# NAME

GIS::Distance::Vincenty - Thaddeus Vincenty distance calculations.

# DESCRIPTION

For the benefit of the terminally obsessive (as well as the genuinely needy), Thaddeus Vincenty devised formulae for calculating geodesic distances between a pair of latitude/longitude points on the earth's surface, using an accurate ellipsoidal model of the earth.

Vincenty's formula is accurate to within 0.5mm, or 0.000015", on the ellipsoid being used. Calculations based on a spherical model, such as the (much simpler) Haversine, are accurate to around 0.3% (which is still good enough for most purposes).

The accuracy quoted by Vincenty applies to the theoretical ellipsoid being used, which will differ (to varying degree) from the real earth geoid. If you happen to be located in Colorado, 2km above msl, distances will be 0.03% greater. In the UK, if you measure the distance from Land's End to John O' Groats using WGS-84, it will be 28m - 0.003% - greater than using the Airy ellipsoid, which provides a better fit for the UK.

Take a look at the GIS::Distance::ALT formula for a much quicker alternative with nearly the same accuracy.

A faster (XS) version of this formula is available as GIS::Distance::Fast::Vincenty.

Normally this module is not used directly. Instead GIS::Distance is used which in turn interfaces with the various formula classes.

# FORMULA

``````    a, b = major & minor semiaxes of the ellipsoid
f = flattening (a-b)/a
L = lon2 - lon1
u1 = atan((1-f) * tan(lat1))
u2 = atan((1-f) * tan(lat2))
sin_u1 = sin(u1)
cos_u1 = cos(u1)
sin_u2 = sin(u2)
cos_u2 = cos(u2)
lambda = L
lambda_pi = 2PI
while abs(lambda-lambda_pi) > 1e-12
sin_lambda = sin(lambda)
cos_lambda = cos(lambda)
sin_sigma = sqrt((cos_u2 * sin_lambda) * (cos_u2*sin_lambda) +
(cos_u1*sin_u2-sin_u1*cos_u2*cos_lambda) * (cos_u1*sin_u2-sin_u1*cos_u2*cos_lambda))
cos_sigma = sin_u1*sin_u2 + cos_u1*cos_u2*cos_lambda
sigma = atan2(sin_sigma, cos_sigma)
alpha = asin(cos_u1 * cos_u2 * sin_lambda / sin_sigma)
cos_sq_alpha = cos(alpha) * cos(alpha)
cos2sigma_m = cos_sigma - 2*sin_u1*sin_u2/cos_sq_alpha
cc = f/16*cos_sq_alpha*(4+f*(4-3*cos_sq_alpha))
lambda_pi = lambda
lambda = L + (1-cc) * f * sin(alpha) *
(sigma + cc*sin_sigma*(cos2sigma_m+cc*cos_sigma*(-1+2*cos2sigma_m*cos2sigma_m)))
}
usq = cos_sq_alpha*(a*a-b*b)/(b*b);
aa = 1 + usq/16384*(4096+usq*(-768+usq*(320-175*usq)))
bb = usq/1024 * (256+usq*(-128+usq*(74-47*usq)))
delta_sigma = bb*sin_sigma*(cos2sigma_m+bb/4*(cos_sigma*(-1+2*cos2sigma_m*cos2sigma_m)-
bb/6*cos2sigma_m*(-3+4*sin_sigma*sin_sigma)*(-3+4*cos2sigma_m*cos2sigma_m)))
c = b*aa*(sigma-delta_sigma)``````