High-precision coordinate transformation algorithm for equidistant transverse cylindrical projection

The aim of the present study is to design an algorithm for direct and inverse transformation of geodetic coordinates and flat rectangular coordinates of equiintermediate transverse cylindrical projection, based on the use of geocentric coordinate ellipses. Methods. General scientific methods of abstraction, analysis, synthesis, and mathematical modeling have been deployed to substantiate the coordinate transformation algorithm. Results. The proposed study has developed an accurate algorithm for equiintermediate transverse cylindrical projection, which uses geocentric coordinate ellipses, namely, the axial meridian (ellipse abscissa) and the ordinate ellipse perpendicular to it. Within the coordinate zone, the position of a point on the ellipsoid’s surface is uniquely determined by curvilinear coordinates. These coordinates are calculated as arcs of the corresponding ellipses measured from the equator to the intersection point of the axial meridian with the ordinate ellipse, and then from the axial meridian to a given point. The arcs of the corresponding coordinate ellipses are treated as flat rectangular coordinates. To convert these coordinates, proposed transformations use geocentric coordinate angles within the planes of the coordinate ellipses. These angles are functions of geodesic and rectangular coordinates, which facilitate both direct and inverse transformations. In the given algorithm, flat rectangular coordinates are determined with the accuracy of calculating the meridian arc length. At any geodetic latitudes and longitudes values, the errors do not exceed 0.1 mm. Moreover, high accuracy of the inverse transformation is ensured.The paper provides formulas and examples for calculating the flat rectangular coordinates of an equidistant transverse cylindrical projection using geodesic coordinates, the inverse transformation, the scale of distortion, and the angle of meridian convergence. Scientific novelty. The study suggests relying on geocentric coordinate ellipses to substantiate equiintermediate transverse cylindrical projection. Practical value. The algorithm presented in the study offers submillimeter accuracy for the direct and inverse transformation of coordinates in equidistant transverse cylindrical projection at any latitude, applicable to coordinate zones with longitude differences of up to ±90°.