Geodesic
Reconstruction of map projection, its inverse and re-projection
Applications of Mathematics, Tome 63 (2018) no. 4, pp. 455-481 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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This paper focuses on the automatic recognition of map projection, its inverse and re-projection. Our analysis leads to the unconstrained optimization solved by the hybrid BFGS nonlinear least squares technique. The objective function is represented by the squared sum of the residuals. For the map re-projection the partial differential equations of the inverse transformation are derived. They can be applied to any map projection. Illustrative examples of the stereographic and globular Nicolosi projections frequently used in early maps are involved and their inverse formulas are presented.
This paper focuses on the automatic recognition of map projection, its inverse and re-projection. Our analysis leads to the unconstrained optimization solved by the hybrid BFGS nonlinear least squares technique. The objective function is represented by the squared sum of the residuals. For the map re-projection the partial differential equations of the inverse transformation are derived. They can be applied to any map projection. Illustrative examples of the stereographic and globular Nicolosi projections frequently used in early maps are involved and their inverse formulas are presented.
DOI : 10.21136/AM.2018.0096-18
Classification : 34B16, 34C25, 35F50, 35R30, 65K10
Keywords: mathematical cartography; inverse projection; analysis; nonlinear least squares; partial differential equation; optimization; hybrid BFGS; early map; re-projection 
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     title = {Reconstruction of map projection, its inverse and re-projection},
     journal = {Applications of Mathematics},
     pages = {455--481},
     year = {2018},
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     doi = {10.21136/AM.2018.0096-18},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2018.0096-18/}
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Bayer, Tomáš; Kočandrlová, Milada. Reconstruction of map projection, its inverse and re-projection. Applications of Mathematics, Tome 63 (2018) no. 4, pp. 455-481. doi: 10.21136/AM.2018.0096-18

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