# Coverage for pygeodesy/geodesicx/gxarea.py : 90%

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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/1.50/python/index.html>} Copyright (C) Charles Karney (2012-2019) <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__ = '21.06.23' 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 # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.