def test_one_point(self):
dist = geodetic.distance_to_arc(12.3, 44.5, 39.4,
plons=13.4, plats=46.9)
self.assertAlmostEqual(dist, -105.12464364)
dist = geodetic.distance_to_arc(12.3, 44.5, 39.4,
plons=13.4, plats=44.9)
self.assertAlmostEqual(dist, 38.34459954)
def test_one_point(self):
dist = geodetic.distance_to_arc(12.3,
44.5,
39.4,
plons=13.4,
plats=46.9)
self.assertAlmostEqual(dist, -105.12464364)
dist = geodetic.distance_to_arc(12.3,
44.5,
39.4,
plons=13.4,
plats=44.9)
self.assertAlmostEqual(dist, 38.34459954)
def get_rx_distance(self, mesh):
"""
Compute distance between each point of mesh and surface's great circle
arc.
Distance is measured perpendicular to the rupture strike, from
the surface projection of the updip edge of the rupture, with
the down dip direction being positive (this distance is usually
called ``Rx``).
In other words, is the horizontal distance to top edge of rupture
measured perpendicular to the strike. Values on the hanging wall
are positive, values on the footwall are negative.
Base class calls :func:`nhlib.geo.geodetic.distance_to_arc`.
:param mesh:
:class:`~nhlib.geo.mesh.Mesh` of points to calculate Rx-distance
to.
:returns:
Numpy array of distances in km.
"""
top_edge_centroid = self._get_top_edge_centroid()
return geodetic.distance_to_arc(
top_edge_centroid.longitude, top_edge_centroid.latitude,
self.get_strike(), mesh.lons, mesh.lats
)
def get_rx_distance(self, mesh):
"""
Compute distance between each point of mesh and surface's great circle
arc.
Distance is measured perpendicular to the rupture strike, from
the surface projection of the updip edge of the rupture, with
the down dip direction being positive (this distance is usually
called ``Rx``).
In other words, is the horizontal distance to top edge of rupture
measured perpendicular to the strike. Values on the hanging wall
are positive, values on the footwall are negative.
Base class calls :func:`nhlib.geo.geodetic.distance_to_arc`.
:param mesh:
:class:`~nhlib.geo.mesh.Mesh` of points to calculate Rx-distance
to.
:returns:
Numpy array of distances in km.
"""
top_edge_centroid = self._get_top_edge_centroid()
return geodetic.distance_to_arc(top_edge_centroid.longitude,
top_edge_centroid.latitude,
self.get_strike(), mesh.lons,
mesh.lats)
def get_joyner_boore_distance(self, mesh):
"""
See :meth:`superclass' method
<nhlib.geo.surface.base.BaseSurface.get_joyner_boore_distance>`.
This is an optimized version specific to planar surface that doesn't
make use of the mesh.
"""
# we define four great circle arcs that contain four sides
# of projected planar surface:
#
# ↓ II ↓
# I ↓ ↓ I
# ↓ + ↓
# →→→→→TL→→→→1→→→→TR→→→→→ → azimuth direction →
# ↓ - ↓
# ↓ ↓
# III -3+ IV -4+ III ↓
# ↓ ↓ downdip direction
# ↓ + ↓ ↓
# →→→→→BL→→→→2→→→→BR→→→→→
# ↓ - ↓
# I ↓ ↓ I
# ↓ II ↓
#
# arcs 1 and 2 are directed from left corners to right ones (the
# direction has an effect on the sign of the distance to an arc,
# as it shown on the figure), arcs 3 and 4 are directed from top
# corners to bottom ones.
#
# then we measure distance from each of the points in a mesh
# to each of those arcs and compare signs of distances in order
# to find a relative positions of projections of points and
# projection of a surface.
#
# then we consider four special cases (labeled with Roman numerals)
# and either pick one of distances to arcs or a closest distance
# to corner.
#
# indices 0, 2 and 1 represent corners TL, BL and TR respectively.
arcs_lons = self.corner_lons.take([0, 2, 0, 1])
arcs_lats = self.corner_lats.take([0, 2, 0, 1])
downdip_azimuth = (self.strike + 90) % 360
arcs_azimuths = [self.strike, self.strike,
downdip_azimuth, downdip_azimuth]
mesh_lons = mesh.lons.reshape((-1, 1))
mesh_lats = mesh.lats.reshape((-1, 1))
# calculate distances from all the target points to all four arcs
dists_to_arcs = geodetic.distance_to_arc(
arcs_lons, arcs_lats, arcs_azimuths, mesh_lons, mesh_lats
)
# ... and distances from all the target points to each of surface's
# corners' projections (we might not need all of those but it's
# better to do that calculation once for all).
dists_to_corners = geodetic.min_geodetic_distance(
self.corner_lons, self.corner_lats, mesh.lons, mesh.lats
)
