Source code for openquake.hazardlib.geo.utils

# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
# Copyright (C) 2012-2021 GEM Foundation
# OpenQuake is free software: you can redistribute it and/or modify it
# under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# OpenQuake is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# GNU Affero General Public License for more details.
# You should have received a copy of the GNU Affero General Public License
# along with OpenQuake. If not, see <>.

Module :mod:`openquake.hazardlib.geo.utils` contains functions that are common
to several geographical primitives and some other low-level spatial operations.
import math
import logging
import operator
import collections

import numpy
from scipy.spatial import cKDTree
import shapely.geometry

from openquake.baselib.hdf5 import vstr
from openquake.hazardlib.geo import geodetic

U32 = numpy.uint32
F32 = numpy.float32
KM_TO_DEGREES = 0.0089932  # 1 degree == 111 km
DEGREES_TO_RAD = 0.01745329252  # 1 radians = 57.295779513 degrees
spherical_to_cartesian = geodetic.spherical_to_cartesian
SphericalBB = collections.namedtuple('SphericalBB', 'west east north south')
MAX_EXTENT = 5000  # km, decided by M. Simionato
BASE32 = [ch.encode('ascii') for ch in '0123456789bcdefghjkmnpqrstuvwxyz']

[docs]class BBoxError(ValueError): """Bounding box too large"""
[docs]def angular_distance(km, lat=0, lat2=None): """ Return the angular distance of two points at the given latitude. >>> '%.3f' % angular_distance(100, lat=40) '1.174' >>> '%.3f' % angular_distance(100, lat=80) '5.179' """ if lat2 is not None: # use the largest latitude to compute the angular distance lat = max(abs(lat), abs(lat2)) return km * KM_TO_DEGREES / math.cos(lat * DEGREES_TO_RAD)
[docs]class SiteAssociationError(Exception): """Raised when there are no sites close enough"""
class _GeographicObjects(object): """ Store a collection of geographic objects, i.e. objects with lons, lats. It is possible to extract the closest object to a given location by calling the method .get_closest(lon, lat). """ def __init__(self, objects): self.objects = objects if hasattr(objects, 'lons'): lons = objects.lons lats = objects.lats depths = objects.depths elif isinstance(objects, numpy.ndarray): lons = objects['lon'] lats = objects['lat'] try: depths = objects['depth'] except ValueError: # no field of name depth depths = numpy.zeros_like(lons) self.kdtree = cKDTree(spherical_to_cartesian(lons, lats, depths)) def get_closest(self, lon, lat, depth=0): """ Get the closest object to the given longitude and latitude and its distance. :param lon: longitude in degrees :param lat: latitude in degrees :param depth: depth in km (default 0) :returns: (object, distance) """ xyz = spherical_to_cartesian(lon, lat, depth) min_dist, idx = self.kdtree.query(xyz) return self.objects[idx], min_dist def assoc(self, sitecol, assoc_dist, mode): """ :param sitecol: a (filtered) site collection :param assoc_dist: the maximum distance for association :param mode: 'strict', 'warn' or 'filter' :returns: filtered site collection, filtered objects, discarded """ assert mode in 'strict warn filter', mode dic = {} discarded = [] for sid, lon, lat in zip(sitecol.sids, sitecol.lons, sitecol.lats): obj, distance = self.get_closest(lon, lat) if assoc_dist is None: dic[sid] = obj # associate all elif distance <= assoc_dist: dic[sid] = obj # associate within elif mode == 'warn': dic[sid] = obj # associate outside logging.warning( 'The closest vs30 site (%.1f %.1f) is distant more than %d' ' km from site #%d (%.1f %.1f)', obj['lon'], obj['lat'], int(distance), sid, lon, lat) elif mode == 'filter': discarded.append(obj) elif mode == 'strict': raise SiteAssociationError( 'There is nothing closer than %s km ' 'to site (%s %s)' % (assoc_dist, lon, lat)) if not dic: raise SiteAssociationError( 'No sites could be associated within %s km' % assoc_dist) sids = sorted(dic) return (sitecol.filtered(sids), numpy.array([dic[s] for s in sids]), discarded) def assoc2(self, assets_by_site, assoc_dist, mode): """ Associated a list of assets by site to the site collection used to instantiate