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Sven Czarnian
2021-11-22 16:16:36 +01:00
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external/include/GeographicLib/PolygonArea.hpp vendored Normal file
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/**
* \file PolygonArea.hpp
* \brief Header for GeographicLib::PolygonAreaT class
*
* Copyright (c) Charles Karney (2010-2021) <charles@karney.com> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#if !defined(GEOGRAPHICLIB_POLYGONAREA_HPP)
#define GEOGRAPHICLIB_POLYGONAREA_HPP 1
#include <GeographicLib/Geodesic.hpp>
#include <GeographicLib/GeodesicExact.hpp>
#include <GeographicLib/Rhumb.hpp>
#include <GeographicLib/Accumulator.hpp>
namespace GeographicLib {
/**
* \brief 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,
* <a href="https://doi.org/10.1007/s00190-012-0578-z">
* Algorithms for geodesics</a>,
* J. Geodesy <b>87</b>, 43--55 (2013);
* DOI: <a href="https://doi.org/10.1007/s00190-012-0578-z">
* 10.1007/s00190-012-0578-z</a>;
* addenda:
* <a href="https://geographiclib.sourceforge.io/geod-addenda.html">
* geod-addenda.html</a>.
*
* 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 \e 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 \e 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 m<sup>2</sup> 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 10<sup>7</sup> 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<pre>
* 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
* </pre>
* 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<pre>
* 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
* </pre>
*
* @tparam GeodType the geodesic class to use.
*
* Example of use:
* \include example-PolygonArea.cpp
*
* <a href="Planimeter.1.html">Planimeter</a> is a command-line utility
* providing access to the functionality of PolygonAreaT.
**********************************************************************/
template <class GeodType = Geodesic>
class PolygonAreaT {
private:
typedef Math::real real;
GeodType _earth;
real _area0; // Full ellipsoid area
bool _polyline; // Assume polyline (don't close and skip area)
unsigned _mask;
unsigned _num;
int _crossings;
Accumulator<> _areasum, _perimetersum;
real _lat0, _lon0, _lat1, _lon1;
static int transit(real lon1, real lon2) {
// Return 1 or -1 if crossing prime meridian in east or west direction.
// Otherwise return zero.
// Compute lon12 the same way as Geodesic::Inverse.
lon1 = Math::AngNormalize(lon1);
lon2 = Math::AngNormalize(lon2);
real lon12 = Math::AngDiff(lon1, lon2);
// Treat 0 as negative in these tests. This balances +/- 180 being
// treated as positive, i.e., +180.
int cross =
lon1 <= 0 && lon2 > 0 && lon12 > 0 ? 1 :
(lon2 <= 0 && lon1 > 0 && lon12 < 0 ? -1 : 0);
return cross;
}
// an alternate version of transit to deal with longitudes in the direct
// problem.
static int transitdirect(real lon1, real lon2) {
// Compute exactly the parity of
// int(ceil(lon2 / 360)) - int(ceil(lon1 / 360))
using std::remainder;
lon1 = remainder(lon1, real(720));
lon2 = remainder(lon2, real(720));
return ( (lon2 <= 0 && lon2 > -360 ? 1 : 0) -
(lon1 <= 0 && lon1 > -360 ? 1 : 0) );
}
void Remainder(Accumulator<>& a) const { a.remainder(_area0); }
void Remainder(real& a) const {
using std::remainder;
a = remainder(a, _area0);
}
template <typename T>
void AreaReduce(T& area, int crossings, bool reverse, bool sign) const;
public:
/**
* Constructor for PolygonAreaT.
*
* @param[in] earth the Geodesic object to use for geodesic calculations.
* @param[in] polyline if true that treat the points as defining a polyline
* instead of a polygon (default = false).
**********************************************************************/
PolygonAreaT(const GeodType& earth, bool polyline = false)
: _earth(earth)
, _area0(_earth.EllipsoidArea())
, _polyline(polyline)
, _mask(GeodType::LATITUDE | GeodType::LONGITUDE | GeodType::DISTANCE |
(_polyline ? GeodType::NONE :
GeodType::AREA | GeodType::LONG_UNROLL))
{ Clear(); }
/**
* Clear PolygonAreaT, allowing a new polygon to be started.
