NETGeographicLib
1.47

.NET wrapper for GeographicLib::Geodesic. More...
#include <NETGeographicLib/Geodesic.h>
Public Types  
enum  mask { mask::NONE, mask::LATITUDE, mask::LONGITUDE, mask::AZIMUTH, mask::DISTANCE, mask::DISTANCE_IN, mask::REDUCEDLENGTH, mask::GEODESICSCALE, mask::AREA, mask::LONG_UNROLL, mask::ALL } 
Public Member Functions  
~Geodesic ()  
the destructor calls the finalizer. More...  
Constructor  
Geodesic (double a, double f)  
Geodesic ()  
Direct geodesic problem specified in terms of distance.  
double  Direct (double lat1, double lon1, double azi1, double s12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21, [System::Runtime::InteropServices::Out] double% S12) 
double  Direct (double lat1, double lon1, double azi1, double s12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2) 
double  Direct (double lat1, double lon1, double azi1, double s12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2) 
double  Direct (double lat1, double lon1, double azi1, double s12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% m12) 
double  Direct (double lat1, double lon1, double azi1, double s12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21) 
double  Direct (double lat1, double lon1, double azi1, double s12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21) 
Direct geodesic problem specified in terms of arc length.  
void  ArcDirect (double lat1, double lon1, double azi1, double a12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21, [System::Runtime::InteropServices::Out] double% S12) 
void  ArcDirect (double lat1, double lon1, double azi1, double a12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2) 
void  ArcDirect (double lat1, double lon1, double azi1, double a12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2) 
void  ArcDirect (double lat1, double lon1, double azi1, double a12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% s12) 
void  ArcDirect (double lat1, double lon1, double azi1, double a12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% m12) 
void  ArcDirect (double lat1, double lon1, double azi1, double a12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21) 
void  ArcDirect (double lat1, double lon1, double azi1, double a12, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21) 
General version of the direct geodesic solution.  
double  GenDirect (double lat1, double lon1, double azi1, bool arcmode, double s12_a12, Geodesic::mask outmask, [System::Runtime::InteropServices::Out] double% lat2, [System::Runtime::InteropServices::Out] double% lon2, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21, [System::Runtime::InteropServices::Out] double% S12) 
Inverse geodesic problem.  
double  Inverse (double lat1, double lon1, double lat2, double lon2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% azi1, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21, [System::Runtime::InteropServices::Out] double% S12) 
double  Inverse (double lat1, double lon1, double lat2, double lon2, [System::Runtime::InteropServices::Out] double% s12) 
double  Inverse (double lat1, double lon1, double lat2, double lon2, [System::Runtime::InteropServices::Out] double% azi1, [System::Runtime::InteropServices::Out] double% azi2) 
double  Inverse (double lat1, double lon1, double lat2, double lon2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% azi1, [System::Runtime::InteropServices::Out] double% azi2) 
double  Inverse (double lat1, double lon1, double lat2, double lon2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% azi1, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% m12) 
double  Inverse (double lat1, double lon1, double lat2, double lon2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% azi1, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21) 
double  Inverse (double lat1, double lon1, double lat2, double lon2, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% azi1, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21) 
General version of inverse geodesic solution.  
double  GenInverse (double lat1, double lon1, double lat2, double lon2, Geodesic::mask outmask, [System::Runtime::InteropServices::Out] double% s12, [System::Runtime::InteropServices::Out] double% azi1, [System::Runtime::InteropServices::Out] double% azi2, [System::Runtime::InteropServices::Out] double% m12, [System::Runtime::InteropServices::Out] double% M12, [System::Runtime::InteropServices::Out] double% M21, [System::Runtime::InteropServices::Out] double% S12) 
Interface to GeodesicLine.  
