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PolygonArea.cpp
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/**
* \file PolygonArea.cpp
* \brief Implementation for GeographicLib::PolygonAreaT class
*
* Copyright (c) Charles Karney (2010-2023) <karney@alum.mit.edu> and licensed
* under the MIT/X11 License. For more information, see
* https://geographiclib.sourceforge.io/
**********************************************************************/
#include <GeographicLib/PolygonArea.hpp>
namespace GeographicLib {
using namespace std;
template<class GeodType>
int PolygonAreaT<GeodType>::transit(real lon1, real lon2) {
// Return 1 or -1 if crossing prime meridian in east or west direction.
// Otherwise return zero. longitude = +/-0 considered to be positive.
// This is (should be?) compatible with transitdirect which computes
// exactly the parity of
// int(floor((lon1 + lon12) / 360)) - int(floor(lon1 / 360)))
real lon12 = Math::AngDiff(lon1, lon2);
lon1 = Math::AngNormalize(lon1);
lon2 = Math::AngNormalize(lon2);
// N.B. lon12 == 0 gives cross = 0
return
// edge case lon1 = 180, lon2 = 360->0, lon12 = 180 to give 1
lon12 > 0 && ((lon1 < 0 && lon2 >= 0) ||
// lon12 > 0 && lon1 > 0 && lon2 == 0 implies lon1 == 180
(lon1 > 0 && lon2 == 0)) ? 1 :
// non edge case lon1 = -180, lon2 = -360->-0, lon12 = -180
(lon12 < 0 && lon1 >= 0 && lon2 < 0 ? -1 : 0);
// This was the old method (treating +/- 0 as negative). However, with the
// new scheme for handling longitude differences this fails on:
// lon1 = -180, lon2 = -360->-0, lon12 = -180 gives 0 not -1.
// return
// lon1 <= 0 && lon2 > 0 && lon12 > 0 ? 1 :
// (lon2 <= 0 && lon1 > 0 && lon12 < 0 ? -1 : 0);
}
// an alternate version of transit to deal with longitudes in the direct
// problem.
template<class GeodType>
int PolygonAreaT<GeodType>::transitdirect(real lon1, real lon2) {
// Compute exactly the parity of
// int(floor(lon2 / 360)) - int(floor(lon1 / 360))
// C++ C remainder -> [-360, 360]
// Java % -> (-720, 720) switch to IEEEremainder -> [-360, 360]
// JS % -> (-720, 720)
// Python fmod -> (-720, 720) swith to Math.remainder
// Fortran, Octave skip
// If mod function gives result in [-360, 360]
// [0, 360) -> 0; [-360, 0) or 360 -> 1
// If mod function gives result in (-720, 720)
// [0, 360) or [-inf, -360) -> 0; [-360, 0) or [360, inf) -> 1
lon1 = remainder(lon1, real(2 * Math::td));
lon2 = remainder(lon2, real(2 * Math::td));
return ( (lon2 >= 0 && lon2 < Math::td ? 0 : 1) -
(lon1 >= 0 && lon1 < Math::td ? 0 : 1) );
}
template<class GeodType>
void PolygonAreaT<GeodType>::AddPoint(real lat, real lon) {
if (_num == 0) {
_lat0 = _lat1 = lat;
_lon0 = _lon1 = lon;
} else {
real s12, S12, t;
_earth.GenInverse(_lat1, _lon1, lat, lon, _mask,
s12, t, t, t, t, t, S12);
_perimetersum += s12;
if (!_polyline) {
_areasum += S12;
_crossings += transit(_lon1, lon);
}
_lat1 = lat; _lon1 = lon;
}
++_num;
}
template<class GeodType>
void PolygonAreaT<GeodType>::AddEdge(real azi, real s) {
if (_num) { // Do nothing if _num is zero
real lat, lon, S12, t;
_earth.GenDirect(_lat1, _lon1, azi, false, s, _mask,
lat, lon, t, t, t, t, t, S12);
_perimetersum += s;
if (!_polyline) {
_areasum += S12;
_crossings += transitdirect(_lon1, lon);
}
_lat1 = lat; _lon1 = lon;
++_num;
}
}
template<class GeodType>
unsigned PolygonAreaT<GeodType>::Compute(bool reverse, bool sign,
real& perimeter, real& area) const
{
real s12, S12, t;
if (_num < 2) {
perimeter = 0;
if (!_polyline)
area = 0;
return _num;
}
if (_polyline) {
perimeter = _perimetersum();
return _num;
}
_earth.GenInverse(_lat1, _lon1, _lat0, _lon0, _mask,
s12, t, t, t, t, t, S12);
perimeter = _perimetersum(s12);
Accumulator<> tempsum(_areasum);
tempsum += S12;
int crossings = _crossings + transit(_lon1, _lon0);
AreaReduce(tempsum, crossings, reverse, sign);
area = real(0) + tempsum();
return _num;
}
template<class GeodType>
unsigned PolygonAreaT<GeodType>::TestPoint(real lat, real lon,
bool reverse, bool sign,
real& perimeter, real& area) const
{
if (_num == 0) {
perimeter = 0;
if (!_polyline)
area = 0;
return 1;
}
perimeter = _perimetersum();
real tempsum = _polyline ? 0 : _areasum();
int crossings = _crossings;
unsigned num = _num + 1;
for (int i = 0; i < (_polyline ? 1 : 2); ++i) {
real s12, S12, t;
_earth.GenInverse(i == 0 ? _lat1 : lat, i == 0 ? _lon1 : lon,
i != 0 ? _lat0 : lat, i != 0 ? _lon0 : lon,
_mask, s12, t, t, t, t, t, S12);
perimeter += s12;
if (!_polyline) {
tempsum += S12;
crossings += transit(i == 0 ? _lon1 : lon,
i != 0 ? _lon0 : lon);
}
}
if (_polyline)
return num;
AreaReduce(tempsum, crossings, reverse, sign);
area = real(0) + tempsum;
return num;
}
template<class GeodType>
unsigned PolygonAreaT<GeodType>::TestEdge(real azi, real s,
bool reverse, bool sign,
real& perimeter, real& area) const
{
if (_num == 0) { // we don't have a starting point!
