Polygon areas. More...

#include <GeographicLib/PolygonArea.hpp>

Public Member Functions
	PolygonAreaT (const GeodType &earth, bool polyline=false)

void	Clear ()

void	AddPoint (real lat, real lon)

void	AddEdge (real azi, real s)

unsigned	Compute (bool reverse, bool sign, real &perimeter, real &area) const

unsigned	TestPoint (real lat, real lon, bool reverse, bool sign, real &perimeter, real &area) const

unsigned	TestEdge (real azi, real s, bool reverse, bool sign, real &perimeter, real &area) const

Inspector functions
Math::real	EquatorialRadius () const

Math::real	Flattening () const

void	CurrentPoint (real &lat, real &lon) const

unsigned	NumberPoints () const

bool	Polyline () const

Related Functions
(Note that these are not member functions.)
typedef PolygonAreaT< Geodesic >	PolygonArea

typedef PolygonAreaT< GeodesicExact >	PolygonAreaExact

typedef PolygonAreaT< Rhumb >	PolygonAreaRhumb

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

C. F. F. Karney, Algorithms for geodesics, J. Geodesy 87, 43–55 (2013); DOI: 10.1007/s00190-012-0578-z; addenda: geod-addenda.html.

Arbitrarily complex polygons are allowed. In the case self-intersecting of polygons the area is accumulated "algebraically", e.g., the areas of the 2 loops in a figure-8 polygon will partially cancel.

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.

For GeographicLib::PolygonArea (edges defined by Geodesic), an upper bound on the error is about 0.1 m² per vertex. However this is a wildly pessimistic estimate in most cases. A more realistic estimate of the error is given by a test involving 10⁷ approximately regular polygons on the WGS84 ellipsoid. The centers and the orientations of the polygons were uniformly distributed, the number of vertices was log-uniformly distributed in [3, 300], and the center to vertex distance log-uniformly distributed in [0.1 m, 9000 km].

Using double precision (the standard precision for GeographicLib), the maximum error in the perimeter was 200 nm, and the maximum error in the area was

    0.0013 m^2 for perimeter < 10 km
    0.0070 m^2 for perimeter < 100 km
    0.070 m^2 for perimeter < 1000 km
    0.11 m^2 for all perimeters

The errors are given in terms of the perimeter, because it is expected that the errors depend mainly on the number of edges and the edge lengths.

Using long doubles (GEOGRPAHICLIB_PRECISION = 3), the maximum error in the perimeter was 200 pm, and the maximum error in the area was

    0.7 mm^2 for perim < 10 km
    3.2 mm^2 for perimeter < 100 km
    21 mm^2 for perimeter < 1000 km
    45 mm^2 for all perimeters

Template Parameters

GeodType the geodesic class to use.

Example of use:

// Example of using the GeographicLib::PolygonArea class
 
#include <iostream>
#include <exception>
#include <GeographicLib/PolygonArea.hpp>
#include <GeographicLib/Geodesic.hpp>
#include <GeographicLib/Constants.hpp>
 
using namespace std;
using namespace GeographicLib;
 
int main() {
  try {
    Geodesic geod(Constants::WGS84_a(), Constants::WGS84_f());
    // 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";
    // This adds a test for a bug fix for AddEdge.  (Implements the
    // Planimeter29 test in geodtest.c.)
    PolygonArea poly1(geod);
    poly1.AddPoint(0,0);
    poly1.AddEdge(90,1000);
    poly1.AddEdge(0,1000);
    poly1.AddEdge(-90,1000);
    n = poly1.Compute(false, true, perimeter, area);
    // The area should be 1e6.  Prior to the fix it was 1e6 - A/2, where
    // A = ellipsoid 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 97 of file PolygonArea.hpp.

Constructor & Destructor Documentation

◆ PolygonAreaT()

template<class GeodType = Geodesic>

GeographicLib::PolygonAreaT< GeodType >::PolygonAreaT	(	const GeodType &	earth,
		bool	polyline = `false`
	)

inline

Constructor for PolygonAreaT.

Parameters

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

Definition at line 128 of file PolygonArea.hpp.

References GeographicLib::PolygonAreaT< GeodType >::Clear().

Member Function Documentation

◆ Clear()

template<class GeodType = Geodesic>

void GeographicLib::PolygonAreaT< GeodType >::Clear ( )

inline

Clear PolygonAreaT, allowing a new polygon to be started.

