Waterman butterfly projection


Waterman butterfly projection

The Waterman "Butterfly" World Map Projection was created by Steve Waterman and published in 1996. It is an octahedral transformation of a globe, reviving the Butterfly Map principle first developed by Bernard J.S. Cahill (1866-1944) in 1909. Whereas Cahill's approach was that of an architect, Waterman derived his design from his work on close-packing of spheres.

This involved the interpretation of a spherical extraction from cubic closest packed spheres, into a corresponding convex hull. Then for its projection; straight lines were used to define each 5 x 5 section onto this convex hull.

Projection employed an equal length delineation approach for the equator. Latitudes were drawn in three straight line sections ( in each octant ) - from pole to fold-line, fold-line to largest line parallel to equator, and then from there to the equator. The largest line parallel to the equator also has equal length delinations. One particular Waterman Polyhedron best served to minimize land sinues ( breaking up of land masses ) and was therefore chosen.

Like Buckminster Fuller's 1943 Dymaxion Projection, an octahedral Butterfly Map can show all the continents uninterrupted if its octants are divided at the proper meridian, and joined, e.g., at the North Atlantic, as in this version, where the meridian cut is 20° W.

Waterman's 1996 edition is a Beta, approximating an Equal Area approach. A more precise rendering is in preparation, expected by 2008, but the current version nonetheless shows reasonably good size, shape, and position of the continents, especially as compared to a globe. Its graticule (latitude-longitude weave) is done at a 5-degree resolution.

ee also

*Waterman polyhedron
*Bernard J.S. Cahill
*World map

External links

* [http://www.watermanpolyhedron.com Steve Waterman's Home Page]
* [http://odtmaps.com/detail.asp_Q_product_id_E_WAT-26.5x38-V1-proto ODT Resources for World Maps]
* [http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/projPoly.html Carlos A. Furuti, Map Projections: Polyhedral Maps]
* [http://www.progonos.com/furuti/MapProj/Normal/ProjTbl/projTbl.html Carlos A. Furuti, All major map projections]
* [http://www.watermanpolyhedron.com/CART5.html Rotating Waterman as globe Izidor Hafner]
* [http://in-betweener.org/flatworlds/maps/earth-literacy-UNESCO-60th.html Flat Worlds, Earth Literacy, and Map Alphabetism] (Write-up comparing other world maps.)
* [http://www.pnyv.org/index.php?id=495 Positive News Youth Views site] (Waterman selected as their signet.)


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