def translate(self, p1, p2):
"""
Translate the surface for a specific distance along a specific azimuth
direction.
Parameters are two points (instances of :class:`nhlib.geo.point.Point`)
representing the direction and an azimuth for translation. The
resulting surface corner points will be that far along that azimuth
from respective corner points of this surface as ``p2`` is located
with respect to ``p1``.
:returns:
A new :class:`PlanarSurface` object with the same mesh spacing,
dip, strike, width, length and depth but with corners longitudes
and latitudes translated.
"""
azimuth = geodetic.azimuth(p1.longitude, p1.latitude,
p2.longitude, p2.latitude)
distance = geodetic.geodetic_distance(p1.longitude, p1.latitude,
p2.longitude, p2.latitude)
# avoid calling PlanarSurface's constructor
nsurf = object.__new__(PlanarSurface)
# but do call BaseSurface's one
BaseSurface.__init__(nsurf)
nsurf.mesh_spacing = self.mesh_spacing
nsurf.dip = self.dip
nsurf.strike = self.strike
nsurf.corner_lons, nsurf.corner_lats = geodetic.point_at(
self.corner_lons, self.corner_lats, azimuth, distance
)
nsurf.corner_depths = self.corner_depths.copy()
nsurf._init_plane()
nsurf.width = self.width
nsurf.length = self.length
return nsurf
def average_azimuth(self):
"""
Calculate and return weighted average azimuth of all line's segments
in decimal degrees.
Uses formula from
http://en.wikipedia.org/wiki/Mean_of_circular_quantities
>>> from nhlib.geo.point import Point as P
>>> str(Line([P(0, 0), P(1e-5, 1e-5)]).average_azimuth())
'45.0'
>>> str(Line([P(0, 0), P(0, 1e-5), P(1e-5, 1e-5)]).average_azimuth())
'45.0'
>>> line = Line([P(0, 0), P(-2e-5, 0), P(-2e-5, 1.154e-5)])
>>> '%.1f' % line.average_azimuth()
'300.0'
"""
if len(self.points) == 2:
return self.points[0].azimuth(self.points[1])
lons = numpy.array([point.longitude for point in self.points])
lats = numpy.array([point.latitude for point in self.points])
azimuths = geodetic.azimuth(lons[:-1], lats[:-1], lons[1:], lats[1:])
distances = geodetic.geodetic_distance(lons[:-1], lats[:-1],
lons[1:], lats[1:])
azimuths = numpy.radians(azimuths)
# convert polar coordinates to Cartesian ones and calculate
# the average coordinate of each component
avg_x = numpy.mean(distances * numpy.sin(azimuths))
avg_y = numpy.mean(distances * numpy.cos(azimuths))
# find the mean azimuth from that mean vector
azimuth = numpy.degrees(numpy.arctan2(avg_x, avg_y))
if azimuth < 0:
azimuth += 360
return azimuth
def translate(self, p1, p2):
"""
Translate the surface for a specific distance along a specific azimuth
direction.
Parameters are two points (instances of :class:`nhlib.geo.point.Point`)
representing the direction and an azimuth for translation. The
resulting surface corner points will be that far along that azimuth
from respective corner points of this surface as ``p2`` is located
with respect to ``p1``.
:returns:
A new :class:`PlanarSurface` object with the same mesh spacing,
dip, strike, width, length and depth but with corners longitudes
and latitudes translated.
"""
azimuth = geodetic.azimuth(p1.longitude, p1.latitude,
p2.longitude, p2.latitude)
distance = geodetic.geodetic_distance(p1.longitude, p1.latitude,
p2.longitude, p2.latitude)
# avoid calling PlanarSurface's constructor
nsurf = object.__new__(PlanarSurface)
# but do call BaseSurface's one
BaseSurface.__init__(nsurf)
nsurf.mesh_spacing = self.mesh_spacing
nsurf.dip = self.dip
nsurf.strike = self.strike
nsurf.corner_lons, nsurf.corner_lats = geodetic.point_at(
self.corner_lons, self.corner_lats, azimuth, distance
)
nsurf.corner_depths = self.corner_depths.copy()
nsurf._init_plane()
nsurf.width = self.width
nsurf.length = self.length
return nsurf
def average_azimuth(self):
"""
Calculate and return weighted average azimuth of all line's segments
in decimal degrees.