GeographicObjects. :param assets_by_sites: a list of lists of assets :param assoc_dist: the maximum distance for association :param mode: 'strict', 'warn' or 'filter' :returns: filtered site collection, filtered assets by site, discarded """ assert mode in 'strict filter', mode self.objects.filtered # self.objects must be a SiteCollection asset_dt = numpy.dtype( [('asset_ref', vstr), ('lon', F32), ('lat', F32)]) assets_by_sid = collections.defaultdict(list) discarded = [] for assets in assets_by_site: lon, lat = assets[0].location obj, distance = self.get_closest(lon, lat) if distance <= assoc_dist: # keep the assets, otherwise discard them assets_by_sid[obj['sids']].extend(assets) elif mode == 'strict': raise SiteAssociationError( 'There is nothing closer than %s km ' 'to site (%s %s)' % (assoc_dist, lon, lat)) else: discarded.extend(assets) sids = sorted(assets_by_sid) if not sids: raise SiteAssociationError( 'Could not associate any site to any assets within the ' 'asset_hazard_distance of %s km' % assoc_dist) assets_by_site = [ sorted(assets_by_sid[sid], key=operator.attrgetter('ordinal')) for sid in sids] data = [(asset.asset_id,) + asset.location for asset in discarded] discarded = numpy.array(data, asset_dt) return self.objects.filtered(sids), assets_by_site, discarded
[docs]def assoc(objects, sitecol, assoc_dist, mode): """ Associate geographic objects to a site collection. :param objects: something with .lons, .lats or ['lon'] ['lat'], or a list of lists of objects with a .location attribute (i.e. assets_by_site) :param assoc_dist: the maximum distance for association :param mode: if 'strict' fail if at least one site is not associated if 'error' fail if all sites are not associated :returns: (filtered site collection, filtered objects) """ if isinstance(objects, numpy.ndarray) or hasattr(objects, 'lons'): # objects is a geo array with lon, lat fields; used for ShakeMaps return _GeographicObjects(objects).assoc(sitecol, assoc_dist, mode) else: # objects is the list assets_by_site return _GeographicObjects(sitecol).assoc2( objects, assoc_dist, mode)
[docs]def clean_points(points): """ Given a list of :class:`~openquake.hazardlib.geo.point.Point` objects, return a new list with adjacent duplicate points removed. """ if not points: return points result = [points[0]] for point in points: if point != result[-1]: result.append(point) return result
[docs]def line_intersects_itself(lons, lats, closed_shape=False): """ Return ``True`` if line of points intersects itself. Line with the last point repeating the first one considered intersecting itself. The line is defined by lists (or numpy arrays) of points' longitudes and latitudes (depth is not taken into account). :param closed_shape: If ``True`` the line will be checked twice: first time with its original shape and second time with the points sequence being shifted by one point (the last point becomes first, the first turns second and so on). This is useful for checking that the sequence of points defines a valid :class:`~openquake.hazardlib.geo.polygon.Polygon`. """ assert len(lons) == len(lats) if len(lons) <= 3: # line can not intersect itself unless there are # at least four points return False west, east, north, south = get_spherical_bounding_box(lons, lats) proj = OrthographicProjection(west, east, north, south) xx, yy = proj(lons, lats) if not shapely.geometry.LineString(list(zip(xx, yy))).is_simple: return True if closed_shape: xx, yy = proj(numpy.roll(lons, 1), numpy.roll(lats, 1)) if not shapely.geometry.LineString(list(zip(xx, yy))).is_simple: return True return False
[docs]def get_longitudinal_extent(lon1, lon2): """ Return the distance between two longitude values as an angular measure. Parameters represent two longitude values in degrees. :return: Float, the angle between ``lon1`` and ``lon2`` in degrees. Value is positive if ``lon2`` is on the east from ``lon1`` and negative otherwise. Absolute value of the result doesn't exceed 180 for valid parameters values. """ return (lon2 - lon1 + 180) % 360 - 180
