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# -*- coding: utf-8 -*- 

 

u'''A Python version of I{Karney}'s C++ class U{GeodesicLineExact 

<https://GeographicLib.SourceForge.io/C++/doc/classGeographicLib_1_1GeodesicLineExact.html>}. 

 

Copyright (C) U{Charles Karney<mailto:Charles@Karney.com>} (2008-2022) 

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

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

''' 

# make sure int/int division yields float quotient 

from __future__ import division as _; del _ # PYCHOK semicolon 

 

# A copy of comments from Karney's C{GeodesicLineExact.cpp}: 

# 

# This is a reformulation of the geodesic problem. The 

# notation is as follows: 

# - at a general point (no suffix or 1 or 2 as suffix) 

# - phi = latitude 

# - beta = latitude on auxiliary sphere 

# - omega = longitude on auxiliary sphere 

# - lambda = longitude 

# - alpha = azimuth of great circle 

# - sigma = arc length along great circle 

# - s = distance 

# - tau = scaled distance (= sigma at multiples of PI/2) 

# - at northwards equator crossing 

# - beta = phi = 0 

# - omega = lambda = 0 

# - alpha = alpha0 

# - sigma = s = 0 

# - a 12 suffix means a difference, e.g., s12 = s2 - s1. 

# - s and c prefixes mean sin and cos 

 

# from pygeodesy.basics import _xinstanceof # from .karney 

from pygeodesy.constants import NAN, _0_0, _1_0, _180_0, _2__PI 

from pygeodesy.fsums import _COMMASPACE_, fsum_, fsum1_ 

from pygeodesy.geodesicx.gxbases import _cosSeries, _GeodesicBase, \ 

_sincos12, _sin1cos2, _TINY 

# from pygeodesy.interns import _COMMASPACE_ # from .fsums 

from pygeodesy.lazily import _ALL_DOCS, _ALL_MODS as _MODS 

from pygeodesy.karney import _around, _atan2d, Caps, _copysign, GDict, \ 

_fix90, _K_2_0, _norm2, _norm180, \ 

_sincos2, _sincos2d, _xinstanceof 

from pygeodesy.props import Property_RO, _update_all 

from pygeodesy.streprs import pairs 

from pygeodesy.utily import atan2d as _atan2d_reverse, sincos2 

 

from math import atan2, cos, degrees, fabs, floor, radians, sin 

 

__all__ = () 

__version__ = '22.09.12' 

 

_glXs = [] # instances of C{[_]GeodesicLineExact} to be updated 

 

 

def _update_glXs(gX): # see GeodesicExact.C4order and -._ef_reset_k2 

'''(INTERNAL) Zap cached/memoized C{Property[_RO]}s of 

any L{GeodesicLineExact} instances tied to the given 

L{GeodesicExact} instance B{C{gX}}. 

''' 

_xinstanceof(gX, _MODS.geodesicx.GeodesicExact) 

for glX in _glXs: # PYCHOK use weakref? 

if glX._gX is gX: 

_update_all(glX) 

 

 

class _GeodesicLineExact(_GeodesicBase): 

'''(INTERNAL) Base class for L{GeodesicLineExact}. 

''' 

_a13 = _s13 = NAN 

_azi1 = _0_0 

_cchi1 = NAN 

_dn1 = NAN 

_gX = None # Exact only 

_k2 = NAN 

_lat1 = _lon1 = _0_0 

_salp0 = _calp0 = NAN 

_salp1 = _calp1 = NAN 

_somg1 = _comg1 = NAN 

_ssig1 = _csig1 = NAN 

 

def __init__(self, gX, lat1, lon1, azi1, caps, _debug, *salp1_calp1, **name): 

'''(INTERNAL) New C{[_]GeodesicLineExact} instance. 