GeodesicLine^  Line (double lat1, double lon1, double azi1, NETGeographicLib::Mask caps) 
GeodesicLine^  InverseLine (double lat1, double lon1, double lat2, double lon2, NETGeographicLib::Mask caps) 
GeodesicLine^  DirectLine (double lat1, double lon1, double azi1, double s12, NETGeographicLib::Mask caps) 
GeodesicLine^  ArcDirectLine (double lat1, double lon1, double azi1, double a12, NETGeographicLib::Mask caps) 
GeodesicLine^  GenDirectLine (double lat1, double lon1, double azi1, bool arcmode, double s12_a12, NETGeographicLib::Mask caps) 
Inspector functions.  
double  MajorRadius [get] 
double  Flattening [get] 
double  EllipsoidArea [get] 
System::IntPtr^  GetUnmanaged () 
.NET wrapper for GeographicLib::Geodesic.
This class allows .NET applications to access GeographicLib::Geodesic.
The shortest path between two points on a ellipsoid at (lat1, lon1) and (lat2, lon2) is called the geodesic. Its length is s12 and the geodesic from point 1 to point 2 has azimuths azi1 and azi2 at the two end points. (The azimuth is the heading measured clockwise from north. azi2 is the "forward" azimuth, i.e., the heading that takes you beyond point 2 not back to point 1.) In the figure below, latitude if labeled φ, longitude λ (with λ_{12} = λ_{2} − λ_{1}), and azimuth α.
Given lat1, lon1, azi1, and s12, we can determine lat2, lon2, and azi2. This is the direct geodesic problem and its solution is given by the function Geodesic::Direct. (If s12 is sufficiently large that the geodesic wraps more than halfway around the earth, there will be another geodesic between the points with a smaller s12.)
Given lat1, lon1, lat2, and lon2, we can determine azi1, azi2, and s12. This is the inverse geodesic problem, whose solution is given by Geodesic::Inverse. Usually, the solution to the inverse problem is unique. In cases where there are multiple solutions (all with the same s12, of course), all the solutions can be easily generated once a particular solution is provided.
The standard way of specifying the direct problem is the specify the distance s12 to the second point. However it is sometimes useful instead to specify the arc length a12 (in degrees) on the auxiliary sphere. This is a mathematical construct used in solving the geodesic problems. The solution of the direct problem in this form is provided by Geodesic::ArcDirect. An arc length in excess of 180° indicates that the geodesic is not a shortest path. In addition, the arc length between an equatorial crossing and the next extremum of latitude for a geodesic is 90°.
This class can also calculate several other quantities related to geodesics. These are:
Overloaded versions of Geodesic::Direct, Geodesic::ArcDirect, and Geodesic::Inverse allow these quantities to be returned. In addition there are general functions Geodesic::GenDirect, and Geodesic::GenInverse which allow an arbitrary set of results to be computed. The quantities m12, M12, M21 which all specify the behavior of nearby geodesics obey addition rules. If points 1, 2, and 3 all lie on a single geodesic, then the following rules hold:
Additional functionality is provided by the GeodesicLine class, which allows a sequence of points along a geodesic to be computed.
The shortest distance returned by the solution of the inverse problem is (obviously) uniquely defined. However, in a few special cases there are multiple azimuths which yield the same shortest distance. Here is a catalog of those cases:
The calculations are accurate to better than 15 nm (15 nanometers) for the WGS84 ellipsoid. See Sec. 9 of arXiv:1102.1215v1 for details. The algorithms used by this class are based on series expansions using the flattening f as a small parameter. These are only accurate for f < 0.02; however reasonably accurate results will be obtained for f < 0.2. Here is a table of the approximate maximum error (expressed as a distance) for an ellipsoid with the same major radius as the WGS84 ellipsoid and different values of the flattening.
f error 0.01 25 nm 0.02 30 nm 0.05 10 um 0.1 1.5 mm 0.2 300 mm
For very eccentric ellipsoids, use GeodesicExact instead.
The algorithms are described in
For more information on geodesics see Geodesics on an ellipsoid of revolution.
C# Example:
Managed C++ Example:
Visual Basic Example:
INTERFACE DIFFERENCES:
A default constructor has been provided that assumes WGS84 parameters.
The MajorRadius, Flattening, and EllipsoidArea functions are implemented as properties.
