Source code for openquake.hazardlib.geo.polygon

# -*- coding: utf-8 -*-
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Module :mod:`openquake.hazardlib.geo.polygon` defines :class:`Polygon`.
import numpy
import shapely.geometry
import shapely.wkt

from openquake.hazardlib.geo.mesh import Mesh
from openquake.hazardlib.geo import geodetic
from openquake.hazardlib.geo import utils

#: Polygon upsampling step for long edges, in kilometers.
#: See :func:`get_resampled_coordinates`.

[docs]class Polygon(object): """ Polygon objects represent an area on the Earth surface. :param points: The list of :class:`~openquake.hazardlib.geo.point.Point` objects defