def _exs(n, points): # iterate over spherical edge excess
a1, b1 = points[n - 1].to2ab()
ta1 = tan_2(a1)
for i in range(n):
a2, b2 = points[i].to2ab()
db, b2 = unrollPI(b1, b2, wrap=wrap)
ta2, tdb = map1(tan_2, a2, db)
yield atan2(tdb * (ta1 + ta2), 1 + ta1 * ta2)
ta1, b1 = ta2, b2
def areaOf(points, radius=R_M, wrap=True):
'''Calculate the area of a (spherical) polygon (with great circle
arcs joining the points).
@param points: The polygon points (L{LatLon}[]).
@keyword radius: Optional, mean earth radius (C{meter}).
@keyword wrap: Wrap and unroll longitudes (C{bool}).
@return: Polygon area (C{meter}, same units as I{radius}, squared).
@raise TypeError: Some I{points} are not L{LatLon}.
@raise ValueError: Insufficient number of I{points}.
@note: The area is based on Karney's U{'Area of a spherical polygon'
<http://osgeo-org.1560.x6.nabble.com/Area-of-a-spherical-polygon-td3841625.html>}.
@see: L{pygeodesy.areaOf}, L{sphericalNvector.areaOf} and
L{ellipsoidalKarney.areaOf}.
@example:
>>> b = LatLon(45, 1), LatLon(45, 2), LatLon(46, 2), LatLon(46, 1)
>>> areaOf(b) # 8666058750.718977
>>> c = LatLon(0, 0), LatLon(1, 0), LatLon(0, 1)
>>> areaOf(c) # 6.18e9
'''
n, points = _Trll.points2(points, closed=True)
# Area method due to Karney: for each edge of the polygon,
#
# tan(Δλ/2) · (tan(φ1/2) + tan(φ2/2))
# tan(E/2) = ------------------------------------
# 1 + tan(φ1/2) · tan(φ2/2)
#
# where E is the spherical excess of the trapezium obtained by
# extending the edge to the equator-circle vector for each edge
if iterNumpy2(points):
def _exs(n, points): # iterate over spherical edge excess
a1, b1 = points[n - 1].to2ab()
ta1 = tan_2(a1)
for i in range(n):
a2, b2 = points[i].to2ab()
db, b2 = unrollPI(b1, b2, wrap=wrap)
ta2, tdb = map1(tan_2, a2, db)
yield atan2(tdb * (ta1 + ta2), 1 + ta1 * ta2)
ta1, b1 = ta2, b2
s = fsum(_exs(n, points)) * 2
else:
a1, b1 = points[n - 1].to2ab()
s, ta1 = [], tan_2(a1)
for i in range(n):
a2, b2 = points[i].to2ab()
db, b2 = unrollPI(b1, b2, wrap=wrap)
ta2, tdb = map1(tan_2, a2, db)
s.append(atan2(tdb * (ta1 + ta2), 1 + ta1 * ta2))
ta1, b1 = ta2, b2
s = fsum(s) * 2
if isPoleEnclosedBy(points):
s = abs(s) - PI2
return abs(s * radius**2)