The GenDirect, GenInverse, and Line functions accept the "capabilities mask" as a NETGeographicLib::Mask rather than an unsigned.
Definition at line 170 of file Geodesic.h.

strong 
Bit masks for what calculations to do. These masks do double duty. They signify to the GeodesicLine::GeodesicLine constructor and to Geodesic::Line what capabilities should be included in the GeodesicLine object. They also specify which results to return in the general routines Geodesic::GenDirect and Geodesic::GenInverse routines. GeodesicLine::mask is a duplication of this enum.
Enumerator  

NONE 
No capabilities, no output. 
LATITUDE 
Calculate latitude lat2. (It's not necessary to include this as a capability to GeodesicLine because this is included by default.) 
LONGITUDE 
Calculate longitude lon2. 
AZIMUTH 
Calculate azimuths azi1 and azi2. (It's not necessary to include this as a capability to GeodesicLine because this is included by default.) 
DISTANCE 
Calculate distance s12. 
DISTANCE_IN 
Allow distance s12 to be used as input in the direct geodesic problem. 
REDUCEDLENGTH 
Calculate reduced length m12. 
GEODESICSCALE 
Calculate geodesic scales M12 and M21. 
AREA 
Calculate area S12. 
LONG_UNROLL 
Unroll lon2 in the direct calculation. 
ALL 
All capabilities, calculate everything. (LONG_UNROLL is not included in this mask.) 
Definition at line 187 of file Geodesic.h.
NETGeographicLib::Geodesic::Geodesic  (  double  a, 
double  f  
) 
Constructor for a ellipsoid with
[in]  a  equatorial radius (meters). 
[in]  f  flattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid. 
GeographicErr  if a or (1 − f ) a is not positive. 
NETGeographicLib::Geodesic::Geodesic  (  ) 
Constructor for the WGS84 ellipsoid.
Referenced by ~Geodesic().

inline 
the destructor calls the finalizer.
Definition at line 272 of file Geodesic.h.
References ArcDirect(), ArcDirectLine(), Direct(), DirectLine(), GenDirect(), GenDirectLine(), GenInverse(), Geodesic(), Inverse(), InverseLine(), and Line().
double NETGeographicLib::Geodesic::Direct  (  double  lat1, 
double  lon1,  
double  azi1,  
double  s12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21,  
[System::Runtime::InteropServices::Out] double%  S12  
) 
Solve the direct geodesic problem where the length of the geodesic is specified in terms of distance.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  azi1  azimuth at point 1 (degrees). 
[in]  s12  distance between point 1 and point 2 (meters); it can be negative. 
[out]  lat2  latitude of point 2 (degrees). 
[out]  lon2  longitude of point 2 (degrees). 
[out]  azi2  (forward) azimuth at point 2 (degrees). 
[out]  m12  reduced length of geodesic (meters). 
[out]  M12  geodesic scale of point 2 relative to point 1 (dimensionless). 
[out]  M21  geodesic scale of point 1 relative to point 2 (dimensionless). 
[out]  S12  area under the geodesic (meters^{2}). 
lat1 should be in the range [−90°, 90°]. The values of lon2 and azi2 returned are in the range [−180°, 180°).
If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+. An arc length greater that 180° signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180°.)
The following functions are overloaded versions of Geodesic::Direct which omit some of the output parameters. Note, however, that the arc length is always computed and returned as the function value.
Referenced by ~Geodesic().
double NETGeographicLib::Geodesic::Direct  (  double  lat1, 
double  lon1,  
double  azi1,  
double  s12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2  
) 
See the documentation for Geodesic::Direct.
double NETGeographicLib::Geodesic::Direct  (  double  lat1, 
double  lon1,  
double  azi1,  
double  s12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2  
) 
See the documentation for Geodesic::Direct.
double NETGeographicLib::Geodesic::Direct  (  double  lat1, 
double  lon1,  
double  azi1,  
double  s12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  m12  
) 
See the documentation for Geodesic::Direct.
double NETGeographicLib::Geodesic::Direct  (  double  lat1, 
double  lon1,  
double  azi1,  
double  s12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21  
) 
See the documentation for Geodesic::Direct.
double NETGeographicLib::Geodesic::Direct  (  double  lat1, 
double  lon1,  
double  azi1,  
double  s12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21  
) 
See the documentation for Geodesic::Direct.
void NETGeographicLib::Geodesic::ArcDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21,  
[System::Runtime::InteropServices::Out] double%  S12  
) 
Solve the direct geodesic problem where the length of the geodesic is specified in terms of arc length.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  azi1  azimuth at point 1 (degrees). 
[in]  a12  arc length between point 1 and point 2 (degrees); it can be negative. 
[out]  lat2  latitude of point 2 (degrees). 
[out]  lon2  longitude of point 2 (degrees). 
[out]  azi2  (forward) azimuth at point 2 (degrees). 
[out]  s12  distance between point 1 and point 2 (meters). 
[out]  m12  reduced length of geodesic (meters). 
[out]  M12  geodesic scale of point 2 relative to point 1 (dimensionless). 
[out]  M21  geodesic scale of point 1 relative to point 2 (dimensionless). 
[out]  S12  area under the geodesic (meters^{2}). 
lat1 should be in the range [−90°, 90°]. The values of lon2 and azi2 returned are in the range [−180°, 180°).
If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+. An arc length greater that 180° signifies a geodesic which is not a shortest path. (For a prolate ellipsoid, an additional condition is necessary for a shortest path: the longitudinal extent must not exceed of 180°.)
The following functions are overloaded versions of Geodesic::Direct which omit some of the output parameters.
Referenced by ~Geodesic().
void NETGeographicLib::Geodesic::ArcDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2  
) 
See the documentation for Geodesic::ArcDirect.
void NETGeographicLib::Geodesic::ArcDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2  
) 
See the documentation for Geodesic::ArcDirect.
void NETGeographicLib::Geodesic::ArcDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  s12  
) 
See the documentation for Geodesic::ArcDirect.
void NETGeographicLib::Geodesic::ArcDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  m12  
) 
See the documentation for Geodesic::ArcDirect.
void NETGeographicLib::Geodesic::ArcDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21  
) 
See the documentation for Geodesic::ArcDirect.
void NETGeographicLib::Geodesic::ArcDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21  
) 
See the documentation for Geodesic::ArcDirect.
double NETGeographicLib::Geodesic::GenDirect  (  double  lat1, 
double  lon1,  
double  azi1,  
bool  arcmode,  
double  s12_a12,  
Geodesic::mask  outmask,  
[System::Runtime::InteropServices::Out] double%  lat2,  
[System::Runtime::InteropServices::Out] double%  lon2,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21,  
[System::Runtime::InteropServices::Out] double%  S12  
) 
The general direct geodesic problem. Geodesic::Direct and Geodesic::ArcDirect are defined in terms of this function.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  azi1  azimuth at point 1 (degrees). 
[in]  arcmode  boolean flag determining the meaning of the s12_a12. 
[in]  s12_a12  if arcmode is false, this is the distance between point 1 and point 2 (meters); otherwise it is the arc length between point 1 and point 2 (degrees); it can be negative. 
[in]  outmask  a bitor'ed combination of Geodesic::mask values specifying which of the following parameters should be set. 
[out]  lat2  latitude of point 2 (degrees). 
[out]  lon2  longitude of point 2 (degrees). 
[out]  azi2  (forward) azimuth at point 2 (degrees). 
[out]  s12  distance between point 1 and point 2 (meters). 
[out]  m12  reduced length of geodesic (meters). 
[out]  M12  geodesic scale of point 2 relative to point 1 (dimensionless). 
[out]  M21  geodesic scale of point 1 relative to point 2 (dimensionless). 
[out]  S12  area under the geodesic (meters^{2}). 
The Geodesic::mask values possible for outmask are
The function value a12 is always computed and returned and this equals s12_a12 is arcmode is true. If outmask includes Geodesic::DISTANCE and arcmode is false, then s12 = s12_a12. It is not necessary to include Geodesic::DISTANCE_IN in outmask; this is automatically included is arcmode is false.
