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GeographicLib::Rhumb Class Reference

Solve of the direct and inverse rhumb problems. More...

#include <Rhumb.hpp>

Public Types

enum  mask {
  NONE, LATITUDE, LONGITUDE, AZIMUTH,
  DISTANCE, AREA, LONG_UNROLL, ALL
}
 

Public Member Functions

void Direct (real lat1, real lon1, real azi12, real s12, real &lat2, real &lon2, real &S12) const
 
void Direct (real lat1, real lon1, real azi12, real s12, real &lat2, real &lon2) const
 
void GenDirect (real lat1, real lon1, real azi12, real s12, unsigned outmask, real &lat2, real &lon2, real &S12) const
 
void GenInverse (real lat1, real lon1, real lat2, real lon2, unsigned outmask, real &s12, real &azi12, real &S12) const
 
void Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi12, real &S12) const
 
void Inverse (real lat1, real lon1, real lat2, real lon2, real &s12, real &azi12) const
 
RhumbLine Line (real lat1, real lon1, real azi12) const
 
 Rhumb (real a, real f, bool exact=true)
 

Private Types

typedef Math::real real
 

Private Member Functions

real DConformalToRectifying (real chix, real chiy) const
 
real DE (real x, real y) const
 
real Deatanhe (real x, real y) const
 
real DIsometric (real latx, real laty) const
 
real DIsometricToRectifying (real psix, real psiy) const
 
real DRectifying (real latx, real laty) const
 
real DRectifyingToConformal (real mux, real muy) const
 
real DRectifyingToIsometric (real mux, real muy) const
 
void GenDirect (real lat1, real lon1, real azi12, bool, real s12, unsigned outmask, real &lat2, real &lon2, real &, real &, real &, real &, real &, real &S12) const
 
void GenInverse (real lat1, real lon1, real lat2, real lon2, unsigned outmask, real &s12, real &azi12, real &, real &, real &, real &, real &S12) const
 
real MeanSinXi (real psi1, real psi2) const
 

Static Private Member Functions

static real Dasinh (real x, real y)
 
static real Datan (real x, real y)
 
static real Dcosh (real x, real y)
 
static real Dgd (real x, real y)
 
static real Dgdinv (real x, real y)
 
static real Dlog (real x, real y)
 
static real Dsin (real x, real y)
 
static real Dsinh (real x, real y)
 
static real Dtan (real x, real y)
 
static real gd (real x)
 
static real SinCosSeries (bool sinp, real x, real y, const real c[], int n)
 

Private Attributes

real _c2
 
Ellipsoid _ell
 
bool _exact
 
real _R [maxpow_+1]
 

Static Private Attributes

static const int maxpow_ = GEOGRAPHICLIB_RHUMBAREA_ORDER
 
static const int tm_maxord = GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER
 

Friends

template<class T >
class PolygonAreaT
 
class RhumbLine
 

Inspector functions.

Math::real MajorRadius () const
 
Math::real Flattening () const
 
Math::real EllipsoidArea () const
 
static const RhumbWGS84 ()
 

Detailed Description

Solve of the direct and inverse rhumb problems.

The path of constant azimuth between two points on a ellipsoid at (lat1, lon1) and (lat2, lon2) is called the rhumb line (also called the loxodrome). Its length is s12 and its azimuth is azi12. (The azimuth is the heading measured clockwise from north.)

Given lat1, lon1, azi12, and s12, we can determine lat2, and lon2. This is the direct rhumb problem and its solution is given by the function Rhumb::Direct.

Given lat1, lon1, lat2, and lon2, we can determine azi12 and s12. This is the inverse rhumb problem, whose solution is given by Rhumb::Inverse. This finds the shortest such rhumb line, i.e., the one that wraps no more than half way around the earth. If the end points are on opposite meridians, there are two shortest rhumb lines and the east-going one is chosen.

These routines also optionally calculate the area under the rhumb line, S12. This is the area, measured counter-clockwise, of the rhumb line quadrilateral with corners (lat1,lon1), (0,lon1), (0,lon2), and (lat2,lon2).

Note that rhumb lines may be appreciably longer (up to 50%) than the corresponding Geodesic. For example the distance between London Heathrow and Tokyo Narita via the rhumb line is 11400 km which is 18% longer than the geodesic distance 9600 km.

For more information on rhumb lines see rhumb.