perimeter = Math::NaN();
if (!_polyline)
area = Math::NaN();
return 0;
}
unsigned num = _num + 1;
perimeter = _perimetersum() + s;
if (_polyline)
return num;
real tempsum = _areasum();
int crossings = _crossings;
{
real lat, lon, s12, S12, t;
_earth.GenDirect(_lat1, _lon1, azi, false, s, _mask,
lat, lon, t, t, t, t, t, S12);
tempsum += S12;
crossings += transitdirect(_lon1, lon);
_earth.GenInverse(lat, lon, _lat0, _lon0, _mask,
s12, t, t, t, t, t, S12);
perimeter += s12;
tempsum += S12;
crossings += transit(lon, _lon0);
}
AreaReduce(tempsum, crossings, reverse, sign);
area = real(0) + tempsum;
return num;
}
template<class GeodType>
template<typename T>
void PolygonAreaT<GeodType>::AreaReduce(T& area, int crossings,
bool reverse, bool sign) const {
Remainder(area);
if (crossings & 1) area += (area < 0 ? 1 : -1) * _area0/2;
// area is with the clockwise sense. If !reverse convert to
// counter-clockwise convention.
if (!reverse) area *= -1;
// If sign put area in (-_area0/2, _area0/2], else put area in [0, _area0)
if (sign) {
if (area > _area0/2)
area -= _area0;
else if (area <= -_area0/2)
area += _area0;
} else {
if (area >= _area0)
area -= _area0;
else if (area < 0)
area += _area0;
}
}
template class GEOGRAPHICLIB_EXPORT PolygonAreaT<Geodesic>;
template class GEOGRAPHICLIB_EXPORT PolygonAreaT<GeodesicExact>;
template class GEOGRAPHICLIB_EXPORT PolygonAreaT<Rhumb>;
} // namespace GeographicLib
GEOGRAPHICLIB_EXPORT
#define GEOGRAPHICLIB_EXPORT
Definition Constants.hpp:67
real
GeographicLib::Math::real real
Definition GeodSolve.cpp:28
PolygonArea.hpp
Header for GeographicLib::PolygonAreaT class.
GeographicLib::Accumulator
An accumulator for sums.
Definition Accumulator.hpp:40
GeographicLib::Math::AngNormalize
static T AngNormalize(T x)
Definition Math.cpp:66
GeographicLib::Math::td
static constexpr int td
degrees per turn
Definition Math.hpp:149
GeographicLib::Math::NaN
static T NaN()
Definition Math.cpp:277
GeographicLib::Math::AngDiff
static T AngDiff(T x, T y, T &e)
Definition Math.cpp:77
GeographicLib::PolygonAreaT
Polygon areas.
Definition PolygonArea.hpp:97
GeographicLib::PolygonAreaT::AddPoint
void AddPoint(real lat, real lon)
Definition PolygonArea.cpp:64
GeographicLib::PolygonAreaT::Compute
unsigned Compute(bool reverse, bool sign, real &perimeter, real &area) const
Definition PolygonArea.cpp:99
GeographicLib::PolygonAreaT::TestPoint
unsigned TestPoint(real lat, real lon, bool reverse, bool sign, real &perimeter, real &area) const
Definition PolygonArea.cpp:125
GeographicLib::PolygonAreaT::AddEdge
void AddEdge(real azi, real s)
Definition PolygonArea.cpp:83
GeographicLib::PolygonAreaT::TestEdge
unsigned TestEdge(real azi, real s, bool reverse, bool sign, real &perimeter, real &area) const
Definition PolygonArea.cpp:161
GeographicLib
Namespace for GeographicLib.
Definition Accumulator.cpp:12
std
Definition NearestNeighbor.hpp:806