With the LONG_UNROLL bit set, the quantity lon2 − lon1 indicates how many times and in what sense the geodesic encircles the ellipsoid.
Referenced by ~Geodesic().
double NETGeographicLib::Geodesic::Inverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  azi1,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21,  
[System::Runtime::InteropServices::Out] double%  S12  
) 
Solve the inverse geodesic problem.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  lat2  latitude of point 2 (degrees). 
[in]  lon2  longitude of point 2 (degrees). 
[out]  s12  distance between point 1 and point 2 (meters). 
[out]  azi1  azimuth at point 1 (degrees). 
[out]  azi2  (forward) azimuth at point 2 (degrees). 
[out]  m12  reduced length of geodesic (meters). 
[out]  M12  geodesic scale of point 2 relative to point 1 (dimensionless). 
[out]  M21  geodesic scale of point 1 relative to point 2 (dimensionless). 
[out]  S12  area under the geodesic (meters^{2}). 
lat1 and lat2 should be in the range [−90°, 90°]. The values of azi1 and azi2 returned are in the range [−180°, 180°).
If either point is at a pole, the azimuth is defined by keeping the longitude fixed, writing lat = ±(90° − ε), and taking the limit ε → 0+.
The solution to the inverse problem is found using Newton's method. If this fails to converge (this is very unlikely in geodetic applications but does occur for very eccentric ellipsoids), then the bisection method is used to refine the solution.
The following functions are overloaded versions of Geodesic::Inverse which omit some of the output parameters. Note, however, that the arc length is always computed and returned as the function value.
Referenced by ~Geodesic().
double NETGeographicLib::Geodesic::Inverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
[System::Runtime::InteropServices::Out] double%  s12  
) 
See the documentation for Geodesic::Inverse.
double NETGeographicLib::Geodesic::Inverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
[System::Runtime::InteropServices::Out] double%  azi1,  
[System::Runtime::InteropServices::Out] double%  azi2  
) 
See the documentation for Geodesic::Inverse.
double NETGeographicLib::Geodesic::Inverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  azi1,  
[System::Runtime::InteropServices::Out] double%  azi2  
) 
See the documentation for Geodesic::Inverse.
double NETGeographicLib::Geodesic::Inverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  azi1,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  m12  
) 
See the documentation for Geodesic::Inverse.
double NETGeographicLib::Geodesic::Inverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  azi1,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21  
) 
See the documentation for Geodesic::Inverse.
double NETGeographicLib::Geodesic::Inverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  azi1,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21  
) 
See the documentation for Geodesic::Inverse.
double NETGeographicLib::Geodesic::GenInverse  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
Geodesic::mask  outmask,  
[System::Runtime::InteropServices::Out] double%  s12,  
[System::Runtime::InteropServices::Out] double%  azi1,  
[System::Runtime::InteropServices::Out] double%  azi2,  
[System::Runtime::InteropServices::Out] double%  m12,  
[System::Runtime::InteropServices::Out] double%  M12,  
[System::Runtime::InteropServices::Out] double%  M21,  
[System::Runtime::InteropServices::Out] double%  S12  
) 
The general inverse geodesic calculation. Geodesic::Inverse is defined in terms of this function.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  lat2  latitude of point 2 (degrees). 
[in]  lon2  longitude of point 2 (degrees). 
[in]  outmask  a bitor'ed combination of Geodesic::mask values specifying which of the following parameters should be set. 
[out]  s12  distance between point 1 and point 2 (meters). 
[out]  azi1  azimuth at point 1 (degrees). 
[out]  azi2  (forward) azimuth at point 2 (degrees). 
[out]  m12  reduced length of geodesic (meters). 
[out]  M12  geodesic scale of point 2 relative to point 1 (dimensionless). 
[out]  M21  geodesic scale of point 1 relative to point 2 (dimensionless). 
[out]  S12  area under the geodesic (meters^{2}). 
The Geodesic::mask values possible for outmask are
The arc length is always computed and returned as the function value.
Referenced by ~Geodesic().
GeodesicLine ^ NETGeographicLib::Geodesic::Line  (  double  lat1, 
double  lon1,  
double  azi1,  
NETGeographicLib::Mask  caps  
) 
Set up to compute several points on a single geodesic.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  azi1  azimuth at point 1 (degrees). 
[in]  caps  bitor'ed combination of NETGeographicLib::Mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position. 
lat1 should be in the range [−90°, 90°].
The NETGeographicLib::Mask values are
If the point is at a pole, the azimuth is defined by keeping lon1 fixed, writing lat1 = ±(90 − ε), and taking the limit ε → 0+.
Referenced by ~Geodesic().
GeodesicLine ^ NETGeographicLib::Geodesic::InverseLine  (  double  lat1, 
double  lon1,  
double  lat2,  
double  lon2,  
NETGeographicLib::Mask  caps  
) 
Define a GeodesicLine in terms of the inverse geodesic problem.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  lat2  latitude of point 2 (degrees). 
[in]  lon2  longitude of point 2 (degrees). 
[in]  caps  bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position. 
This function sets point 3 of the GeodesicLine to correspond to point 2 of the inverse geodesic problem.
lat1 and lat2 should be in the range [−90°, 90°].
Referenced by ~Geodesic().
GeodesicLine ^ NETGeographicLib::Geodesic::DirectLine  (  double  lat1, 
double  lon1,  
double  azi1,  
double  s12,  
NETGeographicLib::Mask  caps  
) 
Define a GeodesicLine in terms of the direct geodesic problem specified in terms of distance.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  azi1  azimuth at point 1 (degrees). 
[in]  s12  distance between point 1 and point 2 (meters); it can be negative. 
[in]  caps  bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position. 
This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.
lat1 should be in the range [−90°, 90°].
Referenced by ~Geodesic().
GeodesicLine ^ NETGeographicLib::Geodesic::ArcDirectLine  (  double  lat1, 
double  lon1,  
double  azi1,  
double  a12,  
NETGeographicLib::Mask  caps  
) 
Define a GeodesicLine in terms of the direct geodesic problem specified in terms of arc length.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  azi1  azimuth at point 1 (degrees). 
[in]  a12  arc length between point 1 and point 2 (degrees); it can be negative. 
[in]  caps  bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position. 
This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.
lat1 should be in the range [−90°, 90°].
Referenced by ~Geodesic().
GeodesicLine ^ NETGeographicLib::Geodesic::GenDirectLine  (  double  lat1, 
double  lon1,  
double  azi1,  
bool  arcmode,  
double  s12_a12,  
NETGeographicLib::Mask  caps  
) 
Define a GeodesicLine in terms of the direct geodesic problem specified in terms of either distance or arc length.
[in]  lat1  latitude of point 1 (degrees). 
[in]  lon1  longitude of point 1 (degrees). 
[in]  azi1  azimuth at point 1 (degrees). 
[in]  arcmode  boolean flag determining the meaning of the s12_a12. 
[in]  s12_a12  if arcmode is false, this is the distance between point 1 and point 2 (meters); otherwise it is the arc length between point 1 and point 2 (degrees); it can be negative. 
[in]  caps  bitor'ed combination of Geodesic::mask values specifying the capabilities the GeodesicLine object should possess, i.e., which quantities can be returned in calls to GeodesicLine::Position. 
This function sets point 3 of the GeodesicLine to correspond to point 2 of the direct geodesic problem.
lat1 should be in the range [−90°, 90°].
Referenced by ~Geodesic().
System::IntPtr ^ NETGeographicLib::Geodesic::GetUnmanaged  (  ) 
return The unmanaged pointer to the GeographicLib::Geodesic.
This function is for internal use only.

get 
Definition at line 830 of file Geodesic.h.

get 
Definition at line 836 of file Geodesic.h.

get 
Definition at line 844 of file Geodesic.h.