Our previous take on map projections presented the main three types of map projections (Cylindrical, Conic, and Azimuthal Map Projections) and some of the most popular projections of each type such as Lambert Conformal Conic, Mercator, or Robinson map projection.

Although the group of the most popular map projections is relatively limited, there are dozens and dozens different map projection types. They aren’t as popular as Mercator or Lambert Conformal Conic but they exist and are used for a variety of purposes. Most of them are unknown to the regular map users, even though most of us are in contact with them on a daily basis.

For instance, all large digital map systems, like Google Earth, OpenStreetMap project, or Bing Maps all use Web Mercator projection; National Geographic Society stopped using Robinson map projection back in 1998, replacing it with Winkel tripel projection; before it started using Robinson projection the NGS used Van der Grinten projection for more than sixty years.

As we said, many map projection types aren’t well known as a couple of the most popular ones, but they are used all over the world and should be known to all mapping lovers. Let us start with the Web Mercator projection.

Web Mercator projection

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Web Mercator, or Spherical Mercator, is a coordinate system used by all web mapping tools. It was first implemented by Google when the company started working on their Google Maps project.

The projection encompasses almost the entire world, the only regions not included are polar regions (latitudes -85 to 85). Web Mercator is non-conformal, unlike the standard Mercator projection. It is implemented because it can display an extensive diversity of data sets, but since it ignores the ellipticity of Earth it isn't suitable for accurate measurement. The ellipticity of Earth is not included for faster computation.

Gauss–Krüger projection

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Gauss–Krüger projection is the basis of the Universal Transverse Mercator coordinate system (UTM) we showed in our last article. The projection was developed by Carl Friedrich Gauss, a German mathematician, one of the greatest mathematicians of all times. Gauss developed the system in 1825, and in 1912 Johann Heinrich Louis Krüger further developed it. The work on the projection continued until 1923 and the release of the Gauss–Krüger coordinate system and projection.

It is the only conformal generalizations of the transverse Mercator projection with a constant scale on the central meridian and is the most used projection when it comes to accurate large scale mapping. At the moment, the Gauss–Krüger projection is used by many countries such as Canada, South Africa, Germany, Australia and others as a geodetic mapping foundation.

The projection features low distortion near the central meridian, its distortion increases near the right and left boundaries of the projection, and the map is conformal. The shapes of small regions are reasonably well preserved because the point scale of the projection is independent of direction.

Equirectangular projection

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Equirectangular projection, also known as geographic projection, is one of the oldest map projections humans ever created. It dates back to AD 100, according to Ptolemy. The geographic projection made by Marinus of Tyre is a relatively simple map projection with the equator as a standard parallel; Equirectangular projection is neither equal-area nor conformal.

The projection map circles of latitude to horizontal straight lines of constant spacing and meridians to vertical straight lines. It is rarely used for navigation and map projects. On the other hand, the projection met its purpose in thematic mapping. Thematic maps are maps showing a particular theme connected to a specific area. We all saw dozens of thematic maps, like a map of an average income per capita, or a global map showing a percent of patients in each and every country suffering from heart diseases.

Van der Grinten projection

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Van der Grinten projection is interesting because it was used by the National Geographic Society for more than 65 years. The projection was constructed by Alphons J. van der Grinten in 1898, and in 1922 the NGA started using the projection for their maps of the world. Van der Grinten projection was used by the NGA until 1988 when the society started using Robinson projection for its maps.
This projection features straight Equator and central meridian with all other parallels and meridians shown as circular arcs, with nonconcentric meridians regularly spaced along the Equator.

Van der Grinten projection is a compromise map projection, meaning that it is neither equal-area nor conformal, like the previous projection we covered, the Equirectangular projection. It is known for its huge distortion of Polar Regions, and for the fact that it projects the entire Earth in the shape of a circle. The projection saw three modifications, Bludau's modification of the original, with parallels crossing meridians at right angles, Bludau's modification of the original, with straight, horizontal parallels, and the second original projection, bounded by two identical circles with centers spaced 1.2 radii apart; the inner hemisphere is also circular.

Goode homolosine projection

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Developed in 1923 by John Paul Goode, the Goode homolosine projection is an alternative to a classic Mercator projection. It is mostly used for world maps and is known as an "orange-peel map" because of its interruptions, resembling a hand peeled orange rind. The projection is known for its multiple interruptions giving it a unique and interesting view of the world. The projection is pseudocylindrical, equal-area, composite map projection; all latitudes are straight lines.

Goode made the projection by interrupting the Mollweide projection and later further modifying it. The name was made by fusing two names: "homolographic" and "sinusoidal,” since the projections is a combination of the Mollweide and sinusoidal projections. The Mollweide is used for north of 40° 44' and south of -40° 44', while the sinusoidal projection is used between those two latitude values for the equatorial part of the world.

There are a couple of variations of the Goode homolosine projection and their all include interruptions. The most well-known form includes 5 interruptions, dividing the North Atlantic, the South Atlantic, the South Pacific, the Indian Ocean, and the entire east/west meridian of the map. All laitudes are straight lines,
Interruptions are there in order to achieve a minimal distortion of the entire world, with two variations. The first interrupts oceans and is called land-oriented. The second variation interrupts continents and is known as the ocean-oriented. Due to the interrupted nature of the projection, there are six straight longitude lines in total, with each lobe having its own central meridian. The overall central meridian is zero.

Some the features of the Goode homolosine include accurately represented areas, accurate scale along all parallels in the sinusoidal part and the central meridians of the lobes, and the distortion of local angles everywhere except along the central meridians of the lobes and the equator in the sinusoidal portion.

The projection is used by The United States Geological Survey (USGS) Center for Earth Resources Observation and Science (EROS) that provides all data in Goode's homolosine projection.

Mollweide projection

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Mollweide projection is used for world maps. The projection is an equal-area, pseudocylindrical map projection featuring a straight equator perpendicular to a central meridian one-half its length, with other parallels compressing near the poles and other meridians spaced equally at the equator in order to preserve areas.

The projection was invented in 1805 by Karl Brandan Mollweide, a German mathematician, and astronomer. Aside from being used for world maps, the Mollweide projection is utilized for star atlases and maps depicting global distributions. The projection wasn’t popular until Jacques Babinet modified it and presented it as the homalographic in 1857. The most famous use of the Mollweide projection was the map of cosmic microwave background radiation, which took nine years to construct and which gave evidence for the Big Bang.

Waterman butterfly projection

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The Waterman butterfly projection rose from the butterfly map principle first developed by Bernard J.S. Cahill in 1909. The projection was created by Steve Waterman in 1996. The projection shows a globe as a truncated octahedron.
The Waterman projection features a clear projection of the equator, and well as preserved continental shapes, distances and areas (within 10 percent), and angular distortions ( within 20 degrees ). The Waterman butterfly projection isn’t quite popular but it is better than most other world maps.

The projection has two variations, showing the world from Atlantic and Pacific view; in other words, Atlantic variations keeps the Atlantic ocean uninterrupted, while the Pacific view does the same for Pacific ocean. The Atlantic view puts the Atlantic Ocean in focus, with Europe and Africa at the left, and North and South America at the right. Pacific view greatly differs, showing the north-east part of the Pacific Ocean in the middle, with Asia and Australia to the left, and North America along with the rest of the Pacific on the right side of the map.

They there are, some of the not-so-popular-but-still-interesting map projections. Although they aren’t well known among the general population, those projections can be recognized by almost any person, without knowing their names.

They are used for a variety of purposes, although of less extent than the most popular map projections we have shown last time. We hope that you learned something new and that you realized how the world of map projections is varied.