def _test(self, mlons, mlats, mdepths, slons, slats, sdepths,
expected_mpoint_indices):
mlons, mlats, mdepths = [
numpy.array(arr, float) for arr in (mlons, mlats, mdepths)
]
slons, slats, sdepths = [
numpy.array(arr, float) for arr in (slons, slats, sdepths)
]
actual_indices = geodetic.min_distance(mlons,
mlats,
mdepths,
slons,
slats,
sdepths,
indices=True)
numpy.testing.assert_equal(actual_indices, expected_mpoint_indices)
dists = geodetic.min_distance(mlons, mlats, mdepths, slons, slats,
sdepths)
expected_closest_mlons = mlons.flat[expected_mpoint_indices]
expected_closest_mlats = mlats.flat[expected_mpoint_indices]
expected_closest_mdepths = mdepths.flat[expected_mpoint_indices]
expected_distances = geodetic.distance(expected_closest_mlons,
expected_closest_mlats,
expected_closest_mdepths, slons,
slats, sdepths)
self.assertTrue((dists == expected_distances).all())
# testing min_geodetic_distance with the same lons and lats
min_geod_distance = geodetic.min_geodetic_distance(
mlons, mlats, slons, slats)
min_geo_distance2 = geodetic.min_distance(mlons, mlats, mdepths * 0,
slons, slats, sdepths * 0)
numpy.testing.assert_almost_equal(min_geod_distance, min_geo_distance2)
def _test(self, mlons, mlats, mdepths, slons, slats, sdepths,
expected_mpoint_indices):
mlons, mlats, mdepths = [numpy.array(arr, float)
for arr in (mlons, mlats, mdepths)]
slons, slats, sdepths = [numpy.array(arr, float)
for arr in (slons, slats, sdepths)]
actual_indices = geodetic.min_distance(mlons, mlats, mdepths,
slons, slats, sdepths,
indices=True)
numpy.testing.assert_equal(actual_indices, expected_mpoint_indices)
dists = geodetic.min_distance(mlons, mlats, mdepths,
slons, slats, sdepths)
expected_closest_mlons = mlons.flat[expected_mpoint_indices]
expected_closest_mlats = mlats.flat[expected_mpoint_indices]
expected_closest_mdepths = mdepths.flat[expected_mpoint_indices]
expected_distances = geodetic.distance(
expected_closest_mlons, expected_closest_mlats,
expected_closest_mdepths,
slons, slats, sdepths
)
self.assertTrue((dists == expected_distances).all())
# testing min_geodetic_distance with the same lons and lats
min_geod_distance = geodetic.min_geodetic_distance(mlons, mlats,
slons, slats)
min_geo_distance2 = geodetic.min_distance(mlons, mlats, mdepths * 0,
slons, slats, sdepths * 0)
numpy.testing.assert_almost_equal(min_geod_distance, min_geo_distance2)
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):
"""
Compute and return Joyner-Boore distance to each point of ``mesh``.
Point's depth is ignored.
See
:meth:`nhlib.geo.surface.base.BaseSurface.get_joyner_boore_distance`
for definition of this distance.
:returns:
numpy array of distances in km of the same shape as ``mesh``.
Distance value is considered to be zero if a point
lies inside the polygon enveloping the projection of the mesh
or on one of its edges.
"""
# we perform a hybrid calculation (geodetic mesh-to-mesh distance
# and distance on the projection plane for close points). first,
# we find the closest geodetic distance for each point of target
# mesh to this one. in general that distance is greater than
# the exact distance to enclosing polygon of this mesh and it
# depends on mesh spacing. but the difference can be neglected
# if calculated geodetic distance is over some threshold.
distances = geodetic.min_geodetic_distance(self.lons, self.lats,
mesh.lons, mesh.lats)
