1GIS::Distance::VincentyU(s3eprm)Contributed Perl DocumenGtIaSt:i:oDnistance::Vincenty(3pm)
2
3
4

NAME

6       GIS::Distance::Vincenty - Thaddeus Vincenty distance calculations.
7

DESCRIPTION

9       For the benefit of the terminally obsessive (as well as the genuinely
10       needy), Thaddeus Vincenty devised formulae for calculating geodesic
11       distances between a pair of latitude/longitude points on the earth's
12       surface, using an accurate ellipsoidal model of the earth.
13
14       Vincenty's formula is accurate to within 0.5mm, or 0.000015", on the
15       ellipsoid being used. Calculations based on a spherical model, such as
16       the (much simpler) Haversine, are accurate to around 0.3% (which is
17       still good enough for most purposes).
18
19       The accuracy quoted by Vincenty applies to the theoretical ellipsoid
20       being used, which will differ (to varying degree) from the real earth
21       geoid.  If you happen to be located in Colorado, 2km above msl,
22       distances will be 0.03% greater. In the UK, if you measure the distance
23       from Land's End to John O' Groats using WGS-84, it will be 28m - 0.003%
24       - greater than using the Airy ellipsoid, which provides a better fit
25       for the UK.
26
27       Take a look at the GIS::Distance::ALT formula for a much quicker
28       alternative with nearly the same accuracy.
29
30       A faster (XS) version of this formula is available as
31       GIS::Distance::Fast::Vincenty.
32
33       Normally this module is not used directly.  Instead GIS::Distance is
34       used which in turn interfaces with the various formula classes.
35

FORMULA

37           a, b = major & minor semiaxes of the ellipsoid
38           f = flattening (a-b)/a
39           L = lon2 - lon1
40           u1 = atan((1-f) * tan(lat1))
41           u2 = atan((1-f) * tan(lat2))
42           sin_u1 = sin(u1)
43           cos_u1 = cos(u1)
44           sin_u2 = sin(u2)
45           cos_u2 = cos(u2)
46           lambda = L
47           lambda_pi = 2PI
48           while abs(lambda-lambda_pi) > 1e-12
49               sin_lambda = sin(lambda)
50               cos_lambda = cos(lambda)
51               sin_sigma = sqrt((cos_u2 * sin_lambda) * (cos_u2*sin_lambda) +
52                   (cos_u1*sin_u2-sin_u1*cos_u2*cos_lambda) * (cos_u1*sin_u2-sin_u1*cos_u2*cos_lambda))
53               cos_sigma = sin_u1*sin_u2 + cos_u1*cos_u2*cos_lambda
54               sigma = atan2(sin_sigma, cos_sigma)
55               alpha = asin(cos_u1 * cos_u2 * sin_lambda / sin_sigma)
56               cos_sq_alpha = cos(alpha) * cos(alpha)
57               cos2sigma_m = cos_sigma - 2*sin_u1*sin_u2/cos_sq_alpha
58               cc = f/16*cos_sq_alpha*(4+f*(4-3*cos_sq_alpha))
59               lambda_pi = lambda
60               lambda = L + (1-cc) * f * sin(alpha) *
61                   (sigma + cc*sin_sigma*(cos2sigma_m+cc*cos_sigma*(-1+2*cos2sigma_m*cos2sigma_m)))
62           }
63           usq = cos_sq_alpha*(a*a-b*b)/(b*b);
64           aa = 1 + usq/16384*(4096+usq*(-768+usq*(320-175*usq)))
65           bb = usq/1024 * (256+usq*(-128+usq*(74-47*usq)))
66           delta_sigma = bb*sin_sigma*(cos2sigma_m+bb/4*(cos_sigma*(-1+2*cos2sigma_m*cos2sigma_m)-
67             bb/6*cos2sigma_m*(-3+4*sin_sigma*sin_sigma)*(-3+4*cos2sigma_m*cos2sigma_m)))
68           c = b*aa*(sigma-delta_sigma)
69

SEE ALSO

71       ·   <http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf>
72
73       ·   <http://www.movable-type.co.uk/scripts/LatLongVincenty.html>
74

SUPPORT

76       See "SUPPORT" in GIS::Distance.
77

AUTHORS

79       See "AUTHORS" in GIS::Distance.
80

82       See "COPYRIGHT AND LICENSE" in GIS::Distance.
83
84
85
86perl v5.30.1                      2020-01-30      GIS::Distance::Vincenty(3pm)
Impressum