Public Member Functions | Private Types | Static Private Member Functions | Private Attributes | Related Functions | List of all members
GeographicLib::PolygonAreaT< GeodType > Class Template Reference

Polygon areas. More...

#include <PolygonArea.hpp>

Public Member Functions

void AddEdge (real azi, real s)
 
void AddPoint (real lat, real lon)
 
void Clear ()
 
unsigned Compute (bool reverse, bool sign, real &perimeter, real &area) const
 
 PolygonAreaT (const GeodType &earth, bool polyline=false)
 
unsigned TestEdge (real azi, real s, bool reverse, bool sign, real &perimeter, real &area) const
 
unsigned TestPoint (real lat, real lon, bool reverse, bool sign, real &perimeter, real &area) const
 
Inspector functions
Math::real MajorRadius () const
 
Math::real Flattening () const
 
void CurrentPoint (real &lat, real &lon) const
 

Private Types

typedef Math::real real
 

Static Private Member Functions

static int transit (real lon1, real lon2)
 
static int transitdirect (real lon1, real lon2)
 

Private Attributes

real _area0
 
Accumulator _areasum
 
int _crossings
 
GeodType _earth
 
real _lat0
 
real _lat1
 
real _lon0
 
real _lon1
 
unsigned _mask
 
unsigned _num
 
Accumulator _perimetersum
 
bool _polyline
 

Related Functions

(Note that these are not member functions.)

typedef PolygonAreaT< GeodesicPolygonArea
 
typedef PolygonAreaT< GeodesicExactPolygonAreaExact
 
typedef PolygonAreaT< RhumbPolygonAreaRhumb
 

Detailed Description

template<class GeodType = Geodesic>
class GeographicLib::PolygonAreaT< GeodType >

Polygon areas.

This computes the area of a polygon whose edges are geodesics using the method given in Section 6 of

This class lets you add vertices and edges one at a time to the polygon. The sequence must start with a vertex and thereafter vertices and edges can be added in any order. Any vertex after the first creates a new edge which is the shortest geodesic from the previous vertex. In some cases there may be two or many such shortest geodesics and the area is then not uniquely defined. In this case, either add an intermediate vertex or add the edge as an edge (by defining its direction and length).

The area and perimeter are accumulated at two times the standard floating point precision to guard against the loss of accuracy with many-sided polygons. At any point you can ask for the perimeter and area so far. There's an option to treat the points as defining a polyline instead of a polygon; in that case, only the perimeter is computed.

This is a templated class to allow it to be used with Geodesic, GeodesicExact, and Rhumb. GeographicLib::PolygonArea, GeographicLib::PolygonAreaExact, and GeographicLib::PolygonAreaRhumb are typedefs for these cases.

Template Parameters
GeodTypethe geodesic class to use.

Example of use:

// Example of using the GeographicLib::PolygonArea class
#include <iostream>
#include <exception>
using namespace std;
using namespace GeographicLib;
int main() {
try {
// Alternatively: const Geodesic& geod = Geodesic::WGS84();
PolygonArea poly(geod);
poly.AddPoint( 52, 0); // London
poly.AddPoint( 41,-74); // New York
poly.AddPoint(-23,-43); // Rio de Janeiro
poly.AddPoint(-26, 28); // Johannesburg
double perimeter, area;
unsigned n = poly.Compute(false, true, perimeter, area);
cout << n << " " << perimeter << " " << area << "\n";
}
catch (const exception& e) {
cerr << "Caught exception: " << e.what() << "\n";
return 1;
}
}

Planimeter is a command-line utility providing access to the functionality of PolygonAreaT.

Definition at line 65 of file PolygonArea.hpp.

Member Typedef Documentation

template<class GeodType = Geodesic>
typedef Math::real GeographicLib::PolygonAreaT< GeodType >::real
private

Definition at line 67 of file PolygonArea.hpp.

