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| 1 | +/* |
| 2 | +
|
| 3 | +// https://sourceforge.net/p/geographiclib/discussion/1026621/thread/21aaff9f/?page=1#51e7 |
| 4 | +
|
| 5 | +// Find intersection of two geodesics |
| 6 | +
|
| 7 | +#include <iostream> |
| 8 | +#include <iomanip> |
| 9 | +#include <GeographicLib/Gnomonic.hpp> |
| 10 | +#include <GeographicLib/Geodesic.hpp> |
| 11 | +
|
| 12 | +class vector3 { |
| 13 | +public: |
| 14 | + double _x, _y, _z; |
| 15 | + vector3(double x, double y, double z = 1) throw() |
| 16 | + : _x(x) |
| 17 | + , _y(y) |
| 18 | + , _z(z) {} |
| 19 | + vector3 cross(const vector3& b) const throw() { |
| 20 | + return vector3(_y * b._z - _z * b._y, |
| 21 | + _z * b._x - _x * b._z, |
| 22 | + _x * b._y - _y * b._x); |
| 23 | + } |
| 24 | + void norm() throw() { |
| 25 | + _x /= _z; |
| 26 | + _y /= _z; |
| 27 | + _z = 1; |
| 28 | + } |
| 29 | +}; |
| 30 | +
|
| 31 | +int intersect(double lata1, double lona1, double lata2, double lona2, double latb1, double lonb1, double latb2, double lonb2) { |
| 32 | + const GeographicLib::Geodesic& geod = GeographicLib::Geodesic::WGS84(); |
| 33 | + const GeographicLib::Gnomonic gn(geod); |
| 34 | + double |
| 35 | + lat0 = (lata1 + lata2 + latb1 + latb2)/4, |
| 36 | + // Possibly need to deal with longitudes wrapping around |
| 37 | + lon0 = (lona1 + lona2 + lonb1 + lonb2)/4; |
| 38 | + std::cout << std::setprecision(16); |
| 39 | + std::cout << "Initial guess " << lat0 << " " << lon0 << "\n"; |
| 40 | + for (int i = 0; i < 10; ++i) { |
| 41 | + double xa1, ya1, xa2, ya2; |
| 42 | + double xb1, yb1, xb2, yb2; |
| 43 | + gn.Forward(lat0, lon0, lata1, lona1, xa1, ya1); |
| 44 | + gn.Forward(lat0, lon0, lata2, lona2, xa2, ya2); |
| 45 | + gn.Forward(lat0, lon0, latb1, lonb1, xb1, yb1); |
| 46 | + gn.Forward(lat0, lon0, latb2, lonb2, xb2, yb2); |
| 47 | + // See Hartley and Zisserman, Multiple View Geometry, Sec. 2.2.1 |
| 48 | + vector3 va1(xa1, ya1); vector3 va2(xa2, ya2); |
| 49 | + vector3 vb1(xb1, yb1); vector3 vb2(xb2, yb2); |
| 50 | + // la is homogeneous representation of line A1,A2 |
| 51 | + // lb is homogeneous representation of line B1,B2 |
| 52 | + vector3 la = va1.cross(va2); |
| 53 | + vector3 lb = vb1.cross(vb2); |
| 54 | + // p0 is homogeneous representation of intersection of la and lb |
| 55 | + vector3 p0 = la.cross(lb); |
| 56 | + p0.norm(); |
| 57 | + double lat1, lon1; |
| 58 | + gn.Reverse(lat0, lon0, p0._x, p0._y, lat1, lon1); |
| 59 | + std::cout << "Increment " << lat1-lat0 << " " << lon1-lon0 << "\n"; |
| 60 | + lat0 = lat1; |
| 61 | + lon0 = lon1; |
| 62 | + } |
| 63 | + std::cout << "Final result " << lat0 << " " << lon0 << "\n"; |
| 64 | + double azi1, azi2; |
