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For example, a Mercator map printed in a book might have an equatorial width of 13.4 cm corresponding to a globe radius of 2.13 cm and an RF of approximately 1 / 300M (M is used as an abbreviation for 1,000,000 in writing an RF) whereas Mercator's original 1569 map has a width of 198 cm corresponding to a globe radius of 31.5 cm and an ...
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 ...
Since any map projection is a representation of one of those surfaces on a plane, all map projections distort. [5] Tissot's indicatrices on the Mercator projection. The classical way of showing the distortion inherent in a projection is to use Tissot's indicatrix.
One solution is to start from the (x, y) projection plane and construct the image from the values defined in (λ, φ) by using the inverse formulas of the orthographic projection. See References for an ellipsoidal version of the orthographic map projection. [3]
This is an emerging method for delivering styled web maps, combining certain benefits of pre-rendered raster map tiles with vector map data. As with the widely used raster tiled web maps, map data is requested by a client as a set of "tiles" corresponding to square areas of land of a pre-defined size and location. Unlike raster tiled web maps ...
oblique Mercator projection. The oblique Mercator map projection is an adaptation of the standard Mercator projection. The oblique version is sometimes used in national mapping systems. When paired with a suitable geodetic datum, the oblique Mercator delivers high accuracy in zones less than a few degrees in arbitrary directional extent.
Miller projection with 1,000 km indicatrices of distortion. The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4 ⁄ 5, projected according to Mercator, and then the result is multiplied by 5 ⁄ 4 to retain scale along the equator. [1] Hence:
The spherical form of the transverse Mercator projection was one of the seven new projections presented, in 1772, by Johann Heinrich Lambert. [1] [2] (The text is also available in a modern English translation. [3]) Lambert did not name his projections; the name transverse Mercator dates from the second half of the nineteenth century. [4]