Waterman butterfly projection pros and cons

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Waterman butterfly projection pros and cons

This new HDP map belongs to the family of Cylindrical Equal Area projections in which the latitude and longitude lines form a rectangular grid. The HDP retains qualities of the other equal area cylindrical projections, but is more visually satisfying. Commissioned by ODT, Inc. At the present time, the HDP is available only in an 11" x 17" placemat size. Due to the unusual proportions of the new map, ODT also printed eight other map projections for comparison purposes on the border of the map.

The reverse side of the HDP map shows the exact same projection, but with two somewhat startling changes: south is on top; and Australia is shown in the middle of the map. How does such a simple thing as reversing the poles or changing the "centering" influence your impression of what's important? Included on this innovative map are comparison panels as thumbnails across the bottom or top of the map.

Side A has Africa at the center and North at the top. Comparison panels on the bottom include: Buckminster Fuller's Dymaxion World Map new satellite composite version -The Eckert II projection, Leonardo da Vinci's mappamundi fromthe first map of its kind and one of the first world maps that used the name "America"and a Population Cartogram. Side B is the exact same map with the poles reversed South on top and Australia-centered. This new product has a built-in quiz. It asks: Which of the images on both sides of this placemat are "area accurate"?

Below are the panels on the map that explain other alternative projections. Click on the picture for a larger image. Buckminster Fuller's Dymaxion World Map.

The visionary Fuller designed this map to help us recognize that "we're all astronauts aboard a little spaceship called Earth. Directions and spatial relationships, however, tend to be obscure.

This is an equal-area map with poles and central meridians at half the length of the equator. The meridians are broken straight lines. Image courtesy of U. Leonardo da Vinci's mappamundi. This "octant" map is dated approximately This was the first map of its kind. It is noteworthy for at least two other reasons: 1 it was one of the first world maps that used the name "America," and 2 it was one of the first world maps to lay down a south-polar continent.

Some critics believe the map was not really a work by Leonardo himself, since the accuracy and mastery in drawing are not reflective of da Vinci's usual high standards.This means you're free to copy and share these comics but not to sell them. More details. Archive What If? A webcomic of romance, sarcasm, math, and language. It turns out Monday was Steve Waterman's birthday.

His site has posters of his map, plus maybe the world's only Winkel Tripel-critiquing poetry. The comic is one large panel, with different types of map projections listed in two columns. Each listing has an illustration of that projection plus a short paragraph describing the individual who prefers that projection.

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What your favourite Map Projection says about you. Mercator [[A drawing of the Mercator projection is shown. In this the world is distorted to fit into a perfect square, centred on Africa. Robinson [[A drawing of the Robinson projection is shown.

Areas near the poles in this projection are fairly distorted, but the distortion is greatly reduced when moving toward the equator. You like coffee and enjoy the Beatles.

You think the Robinson is the best-looking projection, hands down. Winkel-Tripel [[The Winkel-Tripel projection is similar to the Robinson projection, with less distortion at the poles. However the distortion at equivalent latitudes differs as the longitude varies. You're worried it's getting played out, and are thinking of switching to the Kavrayskiy.

You once left a party in disgust when a guest showed up wearing shoes with toes. Your favourite musical genre is "post-". Hobo-Dyer [[The Hobo-Dyer projection is a cylindrical projection resulting in significant latitudinal distortion. The result is a rectangular image with the poles vertically compressed, and land near the equator stretched. You're conflict-averse and buy organic. A globe! Pierce Quincuncial [[This is a square projection centred over the north pole. The continents stretch out radially from the centre of the map and bits of Antarctica are visible in each corner of the projection.

After you first saw Inceptionyou sat silent in the theater for six hours. It freaks you out to realise that everyone around you has a skeleton inside them.

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You have really looked at your hands. The second column of projections starts here. Van Der Grinten [[This projection displays the continents inside a perfectly circular frame. The continents are displayed with similar distortion to what you would see in the Robinson or Winkel-Tripel projections. You love the Mercator projection; you just wish it weren't so square.

The earth's not a square, it's a circle. You like circles. Today is gonna be a good day! Dymaxion [[The Dymaxion projection attempts to unfold the earth into a polyhedral net, centred on the north pole.

The map has no set shape, instead it looks to be made out of a series of triangles.The Winkel Tripel projection was developed in by Oswald Winkel - Contrary to popular belief, Tripel is not somebody's name; it is a German term meaning a combination of three elements.

Winkel choose the name Tripel because he had developed a compromise projection; it does not eliminate area, direction or distance distortions; rather, it tries to minimize the sum of all three.

Prior tothe Winkel Tripel projection was not considered particularly exceptional. However, in the National Geographic Society announced that it was adopting the Winkel Tripel as its standard projection for maps of the entire world. As a result of this announcement, interest in the Winkel Tripel projection has skyrocketed over the last few years.

The Winkel Tripel is unusual in that it is created by averaging the X and Y coordinates from two other seldom-used projections: the Aitoff and the Equirectangular. The result is a projection that looks a lot like the Robinson but remember that Winkel developed his projection about 42 years before Robinson developed his, so you can't accuse Winkel of plagiarism. However, the Winkel Tripel has a few unique qualities of its own.

