def initialBearingTo(self, other, wrap=False, raiser=False):
'''Compute the initial bearing (forward azimuth) from this
to an other point.
@param other: The other point (spherical L{LatLon}).
@keyword wrap: Wrap and unroll longitudes (C{bool}).
@keyword raiser: Optionally, raise L{CrossError} (C{bool}),
use I{raiser}=C{True} for behavior like
C{sphericalNvector.LatLon.initialBearingTo}.
@return: Initial bearing (compass C{degrees360}).
@raise CrossError: If this and the I{other} point coincide,
provided I{raiser} is C{True} and
L{crosserrors} is C{True}.
@raise TypeError: The I{other} point is not L{LatLon}.
@example:
>>> p1 = LatLon(52.205, 0.119)
>>> p2 = LatLon(48.857, 2.351)
>>> b = p1.initialBearingTo(p2) # 156.2
@JSname: I{bearingTo}.
'''
self.others(other)
a1, b1 = self.to2ab()
a2, b2 = other.to2ab()
# XXX behavior like sphericalNvector.LatLon.initialBearingTo
if raiser and crosserrors() and max(abs(a2 - a1), abs(b2 - b1)) < EPS:
raise CrossError('%s %s: %r' % ('coincident', 'points', other))
return degrees(bearing_(a1, b1, a2, b2, final=False, wrap=wrap))
def isconvex_(points, adjust=False, wrap=True):
'''Determine whether a polygon is convex and clockwise.
@param points: The polygon points (C{LatLon}[]).
@keyword adjust: Adjust the wrapped, unrolled longitudinal delta
by the cosine of the mean latitude (C{bool}).
@keyword wrap: Wrap lat-, wrap and unroll longitudes (C{bool}).
@return: C{+1} if I{points} are convex clockwise, C{-1} for
convex counter-clockwise I{points}, C{0} otherwise.
@raise CrossError: Some I{points} are colinear.
@raise TypeError: Some I{points} are not C{LatLon}.
@raise ValueError: Insufficient number of I{points}.
@example:
>>> t = LatLon(45,1), LatLon(46,1), LatLon(46,2)
>>> isconvex_(t) # +1
>>> f = LatLon(45,1), LatLon(46,2), LatLon(45,2), LatLon(46,1)
>>> isconvex_(f) # 0
'''
def _unroll_adjust(x1, y1, x2, y2, wrap):
x21, x2 = unroll180(x1, x2, wrap=wrap)
if adjust:
x21 *= cos(radians(y1 + y2) * 0.5)
return x21, x2
pts = LatLon2psxy(points, closed=True, radius=None, wrap=wrap)
c, n, s = crosserrors(), len(pts), 0
x1, y1, _ = pts[n - 2]
x2, y2, _ = pts[n - 1]
x21, x2 = _unroll_adjust(x1, y1, x2, y2, False)
for i in range(n):
x3, y3, ll = pts[i]
x32, x3 = _unroll_adjust(x2, y2, x3, y3, wrap if i <
(n - 2) else False)
# get the sign of the distance from point
# x3, y3 to the line from x1, y1 to x2, y2
# <http://WikiPedia.org/wiki/Distance_from_a_point_to_a_line>
s3 = fdot((x3, y3, x1, y1), y2 - y1, -x21, -y2, x2)
if s3 > 0: # x3, y3 on the right
if s < 0: # non-convex
return 0
s = +1
elif s3 < 0: # x3, y3 on the left
if s > 0: # non-convex
return 0
s = -1
elif c and fdot((x32, y1 - y2), y3 - y2, -x21) < 0:
# colinear u-turn: x3, y3 not on the
# opposite side of x2, y2 as x1, y1
raise CrossError('%s %s: %r' % ('colinear', 'point', ll))
x1, y1, x2, y2, x21 = x2, y2, x3, y3, x32
return s # all points on the same side