Definition at line 140 of file PolygonArea.hpp.

References GeographicLib::Math::NaN().

Referenced by GeographicLib::PolygonAreaT< GeodType >::PolygonAreaT().

◆ AddPoint()

template<class GeodType >

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

Add a point to the polygon or polyline.

Parameters

[in]	lat	the latitude of the point (degrees).
[in]	lon	the longitude of the point (degrees).

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

Definition at line 70 of file PolygonArea.cpp.

◆ AddEdge()

template<class GeodType >

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

Add an edge to the polygon or polyline.

Parameters

[in]	azi	azimuth at current point (degrees).
[in]	s	distance 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 89 of file PolygonArea.cpp.

◆ Compute()

template<class GeodType >

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

Return the results so far.

Parameters

[in]	reverse	if true then clockwise (instead of counter-clockwise) traversal counts as a positive area.
[in]	sign	if 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]	perimeter	the perimeter of the polygon or length of the polyline (meters).
[out]	area	the 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 105 of file PolygonArea.cpp.

◆ TestPoint()

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]	lat	the latitude of the test point (degrees).
[in]	lon	the longitude of the test point (degrees).
[in]	reverse	if true then clockwise (instead of counter-clockwise) traversal counts as a positive area.
[in]	sign	if 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]	perimeter	the approximate perimeter of the polygon or length of the polyline (meters).
[out]	area	the 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 131 of file PolygonArea.cpp.

◆ TestEdge()

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]	azi	azimuth at current point (degrees).
[in]	s	distance from current point to final test point (meters).
[in]	reverse	if true then clockwise (instead of counter-clockwise) traversal counts as a positive area.
[in]	sign	if 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]	perimeter	the approximate perimeter of the polygon or length of the polyline (meters).
[out]	area	the approximate area of the polygon (meters²); only set if polyline is false in the constructor.

Returns: the number of points.

Definition at line 167 of file PolygonArea.cpp.

References GeographicLib::Math::NaN().

◆ EquatorialRadius()

template<class GeodType = Geodesic>

Math::real GeographicLib::PolygonAreaT< GeodType >::EquatorialRadius ( ) 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 250 of file PolygonArea.hpp.

◆ Flattening()

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 256 of file PolygonArea.hpp.

◆ CurrentPoint()

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]	lat	the latitude of the point (degrees).
[out]	lon	the 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 267 of file PolygonArea.hpp.

◆ NumberPoints()

template<class GeodType = Geodesic>

unsigned GeographicLib::PolygonAreaT< GeodType >::NumberPoints ( ) const

inline

Report the number of points currently in the polygon or polyline.

Returns: the number of points.

If no points have been added, then 0 is returned.

Definition at line 277 of file PolygonArea.hpp.

◆ Polyline()

template<class GeodType = Geodesic>

bool GeographicLib::PolygonAreaT< GeodType >::Polyline ( ) const

inline

Report whether the current object is a polygon or a polyline.

Returns: true if the object is a polyline.

Definition at line 284 of file PolygonArea.hpp.

Friends And Related Function Documentation

◆ PolygonArea

template<class GeodType = Geodesic>

typedef PolygonAreaT<Geodesic> PolygonArea

Definition at line 294 of file PolygonArea.hpp.

◆ PolygonAreaExact

template<class GeodType = Geodesic>

typedef PolygonAreaT<GeodesicExact> PolygonAreaExact

Definition at line 303 of file PolygonArea.hpp.

◆ PolygonAreaRhumb

template<class GeodType = Geodesic>

typedef PolygonAreaT<Rhumb> PolygonAreaRhumb

Definition at line 310 of file PolygonArea.hpp.

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

Public Member Functions

Related Functions

Detailed Description

Constructor & Destructor Documentation

◆ PolygonAreaT()

Member Function Documentation

◆ Clear()

◆ AddPoint()

◆ AddEdge()

◆ Compute()

◆ TestPoint()

◆ TestEdge()

◆ EquatorialRadius()

◆ Flattening()

◆ CurrentPoint()

◆ NumberPoints()

◆ Polyline()

Friends And Related Function Documentation

◆ PolygonArea

◆ PolygonAreaExact

◆ PolygonAreaRhumb