| 65 | + geod.Inverse(lata1, lona1, lat0, lon0, azi1, azi2); |
| 66 | + std::cout << "Azimuths on line A " << azi2 << " "; |
| 67 | + geod.Inverse(lat0, lon0, lata2, lona2, azi1, azi2); |
| 68 | + std::cout << azi1 << "\n"; |
| 69 | + geod.Inverse(latb1, lonb1, lat0, lon0, azi1, azi2); |
| 70 | + std::cout << "Azimuths on line B " << azi2 << " "; |
| 71 | + geod.Inverse(lat0, lon0, latb2, lonb2, azi1, azi2); |
| 72 | + std::cout << azi1 << "\n"; |
| 73 | +} |
| 74 | +
|
| 75 | +
|
| 76 | +
|
| 77 | +// Find interception of a geodesic from a point |
| 78 | +
|
| 79 | +int intercept(double lata1, lona1, lata2, lona2, double latb1, lonb1) { |
| 80 | + const GeographicLib::Geodesic& geod = GeographicLib::Geodesic::WGS84(); |
| 81 | + const GeographicLib::Gnomonic gn(geod); |
| 82 | + double |
| 83 | + lat0 = (lata1 + lata2)/2, |
| 84 | + // Possibly need to deal with longitudes wrapping around |
| 85 | + lon0 = (lona1 + lona2)/2; |
| 86 | + std::cout << std::setprecision(16); |
| 87 | + std::cout << "Initial guess " << lat0 << " " << lon0 << "\n"; |
| 88 | + for (int i = 0; i < 10; ++i) { |
| 89 | + double xa1, ya1, xa2, ya2; |
| 90 | + double xb1, yb1; |
| 91 | + gn.Forward(lat0, lon0, lata1, lona1, xa1, ya1); |
| 92 | + gn.Forward(lat0, lon0, lata2, lona2, xa2, ya2); |
| 93 | + gn.Forward(lat0, lon0, latb1, lonb1, xb1, yb1); |
| 94 | + // See Hartley and Zisserman, Multiple View Geometry, Sec. 2.2.1 |
| 95 | + vector3 va1(xa1, ya1); vector3 va2(xa2, ya2); |
| 96 | + // la is homogeneous representation of line A1,A2 |
| 97 | + vector3 la = va1.cross(va2); |
| 98 | + vector3 vb1(xb1, yb1); |
| 99 | + // lb is homogeneous representation of line thru B1 perpendicular to la |
| 100 | + vector3 lb(la._y, -la._x, la._x * yb1 - la._y * xb1); |
| 101 | + // p0 is homogeneous representation of intersection of la and lb |
| 102 | + vector3 p0 = la.cross(lb); |
| 103 | + p0.norm(); |
| 104 | + double lat1, lon1; |
| 105 | + gn.Reverse(lat0, lon0, p0._x, p0._y, lat1, lon1); |
| 106 | + std::cout << "Increment " << lat1-lat0 << " " << lon1-lon0 << "\n"; |
| 107 | + lat0 = lat1; |
| 108 | + lon0 = lon1; |
| 109 | + } |
| 110 | + std::cout << "Final result " << lat0 << " " << lon0 << "\n"; |
| 111 | + double azi1, azi2; |
| 112 | + geod.Inverse(lat0, lon0, lata1, lona1, azi1, azi2); |
| 113 | + std::cout << "Azimuth to A1 " << azi1 << "\n"; |
| 114 | + geod.Inverse(lat0, lon0, lata2, lona2, azi1, azi2); |
| 115 | + std::cout << "Azimuth to A2 " << azi1 << "\n"; |
| 116 | + geod.Inverse(lat0, lon0, latb1, lonb1, azi1, azi2); |
| 117 | + std::cout << "Azimuth to B1 " << azi1 << "\n"; |
| 118 | +} |
| 119 | +
|
| 120 | +*/ |
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