#ortelius oval

[map-projection-showdown]

WATERMAN BUTTERFLY vs ORTELIUS OVAL

Waterman Butterfly Polyhedral Compromise

Designed by Steve Waterman in 1996, the Waterman Butterfly projects the globe onto a truncated octahedron, which is unfolded into a "butterfly" shape inspired by Cahill's 1909 projection. The specific octahedron used is based off the convex hull of packed spheres, which is what Waterman was originally working on when he created this projection. Usually presented with Antarctica in a separate circle below the map, see below the cut for this.

It is one of the projections featured in xkcd 977.

Ortelius Oval Miscellaneous Compromise

First created by either Battista Agnese in 1540 or Abraham Ortelius in 1570, (Unknown if Agnese's map is the same construction), this map was used for the world map in what is considered the first modern atlas, the Ortelius' Theatrum Orbis Terrarum. It was widely used for world maps during the 16th and 17th centuries, but has since fallen out of use. The front hemisphere forms a circle that is the same as the Apian I projection.

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Waterman with separate Antarctica:

Political:

Tissot's Indicatrices:

Images created by Tobias Jung (CC BY-SA 4.0) from map-projections.net

[sunnunderthesun]

The Fool's Cap Map of the World is timeless

As someone with no knowledge of Latin, my first impression of the foolscap map was that it depicted the universality of the traditional fool's sagacity. According to Sam Keen, "the authentic life has frequently been pictured under the metaphor of the fool." However, delving into the history of the foolscap map made me realize that I was looking at it in rather a sentimental way as the fool's cap reminded me only of the social status of Shakespeare's wise fools.

Here's the copy of the Cordiform map of the world within the fool's cap held by Newberry Library.

A librarian there informs me, Of the few known copies to exist, Newberry Library's copy was acquired last century by Franco Novacco of Venice, and the library bought his collection ca. 1967.

Robert Burton's Geography of Melancholy states: The “foolscap map,” as it is known among cartographers, measures 360 mm x 480 mm and is printed from a finely executed copper-plate engraving. The map was published separately and anonymously, with no information as to the date or place of publication on it. It is believed to have been published in Antwerp, ca. 1590. The geographical details on the small, oval map that takes the place of the fool’s face identify it as a copy of one of Ortelius’s latest plates; we can date the map with some certainty as being post-1587, since “the prominent south- [west] bulge to the coastline of South America appearing on nearly all maps before this date has been corrected.” While much of our information remains sketchy, we do possess some hard facts about the map. It was based on an earlier foolscap world map by the French mapmaker Jean de Gourmont, which was published in Paris ca. 1575... The earlier foolscap map was made from a woodcut and is somewhat smaller than the later copper engraving; the actual map of the world on the woodcut is a small oval similarly framed within the hood of a jester’s cap, where the face would ordinarily be. As on the anonymous copper engraving, the map on de Gourmont’s woodcut is derived from a world map by Ortelius—but in this case it is Ortelius’s earlier world map of 1570.

Jean de Gourmont's foolscap world map

From The History of Court Fools by Dr. Doran, I learn that around the time Gourmont's map was published, the witty and brave Chicot was a prominent court jester of Henry III of France. The King benefitted from his company, and he would "appeal to Chicot, not as his jester, but as a man of sense, and his friend." Unlike the other French official jesters, Chicot was allowed to go beyond the confines of the palace. But, the consequence of a court fool's bravery and bold humour, if found offensive by the noblemen, could be fatal. Chicot wasn't spared from it either. Even a celebrated "Bouffon de Cour" in the sixteenth century could be subjected to "stripes and imprisonment for being too talkative". There are records of a certain fool who lost his life as a punishment for playfully drawing his wooden sword upon his King who considered the act a treason.

During that period, political satires were published under the names of renowned court jesters like Chicot as the "author could not safely print his own name; and he found not only safety but profit in publishing his book under the name of some more popular fool." It makes me wonder if the maker of the foolscap map, possibly printed in Antwerp in the late sixteenth century, remained anonymous because he was concerned about his safety as the image belittled monarchy.

Studying the foolscap map with all its epigrammatic phrases carefully, I understand that it's the humourous portrayal of a ubiquitous truth — our vanity and endless lust for wealth and power, make the world a mad habitat — at the expense of the fool's costume. Perhaps the creator of the foolscap map was inspired by an official jester who actually lampooned the society in such a self-deprecating fashion. I say self-deprecating for, at that time, a fool wasn't allowed to appear in the royal court of France "without his livery". However, the world map of the sixteenth century can easily be replaced in that image with our modern world map within the fool's cap.

[jkottke]

Urbano Monte's Massive Map of the Earth (1587)

In 1587, Urbano Monte made the largest known early map of Earth. The map consists of 60 panels that were meant to be assembled into a planisphere (a circular map that rotates about a central axis) measuring 10 feet across. The David Rumsey Map Center recently acquired a manuscript of Monte's map and digitally assembled all 60 pieces into the full map (inlined above but click through to zoom/pan).

Of great interest is the attempt Monte makes to make his map not just a geographical tool but to show climate, customs, length of day, distances within regions -- in other words, to create a universal scientific planisphere. In his dedication on tavola XL he specifies how to arrange the sheets of the mappamondo and makes it explicit that the whole map was to be stuck on a wooden panel 5 and a half brachia square (3.25m) so that it could be revolved around a central pivot or pin through the north pole.

The individual map panels looked like this:

Of course, once the image is digital you can map it into all sorts of different projections like Mercator or Ortelius oval projection.

Jeremy Ashkenas even created a rotatable & zoomable globe of Monte's map that is incredibly fun to play with.

[zerostatereflex]

The Enduring Mystery of the ‘Fool’s Cap Map of the World.

“The Fool’s Cap Map of the World “is one of the biggest mysteries in the history of western cartography,” Jacobs writes.“

“In the engraving above, colloquially referred to as the Fool’s Cap Map of the World, the intricate bust of a court jester—complete with bells and bauble—includes a face showing the world as it had been charted in the 16th century. Despite researchers making close examinations of the map, they can only speculate why, when, and by whom this peculiar map was made, explains the map journalist Frank Jacobs on his blog about strange maps. “

“This is what we do know about the map: measuring about 14 inches by 19 inches and printed with a copper-plate engraving, researchers estimate that the map dates between 1580 and 1590. That’s because it matches the Ortelius oval map projections that had become common in the late 16th and early 17th centuries.”

“Traditionally, the fool was one of the only people who could freely criticize the monarchy. Some academics have thus interpreted that the map was created as a commentary on the inaccuracy of depictions and charts of the world in an age where much of it had yet to be thoroughly documented and discovered. Maps of this era were even known to be altered visually to support certain political ends.“

Mystery’s are awesome, :D

[map-projection-showdown]

THE GRAND FINAL

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]

[link to previous rounds' polls and third place playoff]

[map-projection-showdown]

WATERMAN BUTTERFLY vs PEIRCE QUINCUNCIAL

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]

Peirce Quincuncial Polyhedral Conformal Round 1: [Peirce Quincuncial vs Van der Grinten] Round 2: [Peirce Quincuncial vs Natural Earth II] Round 3: [Peirce Quincuncial vs Cahill-Keyes]

This first semi-final compares two projections with similar aims and a similar construction, will the Peirce Quincuncial repeat its victory over the Cahill-Keyes or will the popular butterfly layout propel Waterman's projection to the final!

Both these projections split the globe into octants, but go about flattening the octants slightly differently. Peirce represented each octant with a right-angle triangle, which makes the map into a simpler layout with less interruptions, but causes four points around the equator (the midpoints of the sides) to have large area distortion, though these points are all in the ocean.

Waterman on the other hand followed Cahill's lead and used equilateral triangles with the corners squashed a bit, while this does mean it isn't conformal and is more complex, it has slightly less size distortion. Waterman's projection is also often presented with Antarctica off in its own circle underneath the rest of the map.

[Direct comparison on map-projections.net]

[link to all polls]

[map-projection-showdown]

WATERMAN BUTTERFLY vs CAHILL CONFORMAL BUTTERFLY

Waterman Butterfly Polyhedral Compromise Round 1: [Waterman Butterfly vs Ortelius Oval]

Cahill Conformal Butterfly Polyhedral Conformal Round 1: [Cahill Conformal Butterfly vs Miller Cylindrical]

Two butterfly projections face off in this poll, Waterman's projection which was probably popularised by xkcd 977 (Given that it was published two years before the Wikipedia page was made for it), and Adam's modification of Cahill's original butterfly to make it conformal, which has largely been overshadowed by both Waterman's and the original.

While the Cahill Conformal butterfly is of course conformal, this does invite greater area distortions, in this case at the corners, this is most noticeable in Antarctica, which is definitely larger than on Waterman's projection. However the simpler outline shape of the Cahill is probably more intuitive than the Waterman.

[Direct comparison on map-projections.net]

[link to all polls]

[map-projection-showdown]

WINKEL TRIPEL vs WATERMAN BUTTERFLY

Winkel Tripel Pseudoazimuthal Compromise Round 1: [Winkel Tripel vs Cassini] Round 2: [Winkel Tripel vs McBryde-Thomas No. 4]

Waterman Butterfly Polyhedral Compromise Round 1: [Waterman Butterfly vs Ortelius Oval] Round 2: [Waterman Butterfly vs Cahill Conformal Butterfly]

Two very popular projections that I suspected would make it this far.

The Winkel Tripel has been widely used for atlases and other general purpose world maps since National Geographic started using it in 1998, a lot of people seem to regard it as the best of the more "regular" equatorial aspect projections due to its low distortions.

The Waterman Butterfly on the other hand manages to get even lower distortions by splitting the earth up into an octahedron. Like most polyhedral maps this low distortion does common with a less familiar shape that puts things in places you might not expect.

[Direct comparison on map-projections.net]

[link to all polls]