def test_nonconvex_polygon(self):
coords = [(0, 0), (0, 3), (2, 2), (1, 2), (1, 1), (1, 0), (0, 0)]
for polygon_coords in (coords, list(reversed(coords))):
polygon = shapely.geometry.Polygon(polygon_coords)
pxx = numpy.array([0.5, 0.5, 0.5, 0.5, 0.5])
pyy = numpy.array([0.0, 0.5, 1.0, 2.0, 2.5])
dist = utils.point_to_polygon_distance(polygon, pxx, pyy)
numpy.testing.assert_equal(dist, 0)
pxx = numpy.array([1.5, 3.0, -2.0])
pyy = numpy.array([1.5, 2.0, 2.0])
dist = utils.point_to_polygon_distance(polygon, pxx, pyy)
numpy.testing.assert_almost_equal(dist, [0.5, 1, 2])
def intersects(self, mesh):
"""
Check for intersection with each point of the ``mesh``.
Mesh coordinate values are in decimal degrees.
:param mesh:
:class:`nhlib.geo.mesh.Mesh` instance.
:returns:
Numpy array of `bool` values in the same shapes in the input
coordinate arrays with ``True`` on indexes of points that
lie inside the polygon or on one of its edges and ``False``
for points that neither lie inside nor touch the boundary.
"""
self._init_polygon2d()
pxx, pyy = self._projection(mesh.lons, mesh.lats)
return utils.point_to_polygon_distance(self._polygon2d, pxx, pyy) == 0
def test_2d_array_of_points(self):
pxx = [[-1., 0.3], [-0.25, 0.5]]
pyy = [[2., 1.1], [3.9, -0.3]]
dist = utils.point_to_polygon_distance(self.polygon, pxx, pyy)
numpy.testing.assert_almost_equal(dist,
[[1.4142135, 0.1], [2.9107559, 0.3]])
def test_list_of_points(self):
pxx = [-1., 0.3, -0.25]
pyy = [2., 1.1, 3.9]
dist = utils.point_to_polygon_distance(self.polygon, pxx, pyy)
numpy.testing.assert_almost_equal(dist, [1.4142135, 0.1, 2.9107559])
def test_one_point(self):
dist = utils.point_to_polygon_distance(self.polygon, 0.5, 0.5)
self.assertEqual(dist, 0)
dist = utils.point_to_polygon_distance(self.polygon, 0.5, 1.5)
self.assertAlmostEqual(dist, 0.5)
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 test_2d_array_of_points(self):
pxx = [[-1., 0.3], [-0.25, 0.5]]
pyy = [[2., 1.1], [3.9, -0.3]]
dist = utils.point_to_polygon_distance(self.polygon, pxx, pyy)
numpy.testing.assert_almost_equal(dist, [[1.4142135, 0.1],
[2.9107559, 0.3]])
def test_list_of_points(self):
pxx = [-1., 0.3, -0.25]
pyy = [2., 1.1, 3.9]
dist = utils.point_to_polygon_distance(self.polygon, pxx, pyy)
numpy.testing.assert_almost_equal(dist, [1.4142135, 0.1, 2.9107559])
def test_one_point(self):
dist = utils.point_to_polygon_distance(self.polygon, 0.5, 0.5)
self.assertEqual(dist, 0)
dist = utils.point_to_polygon_distance(self.polygon, 0.5, 1.5)
self.assertAlmostEqual(dist, 0.5)
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