Two-point equidistant projection

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Two-point equidistant projection of Eurasia. All distances are correct from the two points (45degN, 40degE) and (30degN, 110degE). Two-point equidistant projection SW.jpg
Two-point equidistant projection of Eurasia. All distances are correct from the two points (45°N, 40°E) and (30°N, 110°E).
Two-point equidistant projection of the entire world with Tissot's indicatrix of deformation. The two points are Rome, Italy and Luoyang, China. Two-point Equidistant with Tissot's Indicatrices of Distortion.svg
Two-point equidistant projection of the entire world with Tissot's indicatrix of deformation. The two points are Rome, Italy and Luoyang, China.

The two-point equidistant projection is a map projection first described by Hans Maurer in 1919. It is a generalization of the much simpler azimuthal equidistant projection. In this two-point form, two locus points are chosen by the mapmaker to configure the projection. Distances from the two loci to any other point on the map are correct: that is, they scale to the distances of the same points on the sphere.

The projection has been used for all maps of the Asian continent by the National Geographic Society atlases since 1959, [1] though its purpose in that case was to reduce distortion throughout Asia rather than to measure from the two loci. [2] The projection sometimes appears in maps of air routes. The Chamberlin trimetric projection is a logical extension of the two-point idea to three points, but the three-point case only yields a sort of minimum error for distances from the three loci, rather than yielding correct distances. Tobler extended this idea to arbitrarily large number of loci by using automated root-mean-square minimization techniques rather than using closed-form formulae. [3]

See also

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Azimuthal equidistant projection

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Chamberlin trimetric projection

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Cylindrical equal-area projection

In cartography, the cylindrical equal-area projection is a family of cylindrical, equal-area map projections.

Equidistant conic projection

The equidistant conic projection is a conic map projection commonly used for maps of small countries as well as for larger regions such as the continental United States that are elongated east-to-west.

Mercator 1569 world map first map in Mercators projection

The Mercator world map of 1569 is titled Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendate Accommodata. The title shows that Gerardus Mercator aimed to present contemporary knowledge of the geography of the world and at the same time 'correct' the chart to be more useful to sailors. This 'correction', whereby constant bearing sailing courses on the sphere are mapped to straight lines on the plane map, characterizes the Mercator projection. While the map's geography has been superseded by modern knowledge, its projection proved to be one of the most significant advances in the history of cartography, inspiring map historian Nordenskiöld to write "The master of Rupelmonde stands unsurpassed in the history of cartography since the time of Ptolemy." The projection heralded a new era in the evolution of navigation maps and charts and it is still their basis.

Loximuthal projection

In cartography, the loximuthal projection is a map projection introduced by Karl Siemon in 1935, and independently in 1966 by Waldo R. Tobler, who named it. It is characterized by the fact that loxodromes from one chosen central point are shown straight lines, correct in azimuth from the center, and are "true to scale" in the sense that distances measured along such lines are proportional to lengths of the corresponding rhumb lines on the surface of the earth. It is neither an equal-area projection nor conformal.

References

  1. Snyder, J.P. (1993). Flattening the Earth: 2,000 years of map projections. pp. 234–235. ISBN   0226767469.
  2. "Portrait of Earth's largest continent", National Geographic Magazine, vol. 116 no. 6, p. 751, 1959
  3. Tobler, Waldo (April 1986). "Measuring the Similarity of Map Projections". Cartography and Geographic Information Science. 13 (2): 135–139. doi:10.1559/152304086783900103 via Researchgate.