Tissot Equivalent Conic Projection of the Sphere
DOI:
https://doi.org/10.67252/gl.2026.80.3.2Keywords:
Tissot, conic projection, equivalent projectionAbstract
N. A. Tissot is best known in the theory of map projections for the distortion ellipse, now commonly referred to as Tissot’s indicatrix. By contrast, his equal-area conic projection with the smallest maximum angular distortion has received very little attention. This projection is a special case of the Lambert equal-area conic projection. In this article, we examine this projection under the additional constraint of a single standard parallel. Rather than prescribing the standard parallel in advance, Tissot required that the region between two given parallels be mapped with equal area while minimizing the maximum angular distortion. Although Tissot presented only the final formulas, this article provides a detailed derivation of those results. It also illustrates the local linear scale factors along the meridians and parallels with appropriate graphs and presents maps of the Northern Hemisphere and the entire world constructed using this projection.
References
Adams O. S. (1945): General Theory of Equivalent Projections, U.S. Coast and Geodetic Survey Spec. Pub. 236
Deetz C. H., Adams O. S. (1934): Elements of map projection with applications to map and chart construction (4th ed.): U.S. Coast and Geodetic Survey Spec. Pub. 68.
Fiala, F. (1957): Mathematische Kartographie, Veb Verlag Technik Berlin.
Germain A. (1866): Traité des projections des cartes géographiques, représentation plane de la sphère et du sphéroïde, Paris, A. Bertrand.
Graur A. V. (1956): Matematicheskaya kartografiya Leningrad University, 2nd ed. [Russian. 371 p., revised by A. A. Pavlov, Translated to English as Mathematical cartography: St. Louis, Mo., U.S. Air Force, Aeronautical Chart and Information Center, 1970, 671 p.].
Hinks A. R. (1912): Map projections: Cambridge, Eng., Cambridge Univ. Press, 126 p. [2nd ed., 1921, 158 p.].
Kavrayskiy V. V. (1959): Izbrannye trudy. Tom II, Matematicheskaja kartografija, Vypusk 2, Konicheskie i tsilindricheskie proektsii, ih primenenie, Izdannie Upravlenija nachal’nika Gidrograficheskoj sluzhby VMF.
Kerkovits K. (2022): Map projections, Lecture notes for students in Cartography and Geoinformatics Msc programme, Eotvos Lorand University, Faculty of Informatics, Institute of Cartography and Geoinformatics, Budapest.
Lambert J. H. (1772): 6th Chapter: Anmerkungen und Zusatze zur Entwerfung der Land- und Himmelscharten [Notes and comments on the composition of terrestrial and celestial maps]. In: Beytrage zum gebrauche der mathematik und deren anwendung. dritter theil Berlin: Verlag der Buchhandlung der Realschule.
Serapinas B. B. (2005): Matematicheskaya kartografiya, Moscow, Academa.
Snyder J. P. (1987): Map Projections – A Working Manual. U.S. Geological Survey Prof. Paper 1395, 383 p. Reprinted 1989 and 1994 with corrections. https://doi.org/10.3133/pp1395
Snyder J. P. (1993): Flattening the Earth, Two Thousend Years of Map Projections, The University of Chicago Press, Chicago and London.
Snyder J. P., Voxland M. Ph. (1989): An Album of Map Projections, U.S. Geological Survey, Professional Paper 1453. https://doi.org/10.3133/pp1453
Tissot N. A. (1881): Mémoire sur la représentation des surfaces et les projections des cartes géographiques: Paris, Gauthier Villars, 337 p. +60 p. tables. [Details the use of his indicatrix, introduced earlier. Also presents his version of equal-area conic projection. Note: The preamble and first four chapters of this work, p. 1-126, first appeared in Nouvelles Annales de Mathématiques, series 2, 1878, v. 17; 1879, v. 18; 1880, v. 19.].
Tissot N. A. (1887): Die Netzentwürfe geographischer Karten: Stuttgart, German edition and translation by Ernst Hammer.
Tissot N. A. (1889): Изображение одной поверхности на другой и составление географических карт. Preveo Tissotovu knjigu s francuskog na ruski Дмитрий Петрович Рашков. Moskva.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Miljenko Lapaine
This work is licensed under a Creative Commons Attribution 4.0 International License.
