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# -*- coding: utf-8 -*- 

 

u'''Slightly enhanced versions of I{Karney}'s Python classes 

U{PolygonArea<https://GeographicLib.SourceForge.io/1.52/python/ 

code.html#module-geographiclib.polygonarea>} and C{Accumulator}. 

 

Class L{GeodesicAreaExact} is intended to work with instances 

of class L{GeodesicExact} or of I{wrapped} class C{Geodesic} 

I{Karney}'s Python U{geographiclib 

<https://GeographicLib.SourceForge.io/1.52/python/index.html>} 

 

Copyright (C) Charles Karney (2012-2021) <Charles@Karney.com> 

and licensed under the MIT/X11 License. For more information, 

see U{GeographicLib<https://GeographicLib.SourceForge.io>}. 

''' 

# make sure int/int division yields float quotient 

from __future__ import division 

 

from pygeodesy.basics import isodd, unsign0 

from pygeodesy.interns import NAN, NN, _COMMASPACE_, \ 

_0_0, _2_0 

from pygeodesy.karney import GeodesicError, _diff182, \ 

_norm180, _remainder, _3sum2 

from pygeodesy.lazily import _ALL_DOCS, printf 

from pygeodesy.named import callername, _Dict, _NamedBase, pairs 

from pygeodesy.props import Property, Property_RO, property_RO 

# from pygeodesy.streprs import pairs # from .named 

 

from math import fmod 

 

__all__ = () 

__version__ = '21.06.30' 

 

 

class GeodesicAreaExact(_NamedBase): 

'''Area and perimeter of a geodesic polygon, an enhanced 

version of I{Karney}'s Python class U{PolygonArea 

<https://GeographicLib.SourceForge.io/html/python/ 

code.html#module-geographiclib.polygonarea>} using 

the more accurate surface area. 

 

@note: The name of this class C{*Exact} is a misnomer, see 

I{Karney}'s comments at C++ attribute U{GeodesicExact._c2 

<https://GeographicLib.SourceForge.io/html/ 

GeodesicExact_8cpp_source.html>}. 

''' 

_Area = None 

_g_gX = None # Exact or not 

_lat0 = _lon0 = \ 

_lat1 = _lon1 = NAN 

_mask = 0 

_num = 0 

_Peri = None 

_verbose = False 

_xings = 0 

 

def __init__(self, geodesic, polyline=False, name=NN): 

'''New L{GeodesicAreaExact} instance. 

 

@arg geodesic: A geodesic (L{GeodesicExact}, 

I{wrapped} C{Geodesic} or 

L{GeodesicSolve}). 

@kwarg polyline: If C{True} compute perimeter 

only, otherwise area and 

perimeter (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@raise GeodesicError: Invalid B{C{geodesic}}. 

''' 

try: # results returned as L{GDict} 

if not (callable(geodesic._GDictDirect) and 

callable(geodesic._GDictInverse)): 

raise TypeError 

except (AttributeError, TypeError): 

raise GeodesicError(geodesic=geodesic) 

 

self._g_gX = g = geodesic 

# use the class-level Caps since the values 

# differ between GeodesicExact and Geodesic 

self._mask = g.DISTANCE | g.LATITUDE | g.LONGITUDE 

self._Peri = _Accumulator(name='_Peri') 

if not polyline: # perimeter and area 

self._mask |= g.AREA | g.LONG_UNROLL 

self._Area = _Accumulator(name='_Area') 

if g.debug: # inherit debug as verbosity 

self.verbose = True 

if name: 

self.name = name 

 

def AddEdge(self, azi, s): 

'''Add another polygon edge. 

 

@arg azi: Azimuth at the current point (compass C{degrees}). 

@arg s: Length of the edge (C{meter}). 

''' 

if self.num < 1: 

raise GeodesicError(num=self.num) 

r = self._Direct(azi, s) 

p = self._Peri.Add(s) 

if self._Area: 

a = self._Area.Add(r.S12) 

self._xings += r.xing 

else: 

a = _0_0 

self._lat1 = r.lat2 

self._lon1 = r.lon2 

self._num += 1 

if self.verbose: # PYCHOK no cover 

self._print(self.num, p, a, r, lat1=r.lat2, lon1=r.lon2, 

azi=azi, s=s) 

return self.num 

 

def AddPoint(self, lat, lon): 

'''Add another polygon point. 

 

@arg lat: Latitude of the point (C{degrees}). 

@arg lon: Longitude of the point (C{degrees}). 

