#stereographic

THE WATERMAN BUTTERFLY!

Congratulations to Waterman's projection for this highly esteemed prize.

In second and third place we have the Stereographic projection and the Peirce Quincuncial.

WATERMAN BUTTERFLY vs STEREOGRAPHIC

Waterman Butterfly Polyhedral Compromise Round 1: [Waterman Butterfly vs Ortelius Oval] Round 2: [Waterman Butterfly vs Cahill Conformal Butterfly] Round 3: [Waterman Butterfly vs Winkel-Tripel] Semi-Final: [Waterman Butterfly vs Peirce Quincuncial]

Stereographic Azimuthal Conformal Round 1: [Stereographic vs Eckert IV] Round 2: [Stereographic vs Azimuthal Equidistant] Round 3: [Stereographic vs Spilhaus-Adams] Semi-Final: [Stereographic vs Dymaxion]

Honestly two projections that I didn't think would get this far, I expected the final to be either the Peirce Quincuncial or Cahill Butterfly against one of the Lee variants! I find it interesting that both these projections are centred on 20°W rather than the prime meridian like most maps. Since we've already seen these projections for the four previous rounds I won't go into masses of detail here.

Waterman's Butterfly projection, invented in 1996 and inspired by Cahill's 1909 butterfly, is constructed by projecting the surface of the Earth onto a truncated octahedron and then unwrapping it. This results in a compromise projection with very low shape distortion and size distortion. It is also commonly shown with Antarctica placed in it's own little circle at the bottom.

In use since the Ancient Egyptians, each hemisphere of the stereographic projection can be constructed by projecting from a point on the surface of the Earth onto a plane tangent to the point on the globe opposite it like this. This results in a conformal projection that is the only one to represent all small circles as circles rather than ovals.

[Direct comparison on map-projections.net]

Dymaxion Polyhedral Compromise Round 1: [Dymaxion vs Stab-Werner] Round 2: [Dymaxion vs Lee Conformal Tetrahedron] Round 3: [Dymaxion vs Equidistant Conic]

Stereographic Azimuthal Conformal Round 1: [Stereographic vs Eckert IV] Round 2: [Stereographic vs Azimuthal Equidistant] Round 3: [Stereographic vs Spilhaus-Adams]

The second semi-finals sees Buckminster Fuller's futurist map face off against the oldest projection in this tournament, in use since the Ancient Egyptians.

The Dymaxion projection was presented as a new way of looking at the world. Without the constraints of north and south it uses the net of an icosahedron as a basis to show all the continents without interruptions and how they're laid out compared to each other (the Peirce Quincuncial gets close but still splits Antarctica), because of this it's often used for projections that show human migration from Africa across the continents, and because of its accurate shapes and low size distortion it has become a popular choice for people's "favourite projection".

The Stereographic on the other hand has a very simple construction (projecting from a point on the surface to a plane opposite it like this for each hemisphere), and as such has found many uses over the past 2000+ years. Originally used for star charts, it was commonly used for world maps in the 16th and 17th centuries. As it is the only projection that shows all small circles on the globe as circles on the map, it is also often used for mapping circular features such as craters on the Moon, so they show as true circles rather than ovals.

[Direct comparison on map-projections.net]

Stereographic Azimuthal Conformal Round 1: [Stereographic vs Eckert IV] Round 2: [Stereographic vs Azimuthal Equidistant]

Spilhaus-Adams Polyhedral Conformal Round 1: [Spilhaus-Adams vs Danseiji IV] Round 2: [Spilhaus-Adams vs Lee-Concialdi]

Two projections that show how not-conformal a conformal projection can look when area inflation gets involved.

The Stereographic is the oldest projection in the tournament, initially used for star charts long before it came to be used for Earth, it represents each hemisphere conformally in a circle, though the area distortion that grows towards the edge does make Brazil and West Africa look weird.

The Spilhaus-Adams is one of the more unique maps in the tournament, presenting a view of earth the prioritises keeping oceans intact rather than landmasses (And in fact beating two other projections with that aim in previous rounds). Given that it distorts land (especially Argentina and China) to unrecognisability, it is usually shown without the land, see below the cut.

[Direct comparison on map-projections.net]

[link to all polls]

Azimuthal Equidistant Azimuthal Equidistant Round 1: [Azimuthal Equidistant vs Kavrayskiy VII]

Stereographic Azimuthal Conformal Round 1: [Stereographic vs Eckert IV]

Two azimuthal projections face off in this poll, who will win between these two projections that were both first used by the Ancient Egyptians for star charts.

While the images I'm using here show them in different aspects, both of them can be used differently, the stereographic projection is usually shown in two hemispheres as it can't show the whole world from one tangent point, while the azimuthal equidistant is usually shown in a single circle due to its equidistant property.

If you check out the direct comparison below you can see the difference when they both use the same equatorial hemispheres, the stereographic projection being conformal gives it more accurate shapes, but of course also leads to greater size distortion.

[Direct comparison on map-projections.net]

Stereographic Azimuthal Conformal

The oldest projection in this tournament, the Stereographic projection was first used by the ancient Egyptians some time around 200 BCE. It can be used in a polar aspect (like the Azimuthal Equidistant), but the equatorial aspect here is often used for atlases such as this one by Rumold Mercator, who popularised its usage. Prior to the 16th century this projection was mainly used for star charts rather than maps of the world.

Eckert IV Pseudocylindrical Equal-Area

Invented by Max Eckert in 1906, the Eckert IV is one of the more widely used equal-area projections. I have seen it proposed as an better alternative to the sort of people who call for the Gall-Peters to be used in schools, as being pseudocylindrical reduces the shape distortion compared to equal-area cylindrical projections.

Eckert's projections come in pairs, with the odd numbered ones (the Eckert III) being a compromise with evenly spaced parallels, and the even numbered ones being equal-area.

[link to all polls]