**********************************************************************/
void Clear() {
_num = 0;
_crossings = 0;
_areasum = 0;
_perimetersum = 0;
_lat0 = _lon0 = _lat1 = _lon1 = Math::NaN();
}
/**
* Add a point to the polygon or polyline.
*
* @param[in] lat the latitude of the point (degrees).
* @param[in] lon the longitude of the point (degrees).
*
* \e lat should be in the range [&minus;90&deg;, 90&deg;].
**********************************************************************/
void AddPoint(real lat, real lon);
/**
* Add an edge to the polygon or polyline.
*
* @param[in] azi azimuth at current point (degrees).
* @param[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.
**********************************************************************/
void AddEdge(real azi, real s);
/**
* Return the results so far.
*
* @param[in] reverse if true then clockwise (instead of counter-clockwise)
* traversal counts as a positive area.
* @param[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.
* @param[out] perimeter the perimeter of the polygon or length of the
* polyline (meters).
* @param[out] area the area of the polygon (meters<sup>2</sup>); only set
* if \e polyline is false in the constructor.
* @return the number of points.
*
* More points can be added to the polygon after this call.
**********************************************************************/
unsigned Compute(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.
*
* @param[in] lat the latitude of the test point (degrees).
* @param[in] lon the longitude of the test point (degrees).
* @param[in] reverse if true then clockwise (instead of counter-clockwise)
* traversal counts as a positive area.
* @param[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.
* @param[out] perimeter the approximate perimeter of the polygon or length
* of the polyline (meters).
* @param[out] area the approximate area of the polygon
* (meters<sup>2</sup>); only set if polyline is false in the
* constructor.
* @return the number of points.
*
* \e lat should be in the range [&minus;90&deg;, 90&deg;].
**********************************************************************/
unsigned 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 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.
*
* @param[in] azi azimuth at current point (degrees).
* @param[in] s distance from current point to final test point (meters).
* @param[in] reverse if true then clockwise (instead of counter-clockwise)
* traversal counts as a positive area.
* @param[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.
* @param[out] perimeter the approximate perimeter of the polygon or length
* of the polyline (meters).
* @param[out] area the approximate area of the polygon
* (meters<sup>2</sup>); only set if polyline is false in the
* constructor.
* @return the number of points.
**********************************************************************/
unsigned TestEdge(real azi, real s, bool reverse, bool sign,
real& perimeter, real& area) const;
/** \name Inspector functions
**********************************************************************/
///@{
/**
* @return \e a the equatorial radius of the ellipsoid (meters). This is
* the value inherited from the Geodesic object used in the constructor.
**********************************************************************/
Math::real EquatorialRadius() const { return _earth.EquatorialRadius(); }
/**
* @return \e f the flattening of the ellipsoid. This is the value
* inherited from the Geodesic object used in the constructor.
**********************************************************************/
Math::real Flattening() const { return _earth.Flattening(); }
/**
* Report the previous vertex added to the polygon or polyline.
*
* @param[out] lat the latitude of the point (degrees).
* @param[out] lon the longitude of the point (degrees).
*
* If no points have been added, then NaNs are returned. Otherwise, \e lon
* will be in the range [&minus;180&deg;, 180&deg;].
**********************************************************************/
void CurrentPoint(real& lat, real& lon) const
{ lat = _lat1; lon = _lon1; }
/**
* \deprecated An old name for EquatorialRadius().
**********************************************************************/
GEOGRAPHICLIB_DEPRECATED("Use EquatorialRadius()")
Math::real MajorRadius() const { return EquatorialRadius(); }
///@}
};
/**
* @relates PolygonAreaT
*
* Polygon areas using Geodesic. This should be used if the flattening is
* small.
**********************************************************************/
typedef PolygonAreaT<Geodesic> PolygonArea;
/**
* @relates PolygonAreaT
*
* 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.)
**********************************************************************/
typedef PolygonAreaT<GeodesicExact> PolygonAreaExact;
/**
* @relates PolygonAreaT
*
* Polygon areas using Rhumb.
**********************************************************************/
typedef PolygonAreaT<Rhumb> PolygonAreaRhumb;
} // namespace GeographicLib
#endif // GEOGRAPHICLIB_POLYGONAREA_HPP