Abstract: This paper aims at solving the problem of failure of the earth theme algorithm in engineering realization, when the earth line crosses the ±180° longitude line and the equator, and the earth line crosses the ±90° north pole or the south pole. By introducing the discussion mechanism of boundary mutation, an engineering method was developed to solve the Bowring and Vincenty formula boundary problems. The simulation results show that this method solves the problem of calculated failure, when the earth line crosses the ±180° longitude line and the equator, and the earth line crosses the ±90° pole. The proposed method has good adaptability for the sudden change of boundary. On this basis, the calculation precision of the two algorithms for solving the above-mentioned geodesics in different distance ranges was further analyzed. The applicable ranges of two algorithms were pointed out respectively.