''' 

_xinstanceof(gX, _MODS.geodesicx.GeodesicExact) 

if _debug: # PYCHOK no cover 

self._debug |= _debug & Caps._DEBUG_ALL 

# _CapsBase.debug._update(self) 

if salp1_calp1: 

salp1, calp1 = salp1_calp1 

else: 

azi1 = _norm180(azi1) 

# guard against salp0 underflow, 

# also -0 is converted to +0 

salp1, calp1 = _sincos2d(_around(azi1)) 

if name: 

self.name = name 

 

self._gX = gX # GeodesicExact only 

self._lat1 = lat1 = _fix90(lat1) 

self._lon1 = lon1 

self._azi1 = azi1 

self._salp1 = salp1 

self._calp1 = calp1 

# allow lat, azimuth and unrolling of lon 

self._caps = caps | Caps._LINE 

 

sbet1, cbet1 = gX._sinf1cos2d(_around(lat1)) 

self._dn1 = gX._dn(sbet1, cbet1) 

# Evaluate alp0 from sin(alp1) * cos(bet1) = sin(alp0), with alp0 

# in [0, pi/2 - |bet1|]. Alt: calp0 = hypot(sbet1, calp1 * cbet1), 

# but the following is slightly better, consider the case salp1 = 0. 

self._salp0, self._calp0 = _sin1cos2(salp1, calp1, sbet1, cbet1) 

self._k2 = self._calp0**2 * gX.ep2 

# Evaluate sig with tan(bet1) = tan(sig1) * cos(alp1). 

# sig = 0 is nearest northward crossing of equator. 

# With bet1 = 0, alp1 = pi/2, we have sig1 = 0 (equatorial line). 

# With bet1 = pi/2, alp1 = -pi, sig1 = pi/2 

# With bet1 = -pi/2, alp1 = 0 , sig1 = -pi/2 

# Evaluate omg1 with tan(omg1) = sin(alp0) * tan(sig1). 

# With alp0 in (0, pi/2], quadrants for sig and omg coincide. 

# No atan2(0,0) ambiguity at poles since cbet1 = +epsilon. 

# With alp0 = 0, omg1 = 0 for alp1 = 0, omg1 = pi for alp1 = pi. 

self._somg1 = sbet1 * self._salp0 

self._comg1 = c = (cbet1 * calp1) if (sbet1 or calp1) else _1_0 

# Without normalization we have schi1 = somg1. 

self._cchi1 = gX.f1 * self._dn1 * c 

self._ssig1, self._csig1 = _norm2(sbet1, c) # sig1 in (-pi, pi] 

# _norm2(somg1, comg1) # no need to normalize! 

# _norm2(schi1?, cchi1) # no need to normalize! 

if not (caps & Caps.LINE_OFF): 

_glXs.append(self) 

# no need to pre-compute other attrs based on _Caps.X. All are 

# Property_RO's, computed once and cached/memoized until reset 

# when C4order is changed or Elliptic function reset is invoked. 

 

def __del__(self): # XXX use weakref? 

if _glXs: # may be empty or None 

try: # PYCHOK no cover 

_glXs.remove(self) 

except (TypeError, ValueError): 

pass 

self._gX = None 

# _update_all(self) # throws TypeError during Python 2 cleanup 

 

def _update(self, updated, *attrs, **unused): 

if updated: 

_update_all(self, *attrs) 

 

@Property_RO 

def a1(self): 

'''Get the I{equatorial arc} (C{degrees}), the arc length between 

the northward equatorial crossing and the first point. 

''' 

return _atan2d(self._ssig1, self._csig1) # or NAN 

 

equatorarc = a1 

 

@Property_RO 

def a13(self): 

'''Get (spherical) arc length from the first to the reference point (C{degrees}). 

 

@see: Method L{SetArc}. 

''' 

return self._a13 

 

def ArcPosition(self, a12, outmask=Caps.STANDARD): 

'''Find the position on the line given B{C{a12}}. 

 

@arg a12: Spherical arc length from the first point to the 

second point (C{degrees}). 

@kwarg outmask: Bit-or'ed combination of L{Caps} values specifying 

the quantities to be returned. 