[docs]def check_extent(lons, lats, msg=''): """ :param lons: an array of longitudes (more than one) :param lats: an array of latitudes (more than one) :params msg: message to display in case of too large extent :returns: (dx, dy, dz) in km (rounded) """ l1 = len(lons) l2 = len(lats) if l1 < 2: raise ValueError('%s: not enough lons: %s' % (msg, lons)) elif l2 < 2: raise ValueError('%s: not enough lats: %s' % (msg, lats)) elif l1 != l2: raise ValueError('%s: wrong number of lons, lats: (%d, %d)' % (msg, l1, l2)) xs, ys, zs = spherical_to_cartesian(lons, lats).T # (N, 3) -> (3, N) dx = xs.max() - xs.min() dy = ys.max() - ys.min() dz = zs.max() - zs.min() # the goal is to forbid sources absurdely large due to wrong coordinates if dx > MAX_EXTENT or dy > MAX_EXTENT or dz > MAX_EXTENT: raise ValueError('%s: too large: %d km' % (msg, max(dx, dy, dz))) return int(dx), int(dy), int(dz)
[docs]def get_bounding_box(obj, maxdist): """ Return the dilated bounding box of a geometric object. :param obj: an object with method .get_bounding_box, or with an attribute .polygon or a list of locations :param maxdist: maximum distance in km """ if hasattr(obj, 'get_bounding_box'): return obj.get_bounding_box(maxdist) elif hasattr(obj, 'polygon'): bbox = obj.polygon.get_bbox() else: if isinstance(obj, list): # a list of locations lons = numpy.array([loc.longitude for loc in obj]) lats = numpy.array([loc.latitude for loc in obj]) else: # assume an array with fields lon, lat lons, lats = obj['lon'], obj['lat'] min_lon, max_lon = lons.min(), lons.max() if cross_idl(min_lon, max_lon): lons %= 360 bbox = lons.min(), lats.min(), lons.max(), lats.max() a1 = min(maxdist * KM_TO_DEGREES, 90) a2 = angular_distance(maxdist, bbox[1], bbox[3]) delta = bbox[2] - bbox[0] + 2 * a2 if delta > 180: raise BBoxError('The buffer of %d km is too large, the bounding ' 'box is larger than half the globe: %d degrees' % (maxdist, delta)) return bbox[0] - a2, bbox[1] - a1, bbox[2] + a2, bbox[3] + a1
[docs]def get_spherical_bounding_box(lons, lats): """ Given a collection of points find and return the bounding box, as a pair of longitudes and a pair of latitudes. Parameters define longitudes and latitudes of a point collection respectively in a form of lists or numpy arrays. :return: A tuple of four items. These items represent western, eastern, northern and southern borders of the bounding box respectively. Values are floats in decimal degrees. :raises ValueError: If points collection has the longitudinal extent of more than 180 degrees (it is impossible to define a single hemisphere bound to poles that would contain the whole collection). """ ok = numpy.isfinite(lons) if not ok.all(): lons = lons[ok] lats = lats[ok] north, south = numpy.max(lats), numpy.min(lats) west, east = numpy.min(lons), numpy.max(lons) assert (-180 <= west <= 180) and (-180 <= east <= 180), (west, east) if get_longitudinal_extent(west, east) < 0: # points are lying on both sides of the international date line # (meridian 180). the actual west longitude is the lowest positive # longitude and east one is the highest negative. if hasattr(lons, 'flatten'): # fixes test_surface_crossing_international_date_line lons = lons.flatten() west = min(lon for lon in lons if lon > 0) east = max(lon for lon in lons if lon < 0) if not all((get_longitudinal_extent(west, lon) >= 0 and get_longitudinal_extent(lon, east) >= 0) for lon in lons): raise ValueError('points collection has longitudinal extent ' 'wider than 180 deg') return SphericalBB(west, east, north, south)
[docs]class OrthographicProjection(object): """ Callable OrthographicProjection object that can perform both forward and reverse projection (converting from longitudes and latitudes to x and y values on 2d-space and vice versa). The call takes three arguments: first two are numpy arrays of longitudes and latitudes *or* abscissae and ordinates of points to project and the third one is a boolean that allows to choose what operation is requested -- is it forward or reverse one. ``True`` value given to third positional argument (or keyword argument "reverse") indicates that the projection of points in 2d space back to earth surface is needed. The default value for "reverse" argument is ``False``, which means forward projection (degrees to kilometers). Raises ``ValueError`` in forward projection mode if any of the target points is further than 90 degree (along the great circle arc) from the projection center. Parameters are given as floats, representing decimal degrees (first two are longitudes and last two are latitudes). They define a bounding box in a spherical coordinates of the collection of points that is about to be projected. The center point of the projection (coordinates (0, 0) in Cartesian space) is set to the middle point of that bounding box. The resulting projection is defined for spherical coordinates that are not further from the bounding box center than 90 degree on the great circle arc. The result projection is of type `Orthographic <>`_. This projection is prone to distance, area and angle distortions everywhere outside of the center point, but still can be used for checking shapes: verifying if line intersects itself (like in :func:`line_intersects_itself`) or if point is inside of a polygon (like in :meth:`openquake.hazardlib.geo.polygon.Polygon.discretize`). It can be also used for measuring distance to an extent of around 700 kilometers (error doesn't exceed 1 km up until then). """
[docs] @classmethod def from_lons_lats(cls, lons, lats): return cls(*get_spherical_bounding_box(lons, lats))
def __init__(self, west, east, north, south): self.west = west self.east = east self.north = north self.south = south self.lambda0, self.phi0 = numpy.radians( get_middle_point(west, north, east, south)) self.cos_phi0 = numpy.cos(self.phi0) self.sin_phi0 = numpy.sin(self.phi0) self.sin_pi_over_4 = (2 ** 0.5) / 2 def __call__(self, lons, lats, reverse=False): if not reverse: lambdas, phis = numpy.radians(lons), numpy.radians(lats) cos_phis = numpy.cos(phis) lambdas -= self.lambda0 # calculate the sine of the distance between projection center # and each of the points to project sin_dist = numpy.sqrt( numpy.sin((self.phi0 - phis) / 2.0) ** 2.0 + self.cos_phi0 * cos_phis * numpy.sin(lambdas / 2.0) ** 2.0 ) if (sin_dist > self.sin_pi_over_4).any(): raise ValueError('some points are too far from the projection ' 'center lon=%s lat=%s' % (numpy.degrees(self.lambda0), numpy.degrees(self.phi0))) xx = numpy.cos(phis) * numpy.sin(lambdas) yy = (self.cos_phi0 * numpy.sin(phis) - self.sin_phi0 * cos_phis * numpy.cos(lambdas)) return xx * EARTH_RADIUS, yy * EARTH_RADIUS else: # "reverse" mode, arguments are actually abscissae # and ordinates in 2d space xx, yy = lons / EARTH_RADIUS, lats / EARTH_RADIUS cos_c = numpy.sqrt(1 - (xx ** 2 + yy ** 2)) phis = numpy.arcsin(cos_c * self.sin_phi0 + yy * self.cos_phi0) lambdas = numpy.arctan2( xx, self.cos_phi0 * cos_c - yy * self.sin_phi0) xx = numpy.degrees(self.lambda0 + lambdas) yy = numpy.degrees(phis) # shift longitudes greater than 180 back into the western # hemisphere, that is in range [0, -180], and longitudes # smaller than -180, to the heastern emisphere [0, 180] idx = xx >= 180. xx[idx] = xx[idx] - 360. idx = xx <= -180. xx[idx] = xx[idx] + 360. return xx, yy
[docs]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)
[docs]def cartesian_to_spherical(vectors): """ Return the spherical coordinates for coordinates in Cartesian space. This function does an opposite to :func:`spherical_to_cartesian`. :param vectors: Array of 3d vectors in Cartesian space of shape (..., 3) :returns: Tuple of three arrays of the same shape as ``vectors`` representing longitude (decimal degrees), latitude (decimal degrees) and depth (km) in specified order. """ rr = numpy.sqrt(numpy.sum(vectors * vectors, axis=-1)) xx, yy, zz = vectors.T lats = numpy.degrees(numpy.arcsin((zz / rr).clip(-1., 1.))) lons = numpy.degrees(numpy.arctan2(yy, xx)) depths = EARTH_RADIUS - rr return lons.T, lats.T, depths
