The Winkel Tripel projection (Winkel III), a modified azimuthal map projection, is one of three projections proposed by Oswald Winkel in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection: The name Tripel (German for "triple") refers to Winkel's goal of minimizing three kinds of distortion: area, direction and distance.
where is the longitude minus that of the central meridian of the projection, is the latitude, is the standard parallel for the equirectangular projection, and
is the unnormalized cardinal sine function (with the discontinuity removed). In his proposal, Winkel set :
A closed form inverse mapping does not exist, and computing the inverse numerically is somewhat complicated .
Goldberg and Gott show that the Winkel tripel fares well against several other projections analyzed against their measures of distortion, producing small distance errors, small combinations of Tissot indicatrix ellipticity and area errors, and the smallest skewness of any of the projections they studied. By a different metric, Capek’s “Q”, the Winkel tripel ranked ninth among a hundred map projections of the world, behind the common Eckert IV projection and Robinson projections.
In 1998, the Winkel Tripel projection replaced the Robinson projection as the standard projection for world maps made by the National Geographic Society. Many educational institutes and textbooks followed National Geographic's example in adopting the projection, and most of those still use it.
Famous quotes containing the word projection:
“In the case of our main stock of well-worn predicates, I submit that the judgment of projectibility has derived from the habitual projection, rather than the habitual projection from the judgment of projectibility. The reason why only the right predicates happen so luckily to have become well entrenched is just that the well entrenched predicates have thereby become the right ones.”
—Nelson Goodman (b. 1906)