Uses formula from
http://en.wikipedia.org/wiki/Mean_of_circular_quantities
>>> from nhlib.geo.point import Point as P
>>> str(Line([P(0, 0), P(1e-5, 1e-5)]).average_azimuth())
'45.0'
>>> str(Line([P(0, 0), P(0, 1e-5), P(1e-5, 1e-5)]).average_azimuth())
'45.0'
>>> line = Line([P(0, 0), P(-2e-5, 0), P(-2e-5, 1.154e-5)])
>>> '%.1f' % line.average_azimuth()
'300.0'
"""
if len(self.points) == 2:
return self.points[0].azimuth(self.points[1])
lons = numpy.array([point.longitude for point in self.points])
lats = numpy.array([point.latitude for point in self.points])
azimuths = geodetic.azimuth(lons[:-1], lats[:-1], lons[1:], lats[1:])
distances = geodetic.geodetic_distance(lons[:-1], lats[:-1],
lons[1:], lats[1:])
azimuths = numpy.radians(azimuths)
# convert polar coordinates to Cartesian ones and calculate
# the average coordinate of each component
avg_x = numpy.mean(distances * numpy.sin(azimuths))
avg_y = numpy.mean(distances * numpy.cos(azimuths))
# find the mean azimuth from that mean vector
azimuth = numpy.degrees(numpy.arctan2(avg_x, avg_y))
if azimuth < 0:
azimuth += 360
return azimuth
def test_arrays(self):
lons1 = numpy.array([[156.49676849, 150.03697145],
[-77.96053914, -109.36694411]])
lats1 = numpy.array([[-79.78522764, -89.15044328],
[-32.28244296, -25.11092309]])
lons2 = numpy.array([[-84.6732372, 140.08382287],
[82.69227935, -18.9919318]])
lats2 = numpy.array([[82.16896786, 26.16081412],
[41.21501474, -2.88241099]])
eazimuths = numpy.array([[47.07336955, 350.11740733],
[54.46959147, 92.76923701]])
az = geodetic.azimuth(lons1, lats1, lons2, lats2)
self.assertTrue(numpy.allclose(az, eazimuths), str(az))
def test_arrays(self):
lons1 = numpy.array([[156.49676849, 150.03697145],
[-77.96053914, -109.36694411]])
lats1 = numpy.array([[-79.78522764, -89.15044328],
[-32.28244296, -25.11092309]])
lons2 = numpy.array([[-84.6732372, 140.08382287],
[82.69227935, -18.9919318]])
lats2 = numpy.array([[82.16896786, 26.16081412],
[41.21501474, -2.88241099]])
eazimuths = numpy.array([[47.07336955, 350.11740733],
[54.46959147, 92.76923701]])
az = geodetic.azimuth(lons1, lats1, lons2, lats2)
self.assertTrue(numpy.allclose(az, eazimuths), str(az))
def get_middle_point(lon1, lat1, lon2, lat2):
"""
Given two points return the point exactly in the middle lying on the same
great circle arc.
Parameters are point coordinates in degrees.
:returns:
Tuple of longitude and latitude of the point in the middle.
"""
if lon1 == lon2 and lat1 == lat2:
return lon1, lat1
dist = geodetic.geodetic_distance(lon1, lat1, lon2, lat2)
azimuth = geodetic.azimuth(lon1, lat1, lon2, lat2)
return geodetic.point_at(lon1, lat1, azimuth, dist / 2.0)
def get_middle_point(lon1, lat1, lon2, lat2):
"""
Given two points return the point exactly in the middle lying on the same
great circle arc.
Parameters are point coordinates in degrees.
:returns:
Tuple of longitude and latitude of the point in the middle.
"""
if lon1 == lon2 and lat1 == lat2:
return lon1, lat1
dist = geodetic.geodetic_distance(lon1, lat1, lon2, lat2)
azimuth = geodetic.azimuth(lon1, lat1, lon2, lat2)
return geodetic.point_at(lon1, lat1, azimuth, dist / 2.0)
def azimuth(self, point):
"""
Compute the azimuth (in decimal degrees) between this point
and the given point.
:param point:
Destination point.
:type point:
Instance of :class:`Point`
:returns:
The azimuth, value in a range ``[0, 360)``.
:rtype:
float
"""
return geodetic.azimuth(self.longitude, self.latitude, point.longitude,
point.latitude)
def azimuth(self, point):
"""
Compute the azimuth (in decimal degrees) between this point
and the given point.
:param point:
Destination point.
:type point:
Instance of :class:`Point`
:returns:
The azimuth, value in a range ``[0, 360)``.
:rtype:
float
"""
return geodetic.azimuth(self.longitude, self.latitude,
point.longitude, point.latitude)
def test_equator(self):
az = geodetic.azimuth(0, 0, 1, 0)
self.assertEqual(az, 90)
az = geodetic.azimuth(1, 0, 0, 0)
self.assertEqual(az, 270)
def test_meridians(self):
az = geodetic.azimuth(0, 0, 0, 1)
self.assertEqual(az, 0)
az = geodetic.azimuth(0, 2, 0, 1)
self.assertEqual(az, 180)
def test_quadrants(self):
az = geodetic.azimuth(0, 0, [0.01, 0.01, -0.01, -0.01],
[0.01, -0.01, -0.01, 0.01])
self.assertTrue(numpy.allclose(az, [45, 135, 225, 315]), str(az))
def test_LAX_to_JFK(self):
az = geodetic.azimuth(*(LAX + JFK))
self.assertAlmostEqual(az, 360 - 65.8922, places=4)
def test_LAX_to_JFK(self):
az = geodetic.azimuth(*(LAX + JFK))
self.assertAlmostEqual(az, 360 - 65.8922, places=4)
def test_quadrants(self):
az = geodetic.azimuth(0, 0, [0.01, 0.01, -0.01, -0.01],
[0.01, -0.01, -0.01, 0.01])
self.assertTrue(numpy.allclose(az, [45, 135, 225, 315]), str(az))
def test_equator(self):
az = geodetic.azimuth(0, 0, 1, 0)
self.assertEqual(az, 90)
az = geodetic.azimuth(1, 0, 0, 0)
self.assertEqual(az, 270)
def test_meridians(self):
az = geodetic.azimuth(0, 0, 0, 1)
self.assertEqual(az, 0)
az = geodetic.azimuth(0, 2, 0, 1)
self.assertEqual(az, 180)
