"""Define the :class:`~geographiclib.polygonarea.PolygonArea` class
The constructor initializes a empty polygon. The available methods are
* :meth:`~geographiclib.polygonarea.PolygonArea.Clear` reset the
polygon
* :meth:`~geographiclib.polygonarea.PolygonArea.AddPoint` add a vertex
to the polygon
* :meth:`~geographiclib.polygonarea.PolygonArea.AddEdge` add an edge
to the polygon
* :meth:`~geographiclib.polygonarea.PolygonArea.Compute` compute the
properties of the polygon
* :meth:`~geographiclib.polygonarea.PolygonArea.TestPoint` compute the
properties of the polygon with a tentative additional vertex
* :meth:`~geographiclib.polygonarea.PolygonArea.TestEdge` compute the
properties of the polygon with a tentative additional edge
The public attributes for this class are
* :attr:`~geographiclib.polygonarea.PolygonArea.earth`
:attr:`~geographiclib.polygonarea.PolygonArea.polyline`
:attr:`~geographiclib.polygonarea.PolygonArea.area0`
:attr:`~geographiclib.polygonarea.PolygonArea.num`
:attr:`~geographiclib.polygonarea.PolygonArea.lat1`
:attr:`~geographiclib.polygonarea.PolygonArea.lon1`
"""
# polygonarea.py
#
# This is a rather literal translation of the GeographicLib::PolygonArea class
# to python. See the documentation for the C++ class for more information at
#
# https://geographiclib.sourceforge.io/html/annotated.html
#
# The algorithms are derived in
#
# Charles F. F. Karney,
# Algorithms for geodesics, J. Geodesy 87, 43-55 (2013),
# https://doi.org/10.1007/s00190-012-0578-z
# Addenda: https://geographiclib.sourceforge.io/geod-addenda.html
#
# Copyright (c) Charles Karney (2011-2017) <charles@karney.com> and licensed
# under the MIT/X11 License. For more information, see
# https://geographiclib.sourceforge.io/
######################################################################
import math
from geographiclib.geomath import Math
from geographiclib.accumulator import Accumulator
[docs]class PolygonArea(object):
"""Area of a geodesic polygon"""
def _transit(lon1, lon2):
"""Count crossings of prime meridian for AddPoint."""
# 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)
lon12, _ = Math.AngDiff(lon1, lon2)
cross = (1 if lon1 <= 0 and lon2 > 0 and lon12 > 0
else (-1 if lon2 <= 0 and lon1 > 0 and lon12 < 0 else 0))
return cross
_transit = staticmethod(_transit)
def _transitdirect(lon1, lon2):
"""Count crossings of prime meridian for AddEdge."""
# We want to compute exactly
# int(floor(lon2 / 360)) - int(floor(lon1 / 360))
# Since we only need the parity of the result we can use std::remquo but
# this is buggy with g++ 4.8.3 and requires C++11. So instead we do
lon1 = math.fmod(lon1, 720.0); lon2 = math.fmod(lon2, 720.0)
return ( (0 if ((lon2 >= 0 and lon2 < 360) or lon2 < -360) else 1) -
(0 if ((lon1 >= 0 and lon1 < 360) or lon1 < -360) else 1) )
_transitdirect = staticmethod(_transitdirect)
def __init__(self, earth, polyline = False):
"""Construct a PolygonArea object
:param earth: a :class:`~geographiclib.geodesic.Geodesic` object
:param polyline: if true, treat object as a polyline instead of a polygon
Initially the polygon has no vertices.
"""
from geographiclib.geodesic import Geodesic
self.earth = earth
"""The geodesic object (readonly)"""
self.polyline = polyline
"""Is this a polyline? (readonly)"""
self.area0 = 4 * math.pi * earth._c2
"""The total area of the ellipsoid in meter^2 (readonly)"""
self._mask = (Geodesic.LATITUDE | Geodesic.LONGITUDE |
Geodesic.DISTANCE |
(Geodesic.EMPTY if self.polyline else
Geodesic.AREA | Geodesic.LONG_UNROLL))
if not self.polyline: self._areasum = Accumulator()
self._perimetersum = Accumulator()
self.num = 0
"""The current number of points in the polygon (readonly)"""
self.lat1 = Math.nan
"""The current latitude in degrees (readonly)"""
self.lon1 = Math.nan
"""The current longitude in degrees (readonly)"""
self.Clear()
[docs] def Clear(self):
"""Reset to empty polygon."""
self.num = 0
self._crossings = 0
if not self.polyline: self._areasum.Set(0)
self._perimetersum.Set(0)
self._lat0 = self._lon0 = self.lat1 = self.lon1 = Math.nan
[docs] def AddPoint(self, lat, lon):
"""Add the next vertex to the polygon
:param lat: the latitude of the point in degrees
:param lon: the longitude of the point in degrees
This adds an edge from the current vertex to the new vertex.
"""
if self.num == 0:
self._lat0 = self.lat1 = lat
self._lon0 = self.lon1 = lon
else:
_, s12, _, _, _, _, _, _, _, S12 = self.earth._GenInverse(
self.lat1, self.lon1, lat, lon, self._mask)
self._perimetersum.Add(s12)
if not self.polyline:
self._areasum.Add(S12)
self._crossings += PolygonArea._transit(self.lon1, lon)
self.lat1 = lat
self.lon1 = lon
self.num += 1
[docs] def AddEdge(self, azi, s):
"""Add the next edge to the polygon
:param azi: the azimuth at the current the point in degrees
:param s: the length of the edge in meters
This specifies the new vertex in terms of the edge from the current
vertex.