[docs]def triangle_area(e1, e2, e3): """ Get the area of triangle formed by three vectors. Parameters are three three-dimensional numpy arrays representing vectors of triangle's edges in Cartesian space. :returns: Float number, the area of the triangle in squared units of coordinates, or numpy array of shape of edges with one dimension less. Uses Heron formula, see """ # calculating edges length e1_length = numpy.sqrt(numpy.sum(e1 * e1, axis=-1)) e2_length = numpy.sqrt(numpy.sum(e2 * e2, axis=-1)) e3_length = numpy.sqrt(numpy.sum(e3 * e3, axis=-1)) # calculating half perimeter s = (e1_length + e2_length + e3_length) / 2.0 # applying Heron's formula return numpy.sqrt(s * (s - e1_length) * (s - e2_length) * (s - e3_length))
[docs]def normalized(vector): """ Get unit vector for a given one. :param vector: Numpy vector as coordinates in Cartesian space, or an array of such. :returns: Numpy array of the same shape and structure where all vectors are normalized. That is, each coordinate component is divided by its vector's length. """ length = numpy.sum(vector * vector, axis=-1) length = numpy.sqrt(length.reshape(length.shape + (1, ))) return vector / length
[docs]def point_to_polygon_distance(polygon, pxx, pyy): """ Calculate the distance to polygon for each point of the collection on the 2d Cartesian plane. :param polygon: Shapely "Polygon" geometry object. :param pxx: List or numpy array of abscissae values of points to calculate the distance from. :param pyy: Same structure as ``pxx``, but with ordinate values. :returns: Numpy array of distances in units of coordinate system. Points that lie inside the polygon have zero distance. """ pxx = numpy.array(pxx) pyy = numpy.array(pyy) assert pxx.shape == pyy.shape if pxx.ndim == 0: pxx = pxx.reshape((1, )) pyy = pyy.reshape((1, )) result = numpy.array([ polygon.distance(shapely.geometry.Point(pxx.item(i), pyy.item(i))) for i in range(pxx.size) ]) return result.reshape(pxx.shape)
[docs]def fix_lon(lon): """ :returns: a valid longitude in the range -180 <= lon < 180 >>> fix_lon(11) 11 >>> fix_lon(181) -179 >>> fix_lon(-182) 178 """ return (lon + 180) % 360 - 180
[docs]def cross_idl(lon1, lon2, *lons): """ Return True if two longitude values define line crossing international date line. >>> cross_idl(-45, 45) False >>> cross_idl(-180, -179) False >>> cross_idl(180, 179) False >>> cross_idl(45, -45) False >>> cross_idl(0, 0) False >>> cross_idl(-170, 170) True >>> cross_idl(170, -170) True >>> cross_idl(-180, 180) True """ lons = (lon1, lon2) + lons l1, l2 = min(lons), max(lons) # a line crosses the international date line if the end positions # have different sign and they are more than 180 degrees longitude apart return l1 * l2 < 0 and abs(l1 - l2) > 180
[docs]def plane_fit(points): """ This fits an n-dimensional plane to a set of points. See :parameter points: An instance of :class:~numpy.ndarray. The number of columns must be equal to three. :return: A point on the plane and the normal to the plane. """ points = numpy.transpose(points) points = numpy.reshape(points, (numpy.shape(points)[0], -1)) assert points.shape[0] < points.shape[1], points.shape ctr = points.mean(axis=1) x = points - ctr[:, None] M =, x.T) return ctr, numpy.linalg.svd(M)[0][:, -1]
[docs]def bbox2poly(bbox): """ :param bbox: a geographic bounding box West-East-North-South :returns: a list of pairs corrisponding to the bbox polygon """ x1, x2, y2, y1 = bbox # west, east, north, south return (x1, y1), (x2, y1), (x2, y2), (x1, y2), (x1, y1)
# geohash code adapted from Leonard Norrgard's implementation # # see also # length 6 = .61 km resolution, length 5 = 2.4 km resolution, # length 4 = 20 km, length 3 = 78 km # it may turn useful in the future (with SiteCollection.geohash)
[docs]def geohash(lon, lat, length): """ Encode a position given in lon, lat into a geohash of the given lenght >>> geohash(lon=10, lat=45, length=5) b'spzpg' """ lat_interval, lon_interval = (-90.0, 90.0), (-180.0, 180.0) chars = b'' bits = [16, 8, 4, 2, 1] bit = 0 ch = 0 even = True while len(chars) < length: if even: mid = (lon_interval[0] + lon_interval[1]) / 2 if lon > mid: ch |= bits[bit] lon_interval = (mid, lon_interval[1]) else: lon_interval = (lon_interval[0], mid) else: mid = (lat_interval[0] + lat_interval[1]) / 2 if lat > mid: ch |= bits[bit] lat_interval = (mid, lat_interval[1]) else: lat_interval = (lat_interval[0], mid) even = not even if bit < 4: bit += 1 else: chars += BASE32[ch] bit = 0 ch = 0 return chars