Vincenty's Formulae - Inverse Problem

Inverse Problem

Given the coordinates of the two points (φ₁, L₁) and (φ₂, L₂), the inverse problem finds the azimuths α₁, α₂ and the ellipsoidal distance s.

Calculate U₁, U₂ and L, and set initial value of λ = L. Then iteratively evaluate the following equations until λ converges:

When λ has converged to the desired degree of accuracy (10−12 corresponds to approximately 0.06mm), evaluate the following:

Between two nearly antipodal points, the iterative formula may fail to converge; this will occur when the first guess at λ as computed by the equation above is greater than π in absolute value.