Nicolas Auguste Tissot
Encyclopedia
Nicolas Auguste Tissot was a 19th-century French
cartographer, who in 1859 and 1881 published an analysis of the distortion that occurs on map projections. He devised Tissot's indicatrix
, or distortion circle, which when plotted on a map will appear as an ellipse
whose elongation depends on the amount of distortion by the map at that point. The angle and extent of the elongation represents the amount of angular distortion of the map. The size of the ellipse indicates the amount that the area is distorted.
Born in Nancy, Meurthe-et-Moselle
, France, Tissot was trained as an engineer in the French Army
, from which he graduated as capitaine du génie. In the early 1860s he became an instructor in geodesy
at the well-reputed Ecole Polytechnique
in Paris. Around the same time, he indulged a research program meant to determine the best way of cartographic projection for a particular region and presented his findings to the French Académie des Sciences.
In the eighteenth century, the German cartographer Johann H. Lambert had enunciated a mathematical theory of map projections and of the attendant characteristics of distortions that any given projection involved. Carl Friedrich Gauss
had also studied the subject before Tissot's contributions later in the nineteenth century.
Tissot’s research in the mid-1850s on methods for finding good projections for particular regions led him to develop a projection that he saw as optimal. While not quite equal-area or conformal, his projection resulted in “negligible distortion for a very small region.” Subsequently, his optimal projection was adopted by the geographic service of the French Army.
While his first concepts regarding cartographic distortions developed in mid-century, it was only with the publication of Mémoire sur la représentation des surfaces et les projections des cartes géographiques in 1881 that the Tissot’s Indicatrix became popular. 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.”
Tissot employed a graphical device he called the ellipse indicatrice or distortion circle. When plotted on a map it reveals the amount of distortion by the map at the particular point where the ellipse is plotted. He suggested that the angle and extent of the elongation of the distortion circle represented the amount of angular distortion of the map, while the size of the ellipse corresponded to the amount of distortion in area.
In a nineteenth-century cartographic context, in which professionals looked for ways to apply mathematical principles to the science of mapping and the map projection, Tissot’s theory was favorably received, at least in continental Europe. Even in the more restrained Anglo-American academic world, a columnist of Science
, a publication sponsored by the American Association for the Advancement of Science
, hailed Tissot's method and encouraged his readers to study Tissot’s work in the hope that such a study “will lead to the adoption of better projections than those which are at present in use.” The legacy of Tissot’s method is still vivid today, as suggested by the authors of Map Projections for Europe, who argue that since Tissot’s famous analysis regarding distortion, the only major scientific development in the metric interpretation of deformation has been Eduard Imhof
's Verzerrungsgitter, or deformation grid.
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
cartographer, who in 1859 and 1881 published an analysis of the distortion that occurs on map projections. He devised Tissot's indicatrix
Tissot's Indicatrix
Tissot’s indicatrix is a mathematical contrivance presented by French mathematician Nicolas Auguste Tissot in 1859 and 1871 in order to characterize distortions due to map projection...
, or distortion circle, which when plotted on a map will appear as an ellipse
Ellipse
In geometry, an ellipse is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone's axis...
whose elongation depends on the amount of distortion by the map at that point. The angle and extent of the elongation represents the amount of angular distortion of the map. The size of the ellipse indicates the amount that the area is distorted.
Born in Nancy, Meurthe-et-Moselle
Meurthe-et-Moselle
Meurthe-et-Moselle is a department in the Lorraine region of France, named after the Meurthe and Moselle rivers.- History :Meurthe-et-Moselle was created in 1871 at the end of the Franco-Prussian War from the parts of the former departments of Moselle and Meurthe which remained French...
, France, Tissot was trained as an engineer in the French Army
French Army
The French Army, officially the Armée de Terre , is the land-based and largest component of the French Armed Forces.As of 2010, the army employs 123,100 regulars, 18,350 part-time reservists and 7,700 Legionnaires. All soldiers are professionals, following the suspension of conscription, voted in...
, from which he graduated as capitaine du génie. In the early 1860s he became an instructor in geodesy
Geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...
at the well-reputed Ecole Polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
in Paris. Around the same time, he indulged a research program meant to determine the best way of cartographic projection for a particular region and presented his findings to the French Académie des Sciences.
In the eighteenth century, the German cartographer Johann H. Lambert had enunciated a mathematical theory of map projections and of the attendant characteristics of distortions that any given projection involved. Carl Friedrich Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...
had also studied the subject before Tissot's contributions later in the nineteenth century.
Tissot’s research in the mid-1850s on methods for finding good projections for particular regions led him to develop a projection that he saw as optimal. While not quite equal-area or conformal, his projection resulted in “negligible distortion for a very small region.” Subsequently, his optimal projection was adopted by the geographic service of the French Army.
While his first concepts regarding cartographic distortions developed in mid-century, it was only with the publication of Mémoire sur la représentation des surfaces et les projections des cartes géographiques in 1881 that the Tissot’s Indicatrix became popular. 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.”
Tissot employed a graphical device he called the ellipse indicatrice or distortion circle. When plotted on a map it reveals the amount of distortion by the map at the particular point where the ellipse is plotted. He suggested that the angle and extent of the elongation of the distortion circle represented the amount of angular distortion of the map, while the size of the ellipse corresponded to the amount of distortion in area.
In a nineteenth-century cartographic context, in which professionals looked for ways to apply mathematical principles to the science of mapping and the map projection, Tissot’s theory was favorably received, at least in continental Europe. Even in the more restrained Anglo-American academic world, a columnist of Science
Science (journal)
Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....
, a publication sponsored by the American Association for the Advancement of Science
American Association for the Advancement of Science
The American Association for the Advancement of Science is an international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...
, hailed Tissot's method and encouraged his readers to study Tissot’s work in the hope that such a study “will lead to the adoption of better projections than those which are at present in use.” The legacy of Tissot’s method is still vivid today, as suggested by the authors of Map Projections for Europe, who argue that since Tissot’s famous analysis regarding distortion, the only major scientific development in the metric interpretation of deformation has been Eduard Imhof
Eduard Imhof
Eduard Imhof was a professor of cartography at the Swiss Federal Institute of Technology, Zürich, from 1925 - 1965. His fame, which extends far beyond the Institute of Technology, stems from his relief shading work on school maps and atlases. Between 1922 and 1973 Imhof worked on many school maps...
's Verzerrungsgitter, or deformation grid.