''' 

if self.num > 0: 

r = self._Inverse(self.lat1, self.lon1, lat, lon) 

s = r.s12 

p = self._Peri.Add(s) 

if self._Area: 

a = self._Area.Add(r.S12) 

self._xings += r.xing 

else: 

a = _0_0 

else: 

self._lat0 = lat 

self._lon0 = lon 

a = p = s = _0_0 

r = None 

self._lat1 = lat 

self._lon1 = lon 

self._num += 1 

if self.verbose: # PYCHOK no cover 

self._print(self.num, p, a, r, lat1=lat, lon1=lon, s=s) 

return self.num 

 

@Property_RO 

def area0x(self): 

'''Get the ellipsoid's surface area (C{meter} I{squared}), 

more accurate for very I{oblate} ellipsoids. 

''' 

return self.ellipsoid.areax # not .area! 

 

area0 = area0x # for C{geographiclib} compatibility 

 

@Property_RO 

def _area0x_2(self): 

'''Get half the ellipsoid's surface area (C{meter} I{squared}). 

''' 

return self.area0x / _2_0 

 

def Compute(self, reverse=False, sign=True): 

'''Compute the accumulated perimeter and area. 

 

@kwarg reverse: If C{True}, clockwise traversal counts as a 

positive area instead of counter-clockwise 

(C{bool}). 

@kwarg sign: If C{True}, 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: 3-Tuple C{(number, perimeter (meter), area (meter*2))}. 

The C{perimeter} includes the length of a final edge, 

connecting the current to the initial point, if this 

polygon was initialized with C{polyline=False}. And 

C{area=NAN} for perimeter only, C{polyline=True}. 

 

@note: Arbitrarily complex polygons are allowed. In the case 

of self-intersecting polygons, the area is accumulated 

"algebraically". E.g., the areas of the 2 loops in a 

I{figure-8} polygon will partially cancel. 

 

@note: More points and edges can be added after this call. 

''' 

n = self.num 

if n < 2: 

p = _0_0 

a = NAN if self.polyline else _0_0 

r = None 

elif self._Area: 

r = self._Inverse(self.lat1, self.lon1, self.lat0, self.lon0) 

p = self._Peri.Sum(r.s12) 

A = _Accumulator(self._Area.Sum(r.S12)) 

a = self._reduce(A, reverse, sign, r.xing) 

else: 

p = self._Peri.Sum() 

a = NAN 

r = None 

if self.verbose: # PYCHOK no cover 

self._print(n, p, a, r, lat0=self.lat0, lon0=self.lon0) 

return n, p, a 

 

def _Direct(self, azi, s): 

'''(INTERNAL) Edge helper. 

''' 

lon1 = self.lon1 

r = self._g_gX._GDictDirect(self.lat1, lon1, azi, False, s, self._mask) 

if self._Area: # aka transitDirect 

# Count crossings of prime meridian exactly as 

# int(ceil(lon2 / 360)) - int(ceil(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 = fmod( lon1, 720) # r.lon1 

lon2 = fmod(r.lon2, 720) 

# int(True) == 1, int(False) == 0 

r.set_(xing=int(lon2 > 360 or -360 < lon2 <= 0) - 

int(lon1 > 360 or -360 < lon1 <= 0)) 

return r 

 

@Property_RO 

def ellipsoid(self): 

'''Get this area's ellipsoid (C{Ellipsoid[2]}). 

''' 

return self._g_gX.ellipsoid 

 

@Property_RO 

def geodesic(self): 

'''Get this area's geodesic object (C{Geodesic[Exact]}). 

''' 

return self._g_gX 

 

earth = geodesic # for C{geographiclib} compatibility 

 

def _Inverse(self, lat1, lon1, lat2, lon2): 

'''(INTERNAL) Point helper. 

''' 

r = self._g_gX._GDictInverse(lat1, lon1, lat2, lon2, self._mask) 

if self._Area: # aka transit 

# count crossings of prime meridian as +1 or -1 

# if in east or west direction, otherwise 0 

lon1 = _norm180(lon1) 

lon2 = _norm180(lon2) 

lon12, _ = _diff182(lon1, lon2) 

r.set_(xing=int(lon1 <= 0 and lon2 > 0 and lon12 > 0) or 

-int(lon2 <= 0 and lon1 > 0 and lon12 < 0)) 

return r 

 

@property_RO 

def lat0(self): 

'''Get the first point's latitude (C{degrees}). 

''' 

return self._lat0 

 

@property_RO 

def lat1(self): 

'''Get the most recent point's latitude (C{degrees}). 

''' 

return self._lat1 

 

@property_RO 

def lon0(self): 

'''Get the first point's longitude (C{degrees}). 

''' 

return self._lon0 

 

@property_RO 

def lon1(self): 

'''Get the most recent point's longitude (C{degrees}). 