# here we find the points for which calculated mesh-to-mesh
# distance is below a threshold. this threshold is arbitrary:
# lower values increase the maximum possible error, higher
# values reduce the efficiency of that filtering. the maximum
# error is equal to the maximum difference between a distance
# from site to two adjacent points of the mesh and distance
# from site to the line connecting them. thus the error is
# a function of distance threshold and mesh spacing. the error
# is maximum when the site lies on a perpendicular to the line
# connecting points of the mesh and that passes the middle
# point between them. the error then can be calculated as
# ``err = trsh - d = trsh - \sqrt(trsh^2 - (ms/2)^2)``, where
# ``trsh`` and ``d`` are distance to mesh points (the one
# we found on the previous step) and distance to the line
# connecting them (the actual distance) and ``ms`` is mesh
# spacing. the threshold of 40 km gives maximum error of 314
# meters for meshes with spacing of 10 km and 5.36 km for
# meshes with spacing of 40 km. if mesh spacing is over
# ``(trsh / \sqrt(2)) * 2`` then points lying in the middle
# of mesh cells (that is inside the polygon) will be filtered
# out by the threshold and have positive distance instead of 0.
# so for threshold of 40 km mesh spacing should not be more
# than 56 km (typical values are 5 to 10 km).
[idxs] = (distances < 40).nonzero()
if not len(idxs):
# no point is close enough, return distances as they are
return distances
# for all the points that are closer than the threshold we need
# to recalculate the distance and set it to zero, if point falls
# inside the enclosing polygon of the mesh. for doing that we
# project both this mesh and the points of the second mesh--selected
# by distance threshold--to the same Cartesian space, define
# minimum shapely polygon enclosing the mesh and calculate point
# to polygon distance, which gives the most accurate value
# of distance in km (and that value is zero for points inside
# the polygon).
proj, polygon = self._get_proj_enclosing_polygon()
if not isinstance(polygon, shapely.geometry.Polygon):
# either line or point is our enclosing polygon. draw
# a square with side of 10 m around in order to have
# a proper polygon instead.
polygon = polygon.buffer(self.DIST_TOLERANCE, 1)
mesh_lons, mesh_lats = mesh.lons.take(idxs), mesh.lats.take(idxs)
mesh_xx, mesh_yy = proj(mesh_lons, mesh_lats)
distances_2d = geo_utils.point_to_polygon_distance(polygon,
mesh_xx, mesh_yy)
# replace geodetic distance values for points-closer-than-the-threshold
# by more accurate point-to-polygon distance values.
distances.put(idxs, distances_2d)
return distances
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):
"""
Compute and return Joyner-Boore distance to each point of ``mesh``.
Point's depth is ignored.
See
:meth:`nhlib.geo.surface.base.BaseSurface.get_joyner_boore_distance`
for definition of this distance.
:returns:
numpy array of distances in km of the same shape as ``mesh``.
Distance value is considered to be zero if a point
lies inside the polygon enveloping the projection of the mesh
or on one of its edges.
"""
# we perform a hybrid calculation (geodetic mesh-to-mesh distance
# and distance on the projection plane for close points). first,
# we find the closest geodetic distance for each point of target
# mesh to this one. in general that distance is greater than
# the exact distance to enclosing polygon of this mesh and it
# depends on mesh spacing. but the difference can be neglected
# if calculated geodetic distance is over some threshold.
distances = geodetic.min_geodetic_distance(self.lons, self.lats,
mesh.lons, mesh.lats)
# here we find the points for which calculated mesh-to-mesh
# distance is below a threshold. this threshold is arbitrary:
# lower values increase the maximum possible error, higher
# values reduce the efficiency of that filtering. the maximum
# error is equal to the maximum difference between a distance
# from site to two adjacent points of the mesh and distance
# from site to the line connecting them. thus the error is
# a function of distance threshold and mesh spacing. the error
# is maximum when the site lies on a perpendicular to the line
# connecting points of the mesh and that passes the middle
# point between them. the error then can be calculated as
# ``err = trsh - d = trsh - \sqrt(trsh^2 - (ms/2)^2)``, where
# ``trsh`` and ``d`` are distance to mesh points (the one
# we found on the previous step) and distance to the line
# connecting them (the actual distance) and ``ms`` is mesh
# spacing. the threshold of 40 km gives maximum error of 314
# meters for meshes with spacing of 10 km and 5.36 km for
# meshes with spacing of 40 km. if mesh spacing is over
# ``(trsh / \sqrt(2)) * 2`` then points lying in the middle
# of mesh cells (that is inside the polygon) will be filtered
# out by the threshold and have positive distance instead of 0.
# so for threshold of 40 km mesh spacing should not be more
# than 56 km (typical values are 5 to 10 km).
[idxs] = (distances < 40).nonzero()
if not len(idxs):
# no point is close enough, return distances as they are
return distances
# for all the points that are closer than the threshold we need
# to recalculate the distance and set it to zero, if point falls
# inside the enclosing polygon of the mesh. for doing that we
# project both this mesh and the points of the second mesh--selected
# by distance threshold--to the same Cartesian space, define
# minimum shapely polygon enclosing the mesh and calculate point
# to polygon distance, which gives the most accurate value
# of distance in km (and that value is zero for points inside
# the polygon).
proj, polygon = self._get_proj_enclosing_polygon()
if not isinstance(polygon, shapely.geometry.Polygon):
# either line or point is our enclosing polygon. draw
# a square with side of 10 m around in order to have
# a proper polygon instead.
polygon = polygon.buffer(self.DIST_TOLERANCE, 1)
mesh_lons, mesh_lats = mesh.lons.take(idxs), mesh.lats.take(idxs)
mesh_xx, mesh_yy = proj(mesh_lons, mesh_lats)
distances_2d = geo_utils.point_to_polygon_distance(
polygon, mesh_xx, mesh_yy)
# replace geodetic distance values for points-closer-than-the-threshold
# by more accurate point-to-polygon distance values.
distances.put(idxs, distances_2d)
return distances
