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| Winkel Tripel projection | |
|---|---|
| Name | Winkel Tripel projection |
| Type | compromise map projection |
| Inventor | Oswald Winkel |
| Introduced | 1921 |
| Family | azimuthal–cylindrical hybrid |
| Projection | arithmetic mean of Aitoff and equirectangular |
Winkel Tripel projection is a compromise map projection created to reduce overall distortion of area, direction, and distance on world maps. Invented in 1921 by Oswald Winkel, it combines elements of the Aitoff projection and the equirectangular projection to produce visually pleasing world maps used by cartographers, publishers, and institutions. The projection gained prominence through adoption by organizations such as the National Geographic Society and in atlases produced by the Times Atlas and other cartographic publishers.
Oswald Winkel introduced the projection in 1921 in response to competing proposals such as the Mercator projection, the Robinson projection, and the Aitoff projection. Winkel sought a practical compromise among designs pioneered by Gerardus Mercator, John P. Snyder, and earlier figures associated with the development of map projections like Adrien-Marie Legendre and Johann Heinrich Lambert. The projection entered broader cartographic discourse during the 20th century with debates involving institutions including the National Geographic Society, the Royal Geographical Society, and commercial atlas makers such as the Times Atlas of the World and Miller Atlas publishers. During the latter half of the 20th century, cartographers like Arno Peters and Christopher Saxton prompted renewed public interest in alternatives to traditional projections, indirectly increasing attention to Winkel’s design.
The Winkel Tripel is defined as the arithmetic mean of the coordinates of the Aitoff projection and the equirectangular projection (also called the equidistant cylindrical or plate carrée). For a point with longitude λ and latitude φ relative to a chosen central meridian and equator, the equirectangular coordinates are x1 = λ cos φ0, y1 = φ (with standard parallel φ0 often set to 0), while the Aitoff coordinates x2 and y2 are computed via an auxiliary azimuthal equidistant transform involving the half-longitude and the central angle; the Winkel Tripel coordinates are then x = (x1 + x2)/2 and y = (y1 + y2)/2. Implementations used by mapping libraries and GIS systems follow the formulations codified in resources associated with agencies such as United States Geological Survey and software projects like PROJ (cartographic projections library) and GDAL. Parameter choices, including the standard parallel and central meridian (e.g., Prime Meridian at Greenwich), determine the visual balance between distortion types and are specified in many atlas and GIS configuration files.
As a compromise projection, the Winkel Tripel does not preserve any single metric globally: it is neither conformal like the Mercator projection nor equal-area like the Mollweide projection or Lambert azimuthal equal-area projection. It minimizes a weighted sum of angular and area distortion similar in spirit to measures used in studies by cartographers at institutions such as the Royal Geographical Society and the National Academy of Sciences. Distortion characteristics are commonly visualized with Tissot’s indicatrices and quantified by root-mean-square angular and areal error metrics used in analyses by universities including Massachusetts Institute of Technology and University of Cambridge. The projection produces moderate distortion near the poles comparable to the Robinson projection while reducing extreme polar enlargement characteristic of the Mercator; polar regions remain compressed relative to true scale similar to many pseudocylindrical projections favored by atlas makers like Hermann Fischer and publishers such as Oxford University Press.
The Winkel Tripel achieved wide exposure after adoption by the National Geographic Society for its world maps in the late 20th century, replacing the Robinson projection in many editions of National Geographic Atlas of the World. Commercial atlas publishers including Times Atlas, Rand McNally, and HarperCollins have used the projection on world maps and wall charts. Academic and educational materials from institutions such as Harvard University, Stanford University, and University of Oxford reference the projection when illustrating tradeoffs among projections in courses and textbooks. GIS and cartographic software packages—including Esri, QGIS, and GRASS GIS—provide routines for rendering the projection, and online mapping platforms and encyclopedias have displayed global overviews using Winkel Tripel to balance aesthetics and distortion.
Compared with the Mercator projection, Winkel Tripel greatly reduces area exaggeration near the poles while sacrificing conformality, making it preferable for world maps in geography textbooks and atlases published by National Geographic and Times Atlas. Against the Robinson projection, Winkel Tripel often yields lower combined angular and areal error metrics reported in cartographic literature from institutions like Columbia University and University of Wisconsin–Madison. When set against equal-area projections such as the Albers projection or Mollweide projection, Winkel Tripel prioritizes visual balance over strict area preservation favored by scientific thematic maps used by organizations like the Food and Agriculture Organization and United Nations statistical agencies. Comparisons in peer-reviewed journals often reference benchmark work by cartographers at Pennsylvania State University and University College London.
Several adaptations of the Winkel Tripel adjust the standard parallel, central meridian, or weighting between the Aitoff and equirectangular components to emphasize area or angular fidelity; such parameterized variants are implemented in projection libraries like PROJ (cartographic projections library) and used by GIS practitioners at National Oceanic and Atmospheric Administration and British Antarctic Survey. Hybrid approaches blend Winkel Tripel principles with pseudocylindrical modifications derived from the Eckert projections or azimuthal transforms developed in research at institutions like Technical University of Munich and Delft University of Technology. The projection’s conceptual framework influenced newer compromise projections proposed in academic conferences hosted by organizations such as the International Cartographic Association and featured in proceedings involving cartographers from University of California, Berkeley and University of Toronto.