 

@return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2, 

lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1}, 

C{lon1}, C{azi1} and arc length C{a12} always included, 

except when C{a12=NAN}. 

 

@note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1}, 

C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and 

C{a12} entries are returned, except when C{a12=NAN}. 

''' 

return self._GDictPosition(True, a12, outmask) 

 

@Property_RO 

def azi0(self): 

'''Get the I{equatorial azimuth}, the azimuth of this geodesic line 

as it crosses the equator in a northward direction (C{degrees90}). 

''' 

return _atan2d(*self.azi0_sincos2) # or NAN 

 

equatorazimuth = azi0 

 

@Property_RO 

def azi0_sincos2(self): 

'''Get the sine and cosine of the I{equatorial azimuth} (2-tuple C{(sin, cos)}). 

''' 

return self._salp0, self._calp0 

 

@Property_RO 

def azi1(self): 

'''Get the azimuth at the first point (compass C{degrees}). 

''' 

return self._azi1 

 

@Property_RO 

def azi1_sincos2(self): 

'''Get the sine and cosine of the first point's azimuth (2-tuple C{(sin, cos)}). 

''' 

return self._salp1, self._calp1 

 

@Property_RO 

def _B41(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return _cosSeries(self._C4a, self._ssig1, self._csig1) 

 

@Property_RO 

def _C4a(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return self.geodesic._C4f_k2(self._k2) 

 

@Property_RO 

def _caps_DISTANCE_IN(self): 

'''(INTERNAL) Get C{Caps.DISTANCE_IN} and C{_OUT}. 

''' 

return self.caps & Caps._DISTANCE_IN_OUT 

 

@Property_RO 

def _D0k2(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return self._eF.cD * _2__PI * self._k2 

 

@Property_RO 

def _D1(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return self._eF.deltaD(self._ssig1, self._csig1, self._dn1) 

 

@Property_RO 

def _E0b(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return self._eF.cE * _2__PI * self.geodesic.b 

 

@Property_RO 

def _E1(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return self._eF.deltaE(self._ssig1, self._csig1, self._dn1) 

 

@Property_RO 

def _eF(self): 

'''(INTERNAL) Cached/memoized C{Elliptic} function. 

''' 

# see .gx.GeodesicExact._ef_reset_k2 

return _MODS.elliptic.Elliptic(k2=-self._k2, alpha2=-self.geodesic.ep2) 

 

def _GDictPosition(self, arcmode, s12_a12, outmask): # MCCABE 17 

'''(INTERNAL) Generate a new position along the geodesic. 

 

@return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2, 

lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1}, 

C{lon1}, C{azi1} and arc length C{a12} always included, 

except when C{a12=NAN}. 

''' 

r = GDict(a12=NAN, s12=NAN) # note both a12 and s12, always 

if not (arcmode or self._caps_DISTANCE_IN): # PYCHOK no cover 

return r # Uninitialized or impossible distance requested 

 

if self._debug: # PYCHOK no cover 

outmask |= self._debug & Caps._DEBUG_DIRECT_LINE 

outmask &= self._caps & Caps._OUT_MASK 

 

eF = self._eF 

gX = self.geodesic # ._gX 

 

if arcmode: 

# s12_a12 is spherical arc length 

E2 = _0_0 

sig12 = radians(s12_a12) 

if _K_2_0: 

ssig12, csig12 = sincos2(sig12) # utily, no NEG0 

else: # PYCHOK no cover 

a = fabs(s12_a12) # 0 <= fabs(_remainder(s12_a12, _180_0)) <= 90 

a -= floor(a / _180_0) * _180_0 # 0 <= 0 < 180 

ssig12 = _0_0 if a == 0 else sin(sig12) 

csig12 = _0_0 if a == 90 else cos(sig12) 

else: # s12_a12 is distance 

t = s12_a12 / self._E0b 

s, c = _sincos2(t) # tau12 

# tau2 = tau1 + tau12 

E2 = -eF.deltaEinv(*_sincos12(-s, c, *self._stau1_ctau1)) 

sig12 = fsum1_(self._E1, -E2, t) # == t - (E2 - E1) 

ssig12, csig12 = _sincos2(sig12) 