"""
if self.num != 0:
_, lat, lon, _, _, _, _, _, S12 = self.earth._GenDirect(
self.lat1, self.lon1, azi, False, s, self._mask)
self._perimetersum.Add(s)
if not self.polyline:
self._areasum.Add(S12)
self._crossings += PolygonArea._transitdirect(self.lon1, lon)
self.lat1 = lat
self.lon1 = lon
self.num += 1
# return number, perimeter, area
[docs] def Compute(self, reverse = False, sign = True):
"""Compute the properties of the polygon
:param reverse: if true then clockwise (instead of
counter-clockwise) traversal counts as a positive area
:param 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
:return: a tuple of number, perimeter (meters), area (meters^2)
If the object is a polygon (and not a polygon), the perimeter
includes the length of a final edge connecting the current point to
the initial point. If the object is a polyline, then area is nan.
More points can be added to the polygon after this call.
"""
if self.polyline: area = Math.nan
if self.num < 2:
perimeter = 0.0
if not self.polyline: area = 0.0
return self.num, perimeter, area
if self.polyline:
perimeter = self._perimetersum.Sum()
return self.num, perimeter, area
_, s12, _, _, _, _, _, _, _, S12 = self.earth._GenInverse(
self.lat1, self.lon1, self._lat0, self._lon0, self._mask)
perimeter = self._perimetersum.Sum(s12)
tempsum = Accumulator(self._areasum)
tempsum.Add(S12)
crossings = self._crossings + PolygonArea._transit(self.lon1, self._lon0)
if crossings & 1:
tempsum.Add( (1 if tempsum.Sum() < 0 else -1) * self.area0/2 )
# area is with the clockwise sense. If !reverse convert to
# counter-clockwise convention.
if not reverse: tempsum.Negate()
# If sign put area in (-area0/2, area0/2], else put area in [0, area0)
if sign:
if tempsum.Sum() > self.area0/2:
tempsum.Add( -self.area0 )
elif tempsum.Sum() <= -self.area0/2:
tempsum.Add( self.area0 )
else:
if tempsum.Sum() >= self.area0:
tempsum.Add( -self.area0 )
elif tempsum.Sum() < 0:
tempsum.Add( self.area0 )
area = 0.0 + tempsum.Sum()
return self.num, perimeter, area
# return number, perimeter, area
[docs] def TestPoint(self, lat, lon, reverse = False, sign = True):
"""Compute the properties for a tentative additional vertex
:param lat: the latitude of the point in degrees
:param lon: the longitude of the point in degrees
:param reverse: if true then clockwise (instead of
counter-clockwise) traversal counts as a positive area
:param 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
:return: a tuple of number, perimeter (meters), area (meters^2)
"""
if self.polyline: area = Math.nan
if self.num == 0:
perimeter = 0.0
if not self.polyline: area = 0.0
return 1, perimeter, area
perimeter = self._perimetersum.Sum()
tempsum = 0.0 if self.polyline else self._areasum.Sum()
crossings = self._crossings; num = self.num + 1
for i in ([0] if self.polyline else [0, 1]):
_, s12, _, _, _, _, _, _, _, S12 = self.earth._GenInverse(
self.lat1 if i == 0 else lat, self.lon1 if i == 0 else lon,
self._lat0 if i != 0 else lat, self._lon0 if i != 0 else lon,
self._mask)
perimeter += s12
if not self.polyline:
tempsum += S12
crossings += PolygonArea._transit(self.lon1 if i == 0 else lon,
self._lon0 if i != 0 else lon)
if self.polyline:
return num, perimeter, area
if crossings & 1:
tempsum += (1 if tempsum < 0 else -1) * self.area0/2
# area is with the clockwise sense. If !reverse convert to
# counter-clockwise convention.
if not reverse: tempsum *= -1
# If sign put area in (-area0/2, area0/2], else put area in [0, area0)
if sign:
if tempsum > self.area0/2:
tempsum -= self.area0
elif tempsum <= -self.area0/2:
tempsum += self.area0
else:
if tempsum >= self.area0:
tempsum -= self.area0
elif tempsum < 0:
tempsum += self.area0
area = 0.0 + tempsum
return num, perimeter, area
# return num, perimeter, area
[docs] def TestEdge(self, azi, s, reverse = False, sign = True):
"""Compute the properties for a tentative additional edge
:param azi: the azimuth at the current the point in degrees
:param s: the length of the edge in meters
:param reverse: if true then clockwise (instead of
counter-clockwise) traversal counts as a positive area
:param 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
:return: a tuple of number, perimeter (meters), area (meters^2)
"""
if self.num == 0: # we don't have a starting point!
return 0, Math.nan, Math.nan
num = self.num + 1
perimeter = self._perimetersum.Sum() + s
if self.polyline:
return num, perimeter, Math.nan
tempsum = self._areasum.Sum()
crossings = self._crossings
_, lat, lon, _, _, _, _, _, S12 = self.earth._GenDirect(
self.lat1, self.lon1, azi, False, s, self._mask)
tempsum += S12
crossings += PolygonArea._transitdirect(self.lon1, lon)
_, s12, _, _, _, _, _, _, _, S12 = self.earth._GenInverse(
lat, lon, self._lat0, self._lon0, self._mask)
perimeter += s12
tempsum += S12
crossings += PolygonArea._transit(lon, self._lon0)
if crossings & 1:
tempsum += (1 if tempsum < 0 else -1) * self.area0/2
# area is with the clockwise sense. If !reverse convert to
# counter-clockwise convention.
if not reverse: tempsum *= -1
# If sign put area in (-area0/2, area0/2], else put area in [0, area0)
if sign:
if tempsum > self.area0/2:
tempsum -= self.area0
elif tempsum <= -self.area0/2:
tempsum += self.area0
else:
if tempsum >= self.area0:
tempsum -= self.area0
elif tempsum < 0:
tempsum += self.area0
area = 0.0 + tempsum
return num, perimeter, area