# extract from ``dists_to_arcs`` signs (represent relative positions
# of an arc and a point: +1 means on the left hand side, 0 means
# on arc and -1 means on the right hand side) and minimum absolute
# values of distances to each pair of parallel arcs.
ds1, ds2, ds3, ds4 = numpy.sign(dists_to_arcs).transpose()
dists_to_arcs = numpy.abs(dists_to_arcs).reshape(-1, 2, 2).min(axis=-1)
return numpy.select(
# consider four possible relative positions of point and arcs:
condlist=[
# signs of distances to both parallel arcs are the same
# in both pairs, case "I" on a figure above
(ds1 == ds2) & (ds3 == ds4),
# sign of distances to two parallels is the same only
# in one pair, case "II"
ds1 == ds2,
# ... or another (case "III")
ds3 == ds4
# signs are different in both pairs (this is a "default"),
# case "IV"
],
choicelist=[
# case "I": closest distance is the closest distance to corners
dists_to_corners,
# case "II": closest distance is distance to arc "1" or "2",
# whichever is closer
dists_to_arcs[:, 0],
# case "III": closest distance is distance to either
# arc "3" or "4"
dists_to_arcs[:, 1]
],
# default -- case "IV"
default=0
)
def get_joyner_boore_distance(self, mesh):
"""
See :meth:`superclass' method
<nhlib.geo.surface.base.BaseSurface.get_joyner_boore_distance>`.
This is an optimized version specific to planar surface that doesn't
make use of the mesh.
"""
# we define four great circle arcs that contain four sides
# of projected planar surface:
#
# ↓ II ↓
# I ↓ ↓ I
# ↓ + ↓
# →→→→→TL→→→→1→→→→TR→→→→→ → azimuth direction →
# ↓ - ↓
# ↓ ↓
# III -3+ IV -4+ III ↓
# ↓ ↓ downdip direction
# ↓ + ↓ ↓
# →→→→→BL→→→→2→→→→BR→→→→→
# ↓ - ↓
# I ↓ ↓ I
# ↓ II ↓
#
# arcs 1 and 2 are directed from left corners to right ones (the
# direction has an effect on the sign of the distance to an arc,
# as it shown on the figure), arcs 3 and 4 are directed from top
# corners to bottom ones.
#
# then we measure distance from each of the points in a mesh
# to each of those arcs and compare signs of distances in order
# to find a relative positions of projections of points and
# projection of a surface.
#
# then we consider four special cases (labeled with Roman numerals)
# and either pick one of distances to arcs or a closest distance
# to corner.
#
# indices 0, 2 and 1 represent corners TL, BL and TR respectively.
arcs_lons = self.corner_lons.take([0, 2, 0, 1])
arcs_lats = self.corner_lats.take([0, 2, 0, 1])
downdip_azimuth = (self.strike + 90) % 360
arcs_azimuths = [self.strike, self.strike,
downdip_azimuth, downdip_azimuth]
mesh_lons = mesh.lons.reshape((-1, 1))
mesh_lats = mesh.lats.reshape((-1, 1))
# calculate distances from all the target points to all four arcs
dists_to_arcs = geodetic.distance_to_arc(
arcs_lons, arcs_lats, arcs_azimuths, mesh_lons, mesh_lats
)
# ... and distances from all the target points to each of surface's
# corners' projections (we might not need all of those but it's
# better to do that calculation once for all).
dists_to_corners = geodetic.min_geodetic_distance(
self.corner_lons, self.corner_lats, mesh.lons, mesh.lats
)
# extract from ``dists_to_arcs`` signs (represent relative positions
# of an arc and a point: +1 means on the left hand side, 0 means
# on arc and -1 means on the right hand side) and minimum absolute
# values of distances to each pair of parallel arcs.
ds1, ds2, ds3, ds4 = numpy.sign(dists_to_arcs).transpose()
dists_to_arcs = numpy.abs(dists_to_arcs).reshape(-1, 2, 2).min(axis=-1)
return numpy.select(
# consider four possible relative positions of point and arcs:
condlist=[
# signs of distances to both parallel arcs are the same
# in both pairs, case "I" on a figure above
(ds1 == ds2) & (ds3 == ds4),
# sign of distances to two parallels is the same only
# in one pair, case "II"
ds1 == ds2,
# ... or another (case "III")
ds3 == ds4
# signs are different in both pairs (this is a "default"),
# case "IV"
],
choicelist=[
# case "I": closest distance is the closest distance to corners
dists_to_corners,
# case "II": closest distance is distance to arc "1" or "2",
# whichever is closer
dists_to_arcs[:, 0],
# case "III": closest distance is distance to either
# arc "3" or "4"
dists_to_arcs[:, 1]
],
# default -- case "IV"
default=0
)
def test_several_points(self):
plons = numpy.array([3.3, 4.3])
plats = numpy.array([20.3, 15.3])
dists = geodetic.distance_to_arc(4.0, 17.0, -123.0, plons, plats)
expected_dists = [347.61490787, -176.03785187]
self.assertTrue(numpy.allclose(dists, expected_dists))
def test_several_points(self):
plons = numpy.array([3.3, 4.3])
plats = numpy.array([20.3, 15.3])
dists = geodetic.distance_to_arc(4.0, 17.0, -123.0, plons, plats)
expected_dists = [347.61490787, -176.03785187]
self.assertTrue(numpy.allclose(dists, expected_dists))