''' 

return self._lon1 

 

@property_RO 

def num(self): 

'''Get the current number of points (C{int}). 

''' 

return self._num 

 

@Property_RO 

def polyline(self): 

'''Is this perimter only (C{boo}), area NAN? 

''' 

return self._Area is None 

 

def _print(self, n, p, a, r, **kwds): # PYCHOK no cover 

'''(INTERNAL) Print a verbose line. 

''' 

d = _Dict(p=p, s12=r.s12 if r else NAN, **kwds) 

if self._Area: 

d.set_(a=a, S12=r.S12 if r else NAN) 

t = _COMMASPACE_.join(pairs(d, prec=10)) 

printf('%s %s: %s (%s)', self.named2, n, t, callername(up=2)) 

 

def _reduce(self, Area, reverse, sign, xing): 

'''(INTERNAL) Reduce accumulated area to allowed range. 

''' 

a0, a0_2 = self.area0x, self._area0x_2 

a = Area.Remainder(a0) 

if isodd(self._xings + xing): 

a = Area.Add(a0_2 if a < 0 else -a0_2) 

# area is with the clockwise sense. If !reverse 

# convert to counter-clockwise convention. 

if not reverse: 

a = Area.Negate() 

# If sign put area in (-area0x/2, area0x/2], 

# otherwise put area in [0, area0x) 

a0_ = a0 if sign else a0_2 

if a > a0_: 

a = Area.Add(-a0) 

elif a <= -a0_: 

a = Area.Add( a0) 

return unsign0(a) 

 

def Reset(self): 

'''Reset this polygon to empty. 

''' 

if self._Area: 

self._Area.Reset() 

self._Peri.Reset() 

self._lat0 = self._lon0 = \ 

self._lat1 = self._lon1 = NAN 

self._num = self._xings = n = 0 

if self.verbose: # PYCHOK no cover 

printf('%s %s: (%s)', self.named2, n, self.Reset.__name__) 

return n 

 

Clear = Reset 

 

def TestEdge(self, azi, s, reverse=False, sign=True): 

'''Compute the properties for a tentative, additional edge 

 

@arg azi: Azimuth at the current the point (compass C{degrees}). 

@arg s: Length of the edge (C{meter}). 

@kwarg reverse: If C{True}, clockwise traversal counts as a 

positive area instead of counter-clockwise 

(C{bool}). 

@kwarg sign: If C{True}, 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: 3-Tuple C{(number, perimeter (meter), area (meter*2))}. 

 

@raise GeodesicError: No points. 

''' 

n = self.num + 1 

p = self._Peri.Sum(s) 

if self.polyline: 

a, r = NAN, None 

elif n < 2: 

raise GeodesicError(num=self.num) 

else: 

r = self._Direct(azi, s) 

a = self._Area.Sum(r.S12) 

x = r.xing 

r = self._Inverse(r.lat2, r.lon2, self.lat0, self.lon0) 

A = _Accumulator(a + r.S12) 

a = self._reduce(A, reverse, sign, x + r.xing) 

p += r.s12 

if self.verbose: # PYCHOK no cover 

self._print(n, p, a, r, azi=azi, s=s) 

return n, p, a 

 

def TestPoint(self, lat, lon, reverse=False, sign=True): 

'''Compute the properties for a tentative, additional vertex 

 

@arg lat: Latitude of the point (C{degrees}). 

@arg lon: Longitude of the point (C{degrees}). 

@kwarg reverse: If C{True}, clockwise traversal counts as a 

positive area instead of counter-clockwise 

(C{bool}). 

@kwarg sign: If C{True}, 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: 3-Tuple C{(number, perimeter (meter), area (meter*2))}. 

''' 

n = self.num + 1 

if n < 2: 

p = _0_0 

a = NAN if self.polyline else _0_0 

r = None 

else: 

r = self._Inverse(self.lat1, self.lon1, lat, lon) 

p = self._Peri.Sum(r.s12) 

if self._Area: 

a = self._Area.Sum(r.S12) 

x = r.xing 

r = self._Inverse(lat, lon, self.lat0, self.lon0) 

p += r.s12 

A = _Accumulator(a + r.S12) 

a = self._reduce(A, reverse, sign, x + r.xing) 

else: 

a, r = NAN, None 

if self.verbose: # PYCHOK no cover 

self._print(n, p, a, r, lat=lat, lon=lon) 

return n, p, a 

 

def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

'''Return this C{GeodesicExactArea} as string. 

 

@kwarg prec: The C{float} precision, number of decimal digits (0..9). 

