Elaboration of the Soldner projection of a whole ellipsoid and the area of Poland in the wide zone using Jacobi’s elliptic integrals and functions

Aim of project
The main aim of the project is an elaboration of the Soldner projection of a whole ellipsoid and the area of Poland in the wide zone using Jacobi’s elliptic integrals and functions. It is a new approach to the construction of the Soldner projection allowing to expand the use of that projection on a whole ellipsoid. The research will consist of a complete explanation of the Soldner projection. A solution to the direct problem (i.e. to coordinate the transformation between ellipsoid and image plane) and a solution to the indirect problem, which allows the transformation of coordinates from plane to ellipsoid, will be described. The subject of the research is also to determine properties of the Soldner projection of the whole ellipsoid and particularly the wide zone of area of Poland. The task will consist of the determination of distribution of distortion and examination of peculiarities occurring in the projection. Moreover, there will be an analysis of possible applications of the elaborated method.

Expected results
To the present day, the Soldner projection has been used in geodesy and cartography in narrow (2–3 degrees) zones. Formulas have had the simple form of power series limited to a few starting expressions. Application of elliptic function allows to create the Soldner projection of the whole ellipsoid. It will be a new and original method of construction of the Soldner projection. An additional benefi t of the project will be an alternative method of examination of geodetic line on ellipsoid. The elaborated projection may fi nd application in large scale map making.