def triangulate(self):
"""
Convert mesh points to vectors in Cartesian space.
:returns:
Tuple of four elements, each being 2d numpy array of 3d vectors
(the same structure and shape as the mesh itself). Those arrays
are:
#. points vectors,
#. vectors directed from each point (excluding the last column)
to the next one in a same row →,
#. vectors directed from each point (excluding the first row)
to the previous one in a same column ↑,
#. vectors pointing from a bottom left point of each mesh cell
to top right one ↗.
So the last three arrays of vectors allow to construct triangles
covering the whole mesh.
"""
points = geo_utils.spherical_to_cartesian(self.lons, self.lats,
self.depths)
# triangulate the mesh by defining vectors of triangles edges:
# →
along_azimuth = points[:, 1:] - points[:, :-1]
# ↑
updip = points[:-1] - points[1:]
# ↗
diag = points[:-1, 1:] - points[1:, :-1]
return points, along_azimuth, updip, diag
def _polygon_wkt_to_xyz(polygon, as_wkt=False):
'''Converts a polygon in 'POLYGON' wkt format to xyz. If as_wkt is
True, will return the xyz output back as a wkt format, otherwise
it will return an array'''
polygon = wkt.loads(polygon)
polygon = polygon.boundary.xy
number_nodes = len(polygon[0])
xyz = spherical_to_cartesian(polygon[0], polygon[1],
np.zeros(number_nodes, dtype=float))
if as_wkt:
xyz = asPolygon(xyz[:, :-1]).wkt
return xyz
def __init__(self, catalogue):
'''Instantiate
:param catalogue:
Instance of MTKCatalogue Class
'''
self.catalogue = deepcopy(catalogue)
self.time_value = decimal_time(catalogue['year'],
catalogue['month'],
catalogue['day'],
catalogue['hour'],
catalogue['minute'],
catalogue['second'])
self.catalogue_mesh = Mesh(catalogue['longitude'],
catalogue['latitude'],
catalogue['depth'])
if not isinstance(catalogue['xyz'], np.ndarray):
self.catalogue['xyz'] = spherical_to_cartesian(
self.catalogue['longitude'],
self.catalogue['latitude'],
self.catalogue['depth'])
self.number_events = len(catalogue['eventID'])
def _init_plane(self):
"""
Prepare everything needed for projecting arbitrary points on a plane
containing the surface.
"""
tl, tr, bl, br = geo_utils.spherical_to_cartesian(
self.corner_lons, self.corner_lats, self.corner_depths
)
# these two parameters define the plane that contains the surface
# (in 3d Cartesian space): a normal unit vector,
self.normal = geo_utils.normalized(numpy.cross(tl - tr, tl - bl))
# ... and scalar "d" parameter from the plane equation (uses
# an equation (3) from http://mathworld.wolfram.com/Plane.html)
self.d = - (self.normal * tl).sum()
# these two 3d vectors together with a zero point represent surface's
# coordinate space (the way to translate 3d Cartesian space with
# a center in earth's center to 2d space centered in surface's top
# left corner with basis vectors directed to top right and bottom left
# corners. see :meth:`_project`.
self.uv1 = geo_utils.normalized(tr - tl)
self.uv2 = numpy.cross(self.normal, self.uv1)
self.zero_zero = tl
def select_within_polygon(self, polygon, distance=None, **kwargs):
'''Select earthquakes within polygon
:param point:
Centre point as instance of nhlib.geo.polygon.Polygon class
:param distance:
Buffer distance (km) (can take negative values)
:returns:
Selected catalogue (as dictionary) and number of selected events
'''
if distance:
zone_polygon = polygon.dilate(distance)
else:
zone_polygon = polygon
zone_polygon = spherical_to_cartesian(
zone_polygon.lons,
zone_polygon.lats,
np.zeros(len(zone_polygon.lons), dtype=float))
# Initially all points are invalid
valid_id = np.zeros(self.number_events, dtype=bool)
# Make valid all events inside depth range
upper_depth, lower_depth = _check_depth_limits(kwargs)
valid_depth = np.logical_and(self.catalogue['depth'] >= upper_depth,
self.catalogue['depth'] < lower_depth)
# Events outside polygon returned to invalid assignment
valid_id[valid_depth] = points_inside_poly(
self.catalogue['xyz'][valid_depth, :2],
zone_polygon[:, :2])
number_selected = np.sum(valid_id)
valid_id = np.logical_not(valid_id)
return purge_catalogue(self.catalogue, valid_id.astype(int)), \
number_selected
def _project(self, lons, lats, depths):
"""
Project points to a surface's plane.
Parameters are lists or numpy arrays of coordinates of points
to project.
:returns:
A tuple of three items: distances between original points
and surface's plane in km, "x" and "y" coordinates of points'
projections to the plane (in a surface's coordinate space).
"""
points = geo_utils.spherical_to_cartesian(lons, lats, depths)
# uses method from http://www.9math.com/book/projection-point-plane
dists = (self.normal * points).sum(axis=-1) + self.d
t0 = - dists
projs = points + self.normal * t0.reshape(t0.shape + (1, ))
# translate projected points' to surface's coordinate space
vectors2d = projs - self.zero_zero
xx = (vectors2d * self.uv1).sum(axis=-1)
yy = (vectors2d * self.uv2).sum(axis=-1)
return dists, xx, yy
def test_from_vector(self):
point = geo.Point(12.34, -56.78, 91.011)
vector = spherical_to_cartesian(point.longitude, point.latitude,
point.depth)
self.assertEqual(point, geo.Point.from_vector(vector))
def _hypocentres_to_xyz(self):
'''Converts the catalogue hypocentres into a cartesian coordinate
system'''
self.data['xyz'] = spherical_to_cartesian(
self.data['longitude'], self.data['latitude'],
self.data['depth'])
