GIS::Distance::Formula::Vincenty - Thaddeus Vincenty distance calculations.
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, of course).
Note: 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.
NOTE: This formula is still considered alpha quality in GIS::Distance as it hasn't been tested all that much.
Normally this module is not used directly. Instead GIS::Distance is used which in turn interfaces with the various formula classes.
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)
This method is called by GIS::Distance's distance() method.
Aran Clary Deltac <email@example.com>
This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.