
214 Computing in Geographic Information Systems
cosines. The versed sine is 1 −cos θ, and the half-versed-sine
1−cos θ
2
= sin
2
(
θ
2
)
as used above. It was published by Roger Sinnott in Sky and Telescope mag-
azine in 1984 (“Virtues of the Haversine”), though known about for much
longer by navigators. A marginal performance improvement can be obtained
by factoring out the terms which get squared.
12.2.5 Vincenty’s Formula
Thaddeus Vincenty devised a formula for calculating geodesic distances be-
tween a pair of points on the surface of Earth given by latitude and longitude.
This uses an accurate ellipsoidal model of the Earth. While the mathematics
is a