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)

SEE ALSO

       •   <http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf>

       •   <http://www.movable-type.co.uk/scripts/LatLongVincenty.html>

SUPPORT

       See "SUPPORT" in GIS::Distance.

AUTHORS

       See "AUTHORS" in GIS::Distance.

LICENSE

       See "LICENSE" in GIS::Distance.