Rigorous spherical bearing with Soldner coordinates and azimuth angles on sphere

Abstract

Meridian systems, called Soldner coordinates (parallel coordinate) systems, have found wide application in geodesy. In particular, the meridian system constitutes a suitable base for the Gauss-Kruger projection of the ellipsoid and the sphere. Soldner coordinates can be used in Cassini-Soldner projection without any processing. As it is known, the directions of the edges are shown with azimuth angles in the geographic coordinate system and the bearing angles in the Soldner coordinate system. Bearing or azimuth angles are frequently used in geodetic calculations. These angles give the direction of sides in the clockwise direction from a certain initial direction. Both angle values range from 0 to 360 degrees and are usually calculated from the arctan function. But the arctan function returns an angle value between -90 and +90 degrees. Therefore, it is necessary to analyze the quarter for the angle found. For practical computations, the quadrants of the arctangents are determined by the signs of the numerator and denominator in the tangent formulas. Determining the quarter of the angles is done with if…, then…, end..., blocks on the computer. It should be noted that each comparison requires a separate processing time. This study will be given how to calculate both bearing and azimuth angles with direct formulas without any need to examine them. In addition, a solution proposal will be given against the division by zero errors in the bearing and azimuth angles calculations.