New solution method is presented for vision positioning method from straight lines intersecting at two spatial points. The solution method has fast calculation and can guarantee the uniqueness for solution. Application of this method is to satisfy precondition of monotony. This paper studies the geometry of space and gives sufficient proof of the monotonic the algorithm satisfies in the geometric range. In the spatial distribution of linear feature, geometric space can guarantee the convergence of the method. Thus, it can provide sufficient theoretical basis for the practical application of designed iterative method. Meanwhile, it can ensure the calculation speed and the uniqueness of solving methods. Simulation results show that iterative method can converge to right solution in the geometric space and has rapid iteration speed.