Example of use:

// Example of using the GeographicLib::Rhumb class
#include <iostream>
#include <exception>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// Alternatively: const Rhumb& rhumb = Rhumb::WGS84();
{
// Sample direct calculation, travelling about NE from JFK
double lat1 = 40.6, lon1 = -73.8, s12 = 5.5e6, azi12 = 51;
double lat2, lon2;
rhumb.Direct(lat1, lon1, azi12, s12, lat2, lon2);
cout << lat2 << " " << lon2 << "\n";
}
{
// Sample inverse calculation, JFK to LHR
double
lat1 = 40.6, lon1 = -73.8, // JFK Airport
lat2 = 51.6, lon2 = -0.5; // LHR Airport
double s12, azi12;
rhumb.Inverse(lat1, lon1, lat2, lon2, s12, azi12);
cout << s12 << " " << azi12 << "\n";
}
}
catch (const exception& e) {
cerr << "Caught exception: " << e.what() << "\n";
return 1;
}
}

Definition at line 66 of file Rhumb.hpp.

Member Typedef Documentation

◆ real

Definition at line 68 of file Rhumb.hpp.

Member Enumeration Documentation

◆ mask

Bit masks for what calculations to do. They specify which results to return in the general routines Rhumb::GenDirect and Rhumb::GenInverse routines. RhumbLine::mask is a duplication of this enum.

Enumerator
NONE 

No output.

LATITUDE 

Calculate latitude lat2.

LONGITUDE 

Calculate longitude lon2.

AZIMUTH 

Calculate azimuth azi12.

DISTANCE 

Calculate distance s12.

AREA 

Calculate area S12.

LONG_UNROLL 

Unroll lon2 in the direct calculation.

ALL 

Calculate everything. (LONG_UNROLL is not included in this mask.)

Definition at line 190 of file Rhumb.hpp.

Constructor & Destructor Documentation

◆ Rhumb()

GeographicLib::Rhumb::Rhumb ( real  a,
real  f,
bool  exact = true 
)

Constructor for a ellipsoid with

Parameters
[in]aequatorial radius (meters).
[in]fflattening of ellipsoid. Setting f = 0 gives a sphere. Negative f gives a prolate ellipsoid.
[in]exactif true (the default) use an addition theorem for elliptic integrals to compute divided differences; otherwise use series expansion (accurate for |f| < 0.01).
Exceptions
GeographicErrif a or (1 − f) a is not positive.

See rhumb, for a detailed description of the exact parameter.

Definition at line 18 of file src/Rhumb.cpp.

Member Function Documentation

◆ Dasinh()

static real GeographicLib::Rhumb::Dasinh ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 126 of file Rhumb.hpp.

◆ Datan()

static real GeographicLib::Rhumb::Datan ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 104 of file Rhumb.hpp.

◆ DConformalToRectifying()

Math::real GeographicLib::Rhumb::DConformalToRectifying ( real  chix,
real  chiy 
) const
private

Definition at line 292 of file src/Rhumb.cpp.

◆ Dcosh()

static real GeographicLib::Rhumb::Dcosh ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 121 of file Rhumb.hpp.

◆ DE()

Math::real GeographicLib::Rhumb::DE ( real  x,
real  y 
) const
private

Definition at line 176 of file src/Rhumb.cpp.

◆ Deatanhe()

real GeographicLib::Rhumb::Deatanhe ( real  x,
real  y 
) const
inlineprivate

Definition at line 142 of file Rhumb.hpp.

◆ Dgd()

static real GeographicLib::Rhumb::Dgd ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 133 of file Rhumb.hpp.

◆ Dgdinv()

static real GeographicLib::Rhumb::Dgdinv ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 138 of file Rhumb.hpp.

◆ Direct() [1/2]

void GeographicLib::Rhumb::Direct ( real  lat1,
real  lon1,
real  azi12,
real  s12,
real lat2,
real lon2,
real S12 
) const
inline

Solve the direct rhumb problem returning also the area.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi12azimuth of the rhumb line (degrees).
[in]s12distance between point 1 and point 2 (meters); it can be negative.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees).
[out]S12area under the rhumb line (meters2).

lat1 should be in the range [−90°, 90°]. The value of lon2 returned is in the range [−180°, 180°].

If point 1 is a pole, the cosine of its latitude is taken to be 1/ε2 (where ε is 2-52). This position, which is extremely close to the actual pole, allows the calculation to be carried out in finite terms. If s12 is large enough that the rhumb line crosses a pole, the longitude of point 2 is indeterminate (a NaN is returned for lon2 and S12).

Definition at line 271 of file Rhumb.hpp.