Trailing zero decimals are stripped for B{C{prec}} values 

of 1 and above, but kept for negative B{C{prec}} values. 

@kwarg sep: Optional separator to join (C{str}). 

 

@return: Area items (C{str}). 

''' 

n, p, a = self.Compute() 

d = dict(geodesic=self.geodesic, num=n, area=a, 

perimeter=p, polyline=self.polyline) 

return sep.join(pairs(d, prec=prec)) 

 

@Property 

def verbose(self): 

'''Get the C{verbose} option (C{bool}). 

''' 

return self._verbose 

 

@verbose.setter # PYCHOK setter! 

def verbose(self, verbose): 

'''Set the C{verbose} option. 

 

@arg verbose: Print a message after each 

method invokation (C{bool}). 

''' 

self._verbose = bool(verbose) 

 

 

class PolygonArea(GeodesicAreaExact): 

'''For C{geographiclib} compatibility, sub-class of L{GeodesicAreaExact}. 

''' 

def __init__(self, earth, polyline=False, name=NN): 

'''New L{PolygonArea} instance. 

 

@arg earth: A geodesic (L{GeodesicExact}, I{wrapped} 

C{Geodesic} or L{GeodesicSolve}). 

@kwarg polyline: If C{True} perimeter only, otherwise 

area and perimeter (C{bool}). 

@kwarg name: Optional name (C{str}). 

 

@raise GeodesicError: Invalid B{C{earth}}. 

''' 

GeodesicAreaExact.__init__(self, earth, polyline=polyline, name=name) 

 

 

class _Accumulator(_NamedBase): 

'''Like C{math.fsum}, but allowing a running sum. 

 

Original from I{Karney}'s U{geographiclib 

<https://PyPI.org/project/geographiclib>}C{.accumulator}, 

enhanced to return the current sum by most methods. 

''' 

_n = 0 # len() 

_s = _t = _0_0 

 

def __init__(self, y=0, name=NN): 

'''New L{_Accumulator}. 

''' 

if isinstance(y, _Accumulator): 

self._s, self._t, self._n = y._s, y._t, 1 

elif y: 

self._s, self._n = float(y), 1 

if name: 

self.name = name 

 

def Add(self, y): 

'''Add a value. 

 

@return: Current C{sum}. 

''' 

self._n += 1 

self._s, self._t = _3sum2(self._s, self._t, y) 

return self._s # current .Sum() 

 

def Negate(self): 

'''Negate sum. 

 

@return: Current C{sum}. 

''' 

self._s = s = -self._s 

self._t = -self._t 

return s # current .Sum() 

 

@property_RO 

def num(self): 

'''Get the current number of C{Add}itions (C{int}). 

''' 

return self._n 

 

def Remainder(self, y): 

'''Remainder on division by B{C{y}}. 

 

@return: Current C{sum} / B{C{y}}. 

''' 

_remainder(self._s, y) 

self._n = -1 

return self.Add(_0_0) 

 

def Reset(self, y=0): 

'''Set value from argument. 

''' 

self._n, self._s, self._t = 0, float(y), _0_0 

 

Set = Reset 

 

def Sum(self, y=0): 

'''Return C{sum + B{y}}. 

 

@note: B{C{y}} is included in the returned 

result, but I{not} accumulated. 

''' 

if y: 

s = _Accumulator(self, name='_Sum') 

s.Add(y) 

else: 

s = self 

return s._s 

 

def toStr(self, prec=6, sep=_COMMASPACE_, **unused): # PYCHOK signature 

'''Return this C{_Accumulator} as string. 

 

@kwarg prec: The C{float} precision, number of decimal digits (0..9). 

Trailing zero decimals are stripped for B{C{prec}} values 

of 1 and above, but kept for negative B{C{prec}} values. 

@kwarg sep: Optional separator to join (C{str}). 

 

@return: Accumulator (C{str}). 

''' 

d = dict(n=self.num, s=self._s, t=self._t) 

return sep.join(pairs(d, prec=prec)) 

 

 

__all__ += _ALL_DOCS(GeodesicAreaExact, PolygonArea) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2021 -- mrJean1 at Gmail -- All Rights Reserved. 

# 

# Permission is hereby granted, free of charge, to any person obtaining a 

# copy of this software and associated documentation files (the "Software"), 

# to deal in the Software without restriction, including without limitation 

# the rights to use, copy, modify, merge, publish, distribute, sublicense, 

# and/or sell copies of the Software, and to permit persons to whom the 

# Software is furnished to do so, subject to the following conditions: 

# 

# The above copyright notice and this permission notice shall be included 

# in all copies or substantial portions of the Software. 

# 

# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS 

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