 

salp0, calp0 = self._salp0, self._calp0 

ssig1, csig1 = self._ssig1, self._csig1 

 

# sig2 = sig1 + sig12 

ssig2, csig2 = _sincos12(-ssig12, csig12, ssig1, csig1) 

dn2 = eF.fDelta(ssig2, csig2) 

# sin(bet2) = cos(alp0) * sin(sig2) and 

# cbet2 = hypot(salp0, calp0 * csig2). Alt: 

# cbet2 = hypot(csig2, salp0 * ssig2) 

sbet2, cbet2 = _sin1cos2(calp0, salp0, csig2, ssig2) 

if cbet2 == 0: # salp0 = 0, csig2 = 0, break degeneracy 

cbet2 = csig2 = _TINY 

# tan(alp0) = cos(sig2) * tan(alp2) 

salp2 = salp0 

calp2 = calp0 * csig2 # no need to normalize 

 

if (outmask & Caps.DISTANCE): 

if arcmode: # or f_0_01 

E2 = eF.deltaE(ssig2, csig2, dn2) 

# AB1 = _E0 * (E2 - _E1) 

# s12 = _b * (_E0 * sig12 + AB1) 

# = _b * _E0 * (sig12 + (E2 - _E1)) 

# = _b * _E0 * (E2 - _E1 + sig12) 

s12 = self._E0b * fsum1_(E2, -self._E1, sig12) 

else: 

s12 = s12_a12 

r.set_(s12=s12) 

 

if (outmask & Caps._DEBUG_DIRECT_LINE): # PYCHOK no cover 

r.set_(sig12=sig12, dn2=dn2, b=gX.b, e2=gX.e2, f1=gX.f1, 

E0b=self._E0b, E1=self._E1, E2=E2, eFk2=eF.k2, eFa2=eF.alpha2) 

 

if (outmask & Caps.LONGITUDE): 

schi1 = self._somg1 

cchi1 = self._cchi1 

schi2 = ssig2 * salp0 

cchi2 = gX.f1 * dn2 * csig2 # schi2 = somg2 without normalization 

lam12 = salp0 * self._H0e2_f1 * fsum1_(eF.deltaH(ssig2, csig2, dn2), 

-self._H1, sig12) 

if (outmask & Caps.LONG_UNROLL): 

t = _copysign(_1_0, salp0) # east-going? 

tchi1 = t * schi1 

tchi2 = t * schi2 

chi12 = t * fsum1_(atan2(ssig1, csig1), -atan2(ssig2, csig2), 

atan2(tchi2, cchi2), -atan2(tchi1, cchi1), sig12) 

lon2 = self.lon1 + degrees(chi12 - lam12) 

else: 

chi12 = atan2(*_sincos12(schi1, cchi1, schi2, cchi2)) 

lon2 = _norm180(self._lon1_norm180 + _norm180(degrees(chi12 - lam12))) 

r.set_(lon2=lon2) 

if (outmask & Caps._DEBUG_DIRECT_LINE): # PYCHOK no cover 

r.set_(ssig2=ssig2, chi12=chi12, H0e2_f1=self._H0e2_f1, 

csig2=csig2, lam12=lam12, H1=self._H1) 

 

if (outmask & Caps.LATITUDE): 

r.set_(lat2=_atan2d(sbet2, gX.f1 * cbet2)) 

 

if (outmask & Caps.AZIMUTH): 

r.set_(azi2=_atan2d_reverse(salp2, calp2, reverse=outmask & Caps.REVERSE2)) 

 

if (outmask & Caps._REDUCEDLENGTH_GEODESICSCALE): 

dn1 = self._dn1 

J12 = self._D0k2 * fsum_(eF.deltaD(ssig2, csig2, dn2), -self._D1, sig12) 

if (outmask & Caps._DEBUG_DIRECT_LINE): # PYCHOK no cover 

r.set_(ssig1=ssig1, dn1=dn1, D0k2=self._D0k2, 

csig1=csig1, J12=J12, D1=self._D1) 

if (outmask & Caps.REDUCEDLENGTH): 

