"""polygonarea.py: transcription of GeographicLib::PolygonArea class."""
# 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
#
# http://geographiclib.sourceforge.net/html/annotated.html
#
# The algorithms are derived in
#
# Charles F. F. Karney,
# Algorithms for geodesics, J. Geodesy 87, 43-55 (2013),
# https://dx.doi.org/10.1007/s00190-012-0578-z
# Addenda: http://geographiclib.sf.net/geod-addenda.html
#
# Copyright (c) Charles Karney (2011-2014) <charles@karney.com> and licensed
# under the MIT/X11 License. For more information, see
# http://geographiclib.sourceforge.net/
######################################################################
import math
from geographiclib.geomath import Math
from geographiclib.accumulator import Accumulator
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):
from geographiclib.geodesic import Geodesic
self._earth = earth
self._area0 = 4 * math.pi * earth._c2
self._polyline = polyline
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.Clear()
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
def AddPoint(self, lat, lon):
"""Add a vertex to the polygon."""
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
def AddEdge(self, azi, s):
"""Add an edge to the polygon."""
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
def Compute(self, reverse, sign):
"""Return the number, perimeter, and area for the polygon."""
if self._polyline: area = Math.nan
if self._num < 2:
perimeter = 0
if not self._polyline: area = 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 + tempsum.Sum()
return self._num, perimeter, area
# return number, perimeter, area
def TestPoint(self, lat, lon, reverse, sign):
"""Return the results for a tentative additional vertex."""
if self._polyline: area = Math.nan
if self._num == 0:
perimeter = 0
if not self._polyline: area = 0
return 1, perimeter, area
perimeter = self._perimetersum.Sum()
tempsum = 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 + tempsum
return num, perimeter, area
# return number, perimeter, area (for backward compatibility)
def TestCompute(self, lat, lon, reverse, sign):
return self.TestPoint(lat, lon, reverse, sign)
# return num, perimeter, area
def TestEdge(self, azi, s, reverse, sign):
"""Return the results for a tentative additional edge."""
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 + tempsum
return num, perimeter, area
def CurrentPoint(self):
"""Return the current point as a lat, lon tuple."""
return self._lat1, self._lon1
def Area(earth, points, polyline):
"""Return the number, perimeter, and area for a set of vertices."""
poly = PolygonArea(earth, polyline)
for p in points:
poly.AddPoint(p['lat'], p['lon'])
return poly.Compute(False, True)
Area = staticmethod(Area)