Line data Source code
1 : import 'dart:math';
2 :
3 : class Vincenty {
4 : static double distance(double lat1, lon1, lat2, lon2) {
5 : // Port from the existing Android version in method: computeDistanceAndBearing
6 : // https://android.googlesource.com/platform/frameworks/base/+/refs/heads/master/location/java/android/location/Location.java
7 :
8 : // Based on http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
9 : // using the "Inverse Formula" (section 4)
10 : int MAXITERS = 20;
11 :
12 : double a = 6378137.0; // WGS84 major axis
13 : double b = 6356752.3142; // WGS84 semi-major axis
14 4 : double f = (a - b) / a;
15 10 : double aSqMinusBSqOverBSq = (a * a - b * b) / (b * b);
16 2 : double L = lon2 - lon1;
17 : double A = 0.0;
18 8 : double U1 = atan((1.0 - f) * tan(lat1));
19 8 : double U2 = atan((1.0 - f) * tan(lat2));
20 2 : double cosU1 = cos(U1);
21 2 : double cosU2 = cos(U2);
22 2 : double sinU1 = sin(U1);
23 2 : double sinU2 = sin(U2);
24 2 : double cosU1cosU2 = cosU1 * cosU2;
25 2 : double sinU1sinU2 = sinU1 * sinU2;
26 : double sigma = 0.0;
27 : double deltaSigma = 0.0;
28 : double cosSqAlpha = 0.0;
29 : double cos2SM = 0.0;
30 : double cosSigma = 0.0;
31 : double sinSigma = 0.0;
32 : double cosLambda = 0.0;
33 : double sinLambda = 0.0;
34 : double lambda = L; // initial guess
35 4 : for (int iter = 0; iter < MAXITERS; iter++) {
36 : double lambdaOrig = lambda;
37 2 : cosLambda = cos(lambda);
38 2 : sinLambda = sin(lambda);
39 2 : double t1 = cosU2 * sinLambda;
40 8 : double t2 = cosU1 * sinU2 - sinU1 * cosU2 * cosLambda;
41 6 : double sinSqSigma = t1 * t1 + t2 * t2; // (14)
42 2 : sinSigma = sqrt(sinSqSigma);
43 4 : cosSigma = sinU1sinU2 + cosU1cosU2 * cosLambda; // (15)
44 2 : sigma = atan2(sinSigma, cosSigma); // (16)
45 2 : double sinAlpha = (sinSigma == 0) ? 0.0 :
46 4 : cosU1cosU2 * sinLambda / sinSigma; // (17)
47 4 : cosSqAlpha = 1.0 - sinAlpha * sinAlpha;
48 2 : cos2SM = (cosSqAlpha == 0) ? 0.0 :
49 6 : cosSigma - 2.0 * sinU1sinU2 / cosSqAlpha; // (18)
50 2 : double uSquared = cosSqAlpha * aSqMinusBSqOverBSq; // defn
51 6 : A = 1 + (uSquared / 16384.0) * // (3)
52 4 : (4096.0 + uSquared *
53 8 : (-768 + uSquared * (320.0 - 175.0 * uSquared)));
54 4 : double B = (uSquared / 1024.0) * // (4)
55 4 : (256.0 + uSquared *
56 8 : (-128.0 + uSquared * (74.0 - 47.0 * uSquared)));
57 4 : double C = (f / 16.0) *
58 2 : cosSqAlpha *
59 8 : (4.0 + f * (4.0 - 3.0 * cosSqAlpha)); // (10)
60 2 : double cos2SMSq = cos2SM * cos2SM;
61 4 : deltaSigma = B * sinSigma * // (6)
62 6 : (cos2SM + (B / 4.0) *
63 8 : (cosSigma * (-1.0 + 2.0 * cos2SMSq) -
64 6 : (B / 6.0) * cos2SM *
65 8 : (-3.0 + 4.0 * sinSigma * sinSigma) *
66 4 : (-3.0 + 4.0 * cos2SMSq)));
67 2 : lambda = L +
68 8 : (1.0 - C) * f * sinAlpha *
69 6 : (sigma + C * sinSigma *
70 6 : (cos2SM + C * cosSigma *
71 6 : (-1.0 + 2.0 * cos2SM * cos2SM))); // (11)
72 4 : double delta = (lambda - lambdaOrig) / lambda;
73 4 : if (delta.abs() < 1.0e-12) {
74 : break;
75 : }
76 : }
77 6 : double distance = (b * A * (sigma - deltaSigma));
78 : return distance;
79 : }
80 : }
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