# Add parens around (csig1 * ssig2) and (ssig1 * csig2) to 

# ensure accurate cancellation in the case of coincident points. 

r.set_(m12=gX.b * fsum1_(dn2 * (csig1 * ssig2), 

-dn1 * (ssig1 * csig2), 

-J12 * (csig1 * csig2))) 

if (outmask & Caps.GEODESICSCALE): 

t = self._k2 * (ssig2 - ssig1) * (ssig2 + ssig1) / (dn2 + dn1) 

r.set_(M12=csig12 + ssig1 * (t * ssig2 - csig2 * J12) / dn1, 

M21=csig12 - ssig2 * (t * ssig1 - csig1 * J12) / dn2) 

 

if (outmask & Caps.AREA): 

A4 = salp0 * calp0 

if A4: 

# tan(alp) = tan(alp0) * sec(sig) 

# tan(alp2-alp1) = (tan(alp2) - tan(alp1)) / (tan(alp2) * tan(alp1) + 1) 

# = calp0 * salp0 * (csig1 - csig2) / (salp0^2 + calp0^2 * csig1 * csig2) 

# If csig12 > 0, write 

# csig1 - csig2 = ssig12 * (csig1 * ssig12 / (1 + csig12) + ssig1) 

# else 

# csig1 - csig2 = csig1 * (1 - csig12) + ssig12 * ssig1 

# No need to normalize 

salp12 = (((ssig12 * csig1 / (_1_0 + csig12) + ssig1) * ssig12) if csig12 > 0 else 

(csig1 * (_1_0 - csig12) + ssig1 * ssig12)) * A4 

calp12 = salp0**2 + calp0**2 * csig1 * csig2 

A4 *= gX._e2a2 

B41 = self._B41 

B42 = _cosSeries(self._C4a, ssig2, csig2) 

S12 = (B42 - B41) * A4 

else: 

S12 = A4 = B41 = B42 = _0_0 

# alp12 = alp2 - alp1, used in atan2 so no need to normalize 

salp12, calp12 = _sincos12(self._salp1, self._calp1, salp2, calp2) 

# We used to include some patch up code that purported to deal 

# with nearly meridional geodesics properly. However, this turned 

# out to be wrong once salp1 = -0 was allowed (via InverseLine). 

# In fact, the calculation of {s,c}alp12 was already correct 

# (following the IEEE rules for handling signed zeros). So, 

# the patch up code was unnecessary (as well as dangerous). 

if (outmask & Caps._DEBUG_DIRECT_LINE): # PYCHOK no cover 

r.set_(salp12=salp12, salp0=salp0, B41=B41, A4=A4, 

calp12=calp12, calp0=calp0, B42=B42, c2=gX.c2) 

S12 += gX.c2 * atan2(salp12, calp12) 

r.set_(S12=S12) 

 

r.set_(a12=s12_a12 if arcmode else degrees(sig12), 

lat1=self.lat1, # == _fix90(lat1) 

lon1=self.lon1 if (outmask & Caps.LONG_UNROLL) else self._lon1_norm180, 

azi1=_norm180(self.azi1)) 

return r 

 

def _GenPosition(self, arcmode, s12_a12, outmask): 

'''(INTERNAL) Generate a new position along the geodesic. 

 

@return: L{Direct9Tuple}C{(a12, lat2, lon2, azi2, 

s12, m12, M12, M21, S12)}. 

''' 

r = self._GDictPosition(arcmode, s12_a12, outmask) 

return r.toDirect9Tuple() 

 

def _GenSet(self, arcmode, s13_a13): 

'''(INTERNAL) Aka C++ C{GenSetDistance}. 