◆ Direct() [2/2]

void GeographicLib::Rhumb::Direct ( real  lat1,
real  lon1,
real  azi12,
real  s12,
real lat2,
real lon2 
) const
inline

Solve the direct rhumb problem without the area.

Definition at line 280 of file Rhumb.hpp.

◆ DIsometric()

Math::real GeographicLib::Rhumb::DIsometric ( real  latx,
real  laty 
) const
private

Definition at line 213 of file src/Rhumb.cpp.

◆ DIsometricToRectifying()

Math::real GeographicLib::Rhumb::DIsometricToRectifying ( real  psix,
real  psiy 
) const
private

Definition at line 302 of file src/Rhumb.cpp.

◆ Dlog()

static real GeographicLib::Rhumb::Dlog ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 92 of file Rhumb.hpp.

◆ DRectifying()

Math::real GeographicLib::Rhumb::DRectifying ( real  latx,
real  laty 
) const
private

Definition at line 205 of file src/Rhumb.cpp.

◆ DRectifyingToConformal()

Math::real GeographicLib::Rhumb::DRectifyingToConformal ( real  mux,
real  muy 
) const
private

Definition at line 297 of file src/Rhumb.cpp.

◆ DRectifyingToIsometric()

Math::real GeographicLib::Rhumb::DRectifyingToIsometric ( real  mux,
real  muy 
) const
private

Definition at line 315 of file src/Rhumb.cpp.

◆ Dsin()

static real GeographicLib::Rhumb::Dsin ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 111 of file Rhumb.hpp.

◆ Dsinh()

static real GeographicLib::Rhumb::Dsinh ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 116 of file Rhumb.hpp.

◆ Dtan()

static real GeographicLib::Rhumb::Dtan ( real  x,
real  y 
)
inlinestaticprivate

Definition at line 97 of file Rhumb.hpp.

◆ EllipsoidArea()

Math::real GeographicLib::Rhumb::EllipsoidArea ( ) const
inline

Definition at line 410 of file Rhumb.hpp.

◆ Flattening()

Math::real GeographicLib::Rhumb::Flattening ( ) const
inline
Returns
f the flattening of the ellipsoid. This is the value used in the constructor.

Definition at line 408 of file Rhumb.hpp.

◆ gd()

static real GeographicLib::Rhumb::gd ( real  x)
inlinestaticprivate

Definition at line 78 of file Rhumb.hpp.

◆ GenDirect() [1/2]

void GeographicLib::Rhumb::GenDirect ( real  lat1,
real  lon1,
real  azi12,
bool  ,
real  s12,
unsigned  outmask,
real lat2,
real lon2,
real ,
real ,
real ,
real ,
real ,
real S12 
) const
inlineprivate

Definition at line 172 of file Rhumb.hpp.

◆ GenDirect() [2/2]

void GeographicLib::Rhumb::GenDirect ( real  lat1,
real  lon1,
real  azi12,
real  s12,
unsigned  outmask,
real lat2,
real lon2,
real S12 
) const

The general direct rhumb problem. Rhumb::Direct is defined in terms of this function.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi12azimuth of the rhumb line (degrees).
[in]s12distance between point 1 and point 2 (meters); it can be negative.
[in]outmaska bitor'ed combination of Rhumb::mask values specifying which of the following parameters should be set.
[out]lat2latitude of point 2 (degrees).
[out]lon2longitude of point 2 (degrees).
[out]S12area under the rhumb line (meters2).

The Rhumb::mask values possible for outmask are

With the Rhumb::LONG_UNROLL bit set, the quantity lon2lon1 indicates how many times and in what sense the rhumb line encircles the ellipsoid.

Definition at line 171 of file src/Rhumb.cpp.

◆ GenInverse() [1/2]

void GeographicLib::Rhumb::GenInverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
unsigned  outmask,
real s12,
real azi12,
real ,
real ,
real ,
real ,
real S12 
) const
inlineprivate

Definition at line 178 of file Rhumb.hpp.

◆ GenInverse() [2/2]

void GeographicLib::Rhumb::GenInverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
unsigned  outmask,
real s12,
real azi12,
real S12 
) const

The general inverse rhumb problem. Rhumb::Inverse is defined in terms of this function.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]lat2latitude of point 2 (degrees).
[in]lon2longitude of point 2 (degrees).
[in]outmaska bitor'ed combination of Rhumb::mask values specifying which of the following parameters should be set.
[out]s12rhumb distance between point 1 and point 2 (meters).
[out]azi12azimuth of the rhumb line (degrees).
[out]S12area under the rhumb line (meters2).

The Rhumb::mask values possible for outmask are

Definition at line 148 of file src/Rhumb.cpp.

◆ Inverse() [1/2]

void GeographicLib::Rhumb::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real s12,
real azi12,
real S12 
) const
inline

Solve the inverse rhumb problem returning also the area.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]lat2latitude of point 2 (degrees).
[in]lon2longitude of point 2 (degrees).
[out]s12rhumb distance between point 1 and point 2 (meters).
[out]azi12azimuth of the rhumb line (degrees).
[out]S12area under the rhumb line (meters2).

The shortest rhumb line is found. If the end points are on opposite meridians, there are two shortest rhumb lines and the east-going one is chosen. lat1 and lat2 should be in the range [−90°, 90°]. The value of azi12 returned is in the range [−180°, 180°].

If either point is a pole, the cosine of its latitude is taken to be 1/ε2 (where ε is 2-52). This position, which is extremely close to the actual pole, allows the calculation to be carried out in finite terms.

Definition at line 338 of file Rhumb.hpp.

◆ Inverse() [2/2]

void GeographicLib::Rhumb::Inverse ( real  lat1,
real  lon1,
real  lat2,
real  lon2,
real s12,
real azi12 
) const
inline

Solve the inverse rhumb problem without the area.

Definition at line 347 of file Rhumb.hpp.

◆ Line()

RhumbLine GeographicLib::Rhumb::Line ( real  lat1,
real  lon1,
real  azi12 
) const

Set up to compute several points on a single rhumb line.

Parameters
[in]lat1latitude of point 1 (degrees).
[in]lon1longitude of point 1 (degrees).
[in]azi12azimuth of the rhumb line (degrees).
Returns
a RhumbLine object.

lat1 should be in the range [−90°, 90°].

If point 1 is a pole, the cosine of its latitude is taken to be 1/ε2 (where ε is 2-52). This position, which is extremely close to the actual pole, allows the calculation to be carried out in finite terms.

Definition at line 168 of file src/Rhumb.cpp.

◆ MajorRadius()

Math::real GeographicLib::Rhumb::MajorRadius ( ) const
inline
Returns
a the equatorial radius of the ellipsoid (meters). This is the value used in the constructor.

Definition at line 402 of file Rhumb.hpp.

◆ MeanSinXi()

Math::real GeographicLib::Rhumb::MeanSinXi ( real  psi1,
real  psi2 
) const
private

Definition at line 326 of file src/Rhumb.cpp.

◆ SinCosSeries()

Math::real GeographicLib::Rhumb::SinCosSeries ( bool  sinp,
real  x,
real  y,
const real  c[],
int  n 
)
staticprivate

Definition at line 221 of file src/Rhumb.cpp.

◆ WGS84()

const Rhumb & GeographicLib::Rhumb::WGS84 ( )
static

A global instantiation of Rhumb with the parameters for the WGS84 ellipsoid.

Definition at line 142 of file src/Rhumb.cpp.

Friends And Related Function Documentation

◆ PolygonAreaT

template<class T >
friend class PolygonAreaT
friend

Definition at line 70 of file Rhumb.hpp.

◆ RhumbLine

friend class RhumbLine
friend

Definition at line 69 of file Rhumb.hpp.

Member Data Documentation

◆ _c2

real GeographicLib::Rhumb::_c2
private

Definition at line 73 of file Rhumb.hpp.

◆ _ell

Ellipsoid GeographicLib::Rhumb::_ell
private

Definition at line 71 of file Rhumb.hpp.

◆ _exact

bool GeographicLib::Rhumb::_exact
private

Definition at line 72 of file Rhumb.hpp.

◆ _R

real GeographicLib::Rhumb::_R[maxpow_+1]
private

Definition at line 77 of file Rhumb.hpp.

◆ maxpow_

const int GeographicLib::Rhumb::maxpow_ = GEOGRAPHICLIB_RHUMBAREA_ORDER
staticprivate

Definition at line 75 of file Rhumb.hpp.

◆ tm_maxord

const int GeographicLib::Rhumb::tm_maxord = GEOGRAPHICLIB_TRANSVERSEMERCATOR_ORDER
staticprivate

Definition at line 74 of file Rhumb.hpp.


The documentation for this class was generated from the following files:


gtsam
Author(s):
autogenerated on Tue Jul 4 2023 02:46:12