For example, lines of latitude in a Robinson projection are parallel straight lines, while in a Winkel Tripel they are slightly curved, nonparallel lines. Form : The Winkel Tripel has a modified planner form, which means that the developable surface is slightly curved, and not completely flat as it is in a projection with a true planner form.

Prior tothe Winkel Tripel was a fairly obscure projection. However, when the National Geographic Society announced that it was adopting the Winkel Tripel as its standard world projection, it almost certainly ensured that the projection will become much more popular in the near future.

Waterman Butterfly Map

This increase in popularity has been quite evident to those of us who work in the cartography field, and its not hard to find examples of the Winkel Tripel in use: Figure 2 shows an example of the Winkel Tripel projection being used to map the surface of Mars.

Only the future will tell if the popularity of the Winkel Tripel will continue to grow.Waterman first published a map in this arrangement in The arrangement is an unfolding of a globe treated as a truncated octahedronevoking the butterfly map principle first developed by Bernard J. Cahill — in Cahill and Waterman maps can be shown in various profiles, typically linked at the north Pacific or north Atlantic oceans.

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As Cahill was an architecthis approach tended toward forms that could be demonstrated physically, such as by his flattenable rubber-ball map. Waterman, on the other hand, derived his design from his work on close-packing of spheres. This involves connecting the sphere centers from cubic closest-packed spheres into a corresponding convex hull, as demonstrated in the accompanying graphics.

Reproject World Map with World Miller Cylindrical Projection and Save as GeoJSON Using QGIS

These illustrate the W5 sphere cluster, W5 convex hull, and two Waterman projections from the W5 convex hull. To project the sphere to the polyhedron, the Earth is divided into eight octants. Each meridian is drawn as three straight-line segments in its respective octanteach segment defined by its endpoints on two of four "Equal Line Delineations" defined by Waterman. These Equal Line Delineations are the North Polethe northernmost polyhedron edge, the longest line parallel to the equator, and the equator itself.

The intersections of all meridians with any one Equal Line Delineation are equally spaced, and the intersections of all parallels with any one meridian are equally spaced.

Popko notes the projection can be gnomonic too. From Wikipedia, the free encyclopedia. Symmetry: Culture and Science. CreateSpace Independent Publishing Platform.

Map Projections & What They Say About You

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Map projection. History List Portal. By surface. Albers Equidistant Lambert conformal. Bonne Bottomley Polyconic American Werner.

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Gnomonic Orthographic Stereographic. Equidistant Lambert equal-area.Teaching our youth with a Mercator or Robinson or the Winkel Tripel projection in the 21st century is a continuing academic problem that many, perhaps most, are not even aware exists. No other projection systems have been able to handle the management of those characteristics collectively as well.

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Price in Canada and United States All prices include shipping. International All prices include shipping. Payment may be done by Interac e-mail transfer or by using PayPal.Also known as equirectangular, equidistant cylindrical, simple cylindrical, or rectangular, this projection is very simple to construct because it forms a grid of equal rectangles.

Because of its simple calculations, its usage was more common in the past. In this projection, the polar regions are less distorted in scale and area than they are in the Mercator projection. This simple cylindrical projection converts the globe into a Cartesian grid. Each rectangular grid cell has the same size, shape, and area. The grid cells are perfect squares. In this projection, the poles are represented as straight lines across the top and bottom of the grid. Distortion increases as the distance from the standard parallels increases.

North, south, east, and west directions are accurate. General directions are distorted, except locally along the standard parallels. The scale is correct along the meridians and the standard parallels.

Noticeable distortion of all properties away from standard parallels. Best used for city maps or other small areas with map scales large enough to reduce the obvious distortion. Used for simple portrayals of the world or regions with minimal geographic data. This makes the projection useful for index maps. Arc GIS for Desktop.Try as you might, you just cannot flatten an orange peel without tearing, squashing or stretching it. Likewise, when cartographers try to flatten the Earth for a map projection, distortions in terms of shape, distance, direction, or land area are inevitable to creep in.

Depending on the purpose they are trying to serve, the number of possible map projections is limitless. However, which map projection should be used for general purposes, such as, for hanging in classrooms or on TV news? The most popular map projection in the world has been around for years now. Mercator was designed as a navigational tool for sailors as it was most convenient to hand-plot courses with parallel rules and triangles on this map. In most maps, when you try to fix one kind of distortion, you increase another kind of distortion.

However, Mercator is one of those rare maps whose answer to latitudinal distortion was to ensure that the longitudinal distortion is equally bad! On a Mercator projection, Greenland is roughly the same size as Africa.

In reality, Africa is almost 14 times largerand Greenland can fit inside China no less than four times. The map also suggests that Scandinavian countries are larger than India, whereas, India is actually three times the size.

The biggest criticism for the skewed Mercator projection came in from German filmmaker and journalist Arno Peters. Peters argued that by enlarging Europe and North America, Mercator maps were giving white nations a sense of supremacy over non-white nations. His solution? An equal-area projection that would show the correct sizes of countries relative to each other. Not that the Gall-Peters projection came without any flaws. In its quest of removing size distortions, the map stretched some places near the poles horizontally to a shocking degree.

It also stretched land masses vertically near the Equator. American geographer and cartographer Arthur H. Robinson intended the map, which is neither equal-area nor conformal, as a general purpose tool. I started with a kind of artistic approach.


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