Vincenty's formula for Inverse Method

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Presentation transcript:

Vincenty's formula for Inverse Method http://en.wikipedia.org/wiki/Vincenty%27s_formulae

Vincenty's formula for Inverse Method Vincenty's formula is iterative methods used in geodesy to calculate the distance between two points on the surface of an spheroid, developed by Thaddeus Vincenty in 1975. It is based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods such as great-circle distance which assume a spherical Earth.

Vincenty's formula for Inverse Method The inverse method computes the geographical distance and azimuth between two given points. It has been widely used in geodesy because it is accurate to within 0.5 mm (0.020″) on the Earth ellipsoid.

Notations

Given the coordinates of the two points (φ1, λ1) and (φ2, λ2), the inverse method 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:

Online Calculator: http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp

Online Calculator: http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp