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The Waterman "Butterfly" World Map is a map projection created by Steve Waterman. Waterman first published a map in this arrangement in 1996. The arrangement is an unfolding of a polyhedral globe with the shape of a truncated octahedron, evoking the butterfly map principle first developed by Bernard J.S. Cahill (1866–1944) in 1909
Short title: Waterman Butterfly map of the world – coastlines, graticule, and indicatrices: Image title: A map of the world, showing all landmasses with 10° graticule and Tissot's indicatrices of diameter 1,000 km and spacing 30°.
Gott, Goldberg and Vanderbei’s double-sided disk map was designed to minimize all six types of map distortions. Not properly "a" map projection because it is on two surfaces instead of one, it consists of two hemispheric equidistant azimuthal projections back-to-back. [5] [6] [7] 1879 Peirce quincuncial: Other Conformal Charles Sanders Peirce
In the same work as the hemisphere-in-a-square projection, Adams created maps depicting the entire globe in a rhombus, hexagon, and hexagram. [7] [8] Bernard J. S. Cahill invented the "butterfly map", based on the octahedron, in 1909. This was generalized into the Cahill–Keyes projection in 1975 and the Waterman butterfly projection in 1996.
From cover of 1919 pamphlet by Cahill, "The Butterfly Map", 8 p. Bernard Joseph Stanislaus Cahill ( London , January 30, 1866 - Alameda County , October 4, 1944 [ 1 ] [ 2 ] ), American cartographer and architect , was the inventor of the octahedral "Butterfly Map" (published in 1909 and patented in 1913 [ 3 ] ).
The Behrmann projection with Tissot's indicatrices The Mercator projection with Tissot's indicatrices. In cartography, a Tissot's indicatrix (Tissot indicatrix, Tissot's ellipse, Tissot ellipse, ellipse of distortion) (plural: "Tissot's indicatrices") is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize local ...
Cahill's largest published butterfly map, nearly a century ago, was a relatively small 16 x 22" black-and-white version, a desk map. The latest Watermans are 43 x 54", in full color. While I have criticized certain of its design details, the innovation and workmanship of the Waterman butterfly map and projection speak for themselves.
The Cahill–Keyes projection was designed with four fundamental considerations in mind: visual fidelity to a globe, proportional geocells, 10,000 km lengths for each of its octants' three main joined edges, and an M-shape Master-Map profile. The resulting map comprises 8 octants. Each octant is an equilateral triangle with three segments per side.