''' 

if arcmode: 

self.SetArc(s13_a13) 

else: 

self.SetDistance(s13_a13) 

return self # for gx.GeodesicExact.InverseLine and -._GenDirectLine 

 

@Property_RO 

def geodesic(self): 

'''Get the I{exact} geodesic (L{GeodesicExact}). 

''' 

assert isinstance(self._gX, _MODS.geodesicx.GeodesicExact) 

return self._gX 

 

@Property_RO 

def _H0e2_f1(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return self._eF.cH * _2__PI * self.geodesic._e2_f1 

 

@Property_RO 

def _H1(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return self._eF.deltaH(self._ssig1, self._csig1, self._dn1) 

 

@Property_RO 

def lat1(self): 

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

''' 

return self._lat1 

 

@Property_RO 

def lon1(self): 

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

''' 

return self._lon1 

 

@Property_RO 

def _lon1_norm180(self): 

'''(INTERNAL) Cached/memoized. 

''' 

return _norm180(self._lon1) 

 

def Position(self, s12, outmask=Caps.STANDARD): 

'''Find the position on the line given B{C{s12}}. 

 

@arg s12: Distance from the first point to the second (C{meter}). 

@kwarg outmask: Bit-or'ed combination of L{Caps} values specifying 

the quantities to be returned. 

 

@return: A L{GDict} with up to 12 items C{lat1, lon1, azi1, lat2, 

lon2, azi2, m12, a12, s12, M12, M21, S12} with C{lat1}, 

C{lon1}, C{azi1} and arc length C{a12} always included, 

except when C{a12=NAN}. 

 

@note: By default, C{B{outmask}=STANDARD}, meaning thc C{lat1}, 

C{lon1}, C{azi1}, C{lat2}, C{lon2}, C{azi2}, C{s12} and 

C{a12} entries are returned, except when C{a12=NAN}. 

 

@note: This L{GeodesicLineExact} instance must have been 

constructed with capability C{Caps.DISTANCE_IN} set. 

''' 

return self._GDictPosition(False, s12, outmask) 

 

@Property_RO 

def s13(self): 

'''Get the distance from the first to the reference point (C{meter}). 

 

@see: Method L{SetDistance}. 

''' 

return self._s13 

 

def SetArc(self, a13): 

'''Set reference point 3 in terms of distance to the first point. 

 

@arg a13: Spherical arc length from the first to the reference 

point (C{degrees}). 

 

@return: The distance C{s13} (C{meter}) between the first and 

the reference point or C{NAN}. 

''' 

self._a13 = a13 

self._s13 = s13 = self._GDictPosition(True, a13, Caps.DISTANCE).s12 

return s13 

 

def SetDistance(self, s13): 

'''Set reference point 3 in terms of distance to the first point. 

 

@arg s13: Distance from the first to the reference point (C{meter}). 

 

@return: The arc length C{a13} (C{degrees}) between the first 

and the reference point or C{NAN}. 

''' 

self._s13 = s13 

self._a13 = a13 = self._GDictPosition(False, s13, 0).a12 

return a13 # NAN for GeodesicLineExact without Cap.DISTANCE_IN 

 

@Property_RO 

def _stau1_ctau1(self): 

'''(INTERNAL) Cached/memoized. 

''' 

s, c = _sincos2(self._E1) 

# tau1 = sig1 + B11 

return _sincos12(-s, c, self._ssig1, self._csig1) 

# unnecessary because Einv inverts E 

# return -self._eF.deltaEinv(stau1, ctau1) 

 

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

'''Return this C{GeodesicLineExact} 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: Separator to join (C{str}). 

 

@return: C{GeodesicLineExact} (C{str}). 

''' 

d = dict(geodesic=self.geodesic, 

lat1=self.lat1, lon1=self.lon1, azi1=self.azi1, 

a13=self.a13, s13=self.s13) 

return sep.join(pairs(d, prec=prec)) 

 

 

__all__ += _ALL_DOCS(_GeodesicLineExact) 

 

# **) MIT License 

# 

# Copyright (C) 2016-2022 -- 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.