A new method for generating equidistant/equiratio line between two points on the Earth ellipsoid

It is of very great significance to achieve accurate solution of equidistant points/equiratio line between two points at a large regional or global scale. At present, no effective method has been found for equidistant/equiratio line between two points on the Earth ellipsoid. In large scale space, the solution plane of equidistant/equiratio points between two points on the map cannot meet the requirements of high-precision space analysis, due to the existence of map projection deformation. The key to solving the above problems is to establish a method generating the equidistant/equiratio line based on solution to geodesic problem, and implement the entire calculation process on the Earth ellipsoid. Based on the Karney’s direct and inverse formulas, the paper uses the pendulum method to design a cohesive method for calculating the equidistant/equiratio line between two points on the Earth ellipsoid. Several specific examples are selected for experimental verification, which proves that this algorithm can solve the problem of calculating equidistant/equiratio line of two points of different scale line in short distance, medium distance and long distance, and the precision of solving coordinate space is less than 0.00001 m, which can meet the requirements of long distance, wide range and high-precision spatial analysis.