Vincenty's formulae

Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such as great-circle distance. The first (direct) method computes the location of a point that is a given distance and azimuth (direction) from another point. The second (inverse) method computes the geographical distance and azimuth between two given points. They have been widely used in geodesy because they are accurate to within 0.5 mm (0.020 in) on the Earth ellipsoid. Vincenty's goal was to express existing algorithms for geodesics on an ellipsoid in a form that minimized the program length (Vincenty 1975a). His unpublished report (1975b) mentions the use of a Wang 720 desk calculator, which had only a few kilobytes of memory. To obtain good accuracy for long lines, the solution uses the classical solution of Legendre (1806), Bessel (1825), and Helmert (1880) based on the auxiliary sphere. Vincenty relied on formulation of this method given by Rainsford, 1955. Legendre showed that an ellipsoidal geodesic can be exactly mapped to a great circle on the auxiliary sphere by mapping the geographic latitude to reduced latitude and setting the azimuth of the great circle equal to that of the geodesic. The longitude on the ellipsoid and the distance along the geodesic are then given in terms of the longitude on the sphere and the arc length along the great circle by simple integrals. Bessel and Helmert gave rapidly converging series for these integrals, which allow the geodesic to be computed with arbitrary accuracy. In order to minimize the program size, Vincenty took these series, re-expanded them using the first term of each series as the small parameter, and truncated them to . This resulted in compact expressions for the longitude and distance integrals.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (7)

Related concepts (6)

Related courses (1)

Related lectures (5)

Verification of selective laser melting heat source models with operando X-ray diffraction data

Helena Van Swygenhoven, Steven Van Petegem, Samy Hocine

The output obtained from operando X-ray diffraction experiments on Ti-6Al-4V is used to verify the accuracy of four FEM models in predicting the temperature evolution of the solidified domain, the cooling rates of the alpha and beta phases, and the influen ...

ELSEVIER2021

Cohomology Of Large Semiprojective Hyperkahler Varieties

Tamás Hausel

In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkahler manifolds including toric hyperkahler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulti ...

Soc Mathematique France2015

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris, Martin Bauer

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

Geographical distance

Geographical distance or geodetic distance is the distance measured along the surface of the earth. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic problem. Calculating the distance between geographical coordinates is based on some level of abstraction; it does not provide an exact distance, which is unattainable if one attempted to account for every irregularity in the surface of the earth.

Geodesics on an ellipsoid

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface. The solution of a triangulation network on an ellipsoid is therefore a set of exercises in spheroidal trigonometry .

Great-circle distance

The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the length of a straight line between them, but on the sphere there are no straight lines. In spaces with curvature, straight lines are replaced by geodesics.

MATH-126: Geometry for architects II

Ce cours traite des 3 sujets suivants : la perspective, la géométrie descriptive, et une initiation à la géométrie projective.

Surfaces with Constant Curvature MATH-126: Geometry for architects II

Explores surfaces with constant curvature, emphasizing the significance of minimal oriented radius and the properties of pseudo-spheres.

Projections: Projection Suisse ENV-340: Fundamentals of satellite positioning

Explains the Swiss projection system, its coordinate system, advantages, deformation, and examples from France.

Cutting Plane Methods

Explores cutting plane methods, ellipsoid algorithm, and competitive algorithms for optimization.