THE METHODS OF CALCULATION OF ELLIPSOIDAL POLYGONS AREAS BASED ON SOME MAP PROJECTIONS PROPERTIES

P. Pedzich, J. Balcerzak

Warsaw University of Technology, Department of Geodesy and Cartography, Institute of Photogrammetry and Cartography

p.pedzich@gik.pw.edu.pl

Calculation of ellipsoidal polygons is very important problem in geodesy and cartography.

There are known some methods of area calculation of geodetic polygons but they are limited to small figures.

The paper presents some new methods of calculation areas of geodetic polygons which use some basic properties of map projection especially locale scale.

There are presented 4 methods. The first one is based on approximation of polygon by elementary trapezoids limited by parallels and meridians. The second method uses approximation of ellipsoidal polygon by elementary spherical triangles. In the third method there is employed equal-area projection of ellipsoid onto sphere. The forth method uses equal-area projection of ellipsoid into plane. In the end there is presented reduction of area located between curved image of geodetic line and its chord.

Moreover paper presents comparison of these methods and its application to calculation areas of administration districts in Poland.