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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 ...
In the book, Tissot argued for his method, reportedly demonstrating that "whatever the system of transformation, there is at each point on the spherical surface at least one pair of orthogonal directions which will also be orthogonal on the projection." [5] Tissot employed a graphical device he called the ellipse indicatrice or distortion ...
The maturation of complex analysis led to general techniques for conformal mapping, where points of a flat surface are handled as numbers on the complex plane.While working at the United States Coast and Geodetic Survey, the American philosopher Charles Sanders Peirce published his projection in 1879, [2] having been inspired by H. A. Schwarz's 1869 conformal transformation of a circle onto a ...
Tissot's indicatrices on the Mercator projection. The classic way of showing the distortion inherent in a projection is to use Tissot's indicatrix. Nicolas Tissot noted that the scale factors at a point on a map projection, specified by the numbers h and k, define an ellipse at that point. For cylindrical projections, the axes of the ellipse ...
Attribution and Share-Alike required; Any use of this map can be made as long as you credit me (Eric Gaba – Wikimedia Commons user: Sting) as the author and distribute the copies and derivative works under the same license(s) that the one(s) stated below.
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The formulas for the spherical orthographic projection are derived using trigonometry.They are written in terms of longitude (λ) and latitude (φ) on the sphere.Define the radius of the sphere R and the center point (and origin) of the projection (λ 0, φ 0).