Constructor & Destructor Documentation

template<class GeodType = Geodesic>
GeographicLib::PolygonAreaT< GeodType >::PolygonAreaT ( const GeodType &  earth,
bool  polyline = false 
)
inline

Constructor for PolygonAreaT.

Parameters
[in]earththe Geodesic object to use for geodesic calculations.
[in]polylineif true that treat the points as defining a polyline instead of a polygon (default = false).

Definition at line 120 of file PolygonArea.hpp.

Member Function Documentation

template<class GeodType >
void GeographicLib::PolygonAreaT< GeodType >::AddEdge ( real  azi,
real  s 
)

Add an edge to the polygon or polyline.

Parameters
[in]aziazimuth at current point (degrees).
[in]sdistance from current point to next point (meters).

This does nothing if no points have been added yet. Use PolygonAreaT::CurrentPoint to determine the position of the new vertex.

Definition at line 38 of file src/PolygonArea.cpp.

template<class GeodType >
void GeographicLib::PolygonAreaT< GeodType >::AddPoint ( real  lat,
real  lon 
)

Add a point to the polygon or polyline.

Parameters
[in]latthe latitude of the point (degrees).
[in]lonthe longitude of the point (degrees).

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

Definition at line 17 of file src/PolygonArea.cpp.

template<class GeodType = Geodesic>
void GeographicLib::PolygonAreaT< GeodType >::Clear ( )
inline

Clear PolygonAreaT, allowing a new polygon to be started.

Definition at line 132 of file PolygonArea.hpp.

template<class GeodType >
unsigned GeographicLib::PolygonAreaT< GeodType >::Compute ( bool  reverse,
bool  sign,
real perimeter,
real area 
) const

Return the results so far.

Parameters
[in]reverseif true then clockwise (instead of counter-clockwise) traversal counts as a positive area.
[in]signif true then return a signed result for the area if the polygon is traversed in the "wrong" direction instead of returning the area for the rest of the earth.
[out]perimeterthe perimeter of the polygon or length of the polyline (meters).
[out]areathe area of the polygon (meters2); only set if polyline is false in the constructor.
Returns
the number of points.

More points can be added to the polygon after this call.

Definition at line 55 of file src/PolygonArea.cpp.

template<class GeodType = Geodesic>
void GeographicLib::PolygonAreaT< GeodType >::CurrentPoint ( real lat,
real lon 
) const
inline

Report the previous vertex added to the polygon or polyline.

Parameters
[out]latthe latitude of the point (degrees).
[out]lonthe longitude of the point (degrees).

If no points have been added, then NaNs are returned. Otherwise, lon will be in the range [−180°, 180°].

Definition at line 259 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
Math::real GeographicLib::PolygonAreaT< GeodType >::Flattening ( ) const
inline
Returns
f the flattening of the ellipsoid. This is the value inherited from the Geodesic object used in the constructor.

Definition at line 248 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
Math::real GeographicLib::PolygonAreaT< GeodType >::MajorRadius ( ) const
inline
Returns
a the equatorial radius of the ellipsoid (meters). This is the value inherited from the Geodesic object used in the constructor.

Definition at line 242 of file PolygonArea.hpp.

template<class GeodType >
unsigned GeographicLib::PolygonAreaT< GeodType >::TestEdge ( real  azi,
real  s,
bool  reverse,
bool  sign,
real perimeter,
real area 
) const

Return the results assuming a tentative final test point is added via an azimuth and distance; however, the data for the test point is not saved. This lets you report a running result for the perimeter and area as the user moves the mouse cursor. Ordinary floating point arithmetic is used to accumulate the data for the test point; thus the area and perimeter returned are less accurate than if PolygonAreaT::AddEdge and PolygonAreaT::Compute are used.

Parameters
[in]aziazimuth at current point (degrees).
[in]sdistance from current point to final test point (meters).
[in]reverseif true then clockwise (instead of counter-clockwise) traversal counts as a positive area.
[in]signif true then return a signed result for the area if the polygon is traversed in the "wrong" direction instead of returning the area for the rest of the earth.
[out]perimeterthe approximate perimeter of the polygon or length of the polyline (meters).
[out]areathe approximate area of the polygon (meters2); only set if polyline is false in the constructor.
Returns
the number of points.

