriahedron is a polyhedron with a myriad of faces. This projection was developed in 2008 by Jarke J. van Wijk and is described in detail in the article, “Unfolding the Earth: Myriahedral Projections,” in the Cartographic Journal, which you can read at the following link:

https://www.win.tue.nl/~vanwijk/myriahedral/

Examples of myriahedral projections are shown below. As you can see, there are many different ways to define a 2D map using a myriahedral projection.

Myriahedral projectionSource: https://www.win.tue.nl/~vanwijk/myriahedral/geo_aligned_maps.png

AuthaGraph World Map

The latest attempt to accurately map the globe on a 2D surface is the AuthaGraph World Map, made by equally dividing a spherical surface into 96 triangles, transferring it to a tetrahedron while maintaining areas proportions and unfolding it to be a rectangle. The developers explain the basic process as follows:

“…we developed an original world map called ‘AuthaGraph World Map’ which represents all oceans, continents including Antarctica which has been neglected in many existing maps in substantially proper sizes. These fit in a rectangular frame without interruptions and overlaps. The idea of this projection method was developed through an intensive research by modeling spheres and polyhedra. And then we applied the idea to cartography as one of the most useful applications.”

 AuthaGraph World Map 2The AuthaGraph World Map. Source: AuthaGraph

For detailed information on this mapping process, I suggest that you start at the AuthaGraph home page:

http://www.authagraph.com/top/?lang=en

From here, select “Details” for a comprehensive review of the mapping technology behind the AuthaGraph World Map.

Also check out the 4 November 2016 article on the AuthaGraph World Map, “This Might Be the Most Accurate Map of the World,” at the following link:

http://motherboard.vice.com/read/this-might-be-the-most-accurate-world-map-we-have?utm_source=howtogeek&utm_medium=email&utm_campaign=newsletter