Definition at line 151 of file src/PolygonArea.cpp.

template<class GeodType >
unsigned GeographicLib::PolygonAreaT< GeodType >::TestPoint ( real  lat,
real  lon,
bool  reverse,
bool  sign,
real perimeter,
real area 
) const

Return the results assuming a tentative final test point is added; however, the data for the test point is not saved. This lets you report a running result for the perimeter and area as the user moves the mouse cursor. Ordinary floating point arithmetic is used to accumulate the data for the test point; thus the area and perimeter returned are less accurate than if PolygonAreaT::AddPoint and PolygonAreaT::Compute are used.

Parameters
[in]latthe latitude of the test point (degrees).
[in]lonthe longitude of the test point (degrees).
[in]reverseif true then clockwise (instead of counter-clockwise) traversal counts as a positive area.
[in]signif true then return a signed result for the area if the polygon is traversed in the "wrong" direction instead of returning the area for the rest of the earth.
[out]perimeterthe approximate perimeter of the polygon or length of the polyline (meters).
[out]areathe approximate area of the polygon (meters2); only set if polyline is false in the constructor.
Returns
the number of points.

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

Definition at line 98 of file src/PolygonArea.cpp.

template<class GeodType = Geodesic>
static int GeographicLib::PolygonAreaT< GeodType >::transit ( real  lon1,
real  lon2 
)
inlinestaticprivate

Definition at line 76 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
static int GeographicLib::PolygonAreaT< GeodType >::transitdirect ( real  lon1,
real  lon2 
)
inlinestaticprivate

Definition at line 92 of file PolygonArea.hpp.

Friends And Related Function Documentation

template<class GeodType = Geodesic>
typedef PolygonAreaT<Geodesic> PolygonArea
related

Polygon areas using Geodesic. This should be used if the flattening is small.

Definition at line 270 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
typedef PolygonAreaT<GeodesicExact> PolygonAreaExact
related

Polygon areas using GeodesicExact. (But note that the implementation of areas in GeodesicExact uses a high order series and this is only accurate for modest flattenings.)

Definition at line 279 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
typedef PolygonAreaT<Rhumb> PolygonAreaRhumb
related

Polygon areas using Rhumb.

Definition at line 286 of file PolygonArea.hpp.

Member Data Documentation

template<class GeodType = Geodesic>
real GeographicLib::PolygonAreaT< GeodType >::_area0
private

Definition at line 69 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
Accumulator GeographicLib::PolygonAreaT< GeodType >::_areasum
private

Definition at line 74 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
int GeographicLib::PolygonAreaT< GeodType >::_crossings
private

Definition at line 73 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
GeodType GeographicLib::PolygonAreaT< GeodType >::_earth
private

Definition at line 68 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
real GeographicLib::PolygonAreaT< GeodType >::_lat0
private

Definition at line 75 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
real GeographicLib::PolygonAreaT< GeodType >::_lat1
private

Definition at line 75 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
real GeographicLib::PolygonAreaT< GeodType >::_lon0
private

Definition at line 75 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
real GeographicLib::PolygonAreaT< GeodType >::_lon1
private

Definition at line 75 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
unsigned GeographicLib::PolygonAreaT< GeodType >::_mask
private

Definition at line 71 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
unsigned GeographicLib::PolygonAreaT< GeodType >::_num
private

Definition at line 72 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
Accumulator GeographicLib::PolygonAreaT< GeodType >::_perimetersum
private

Definition at line 74 of file PolygonArea.hpp.

template<class GeodType = Geodesic>
bool GeographicLib::PolygonAreaT< GeodType >::_polyline
private

Definition at line 70 of file PolygonArea.hpp.


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


gtsam
Author(s):
autogenerated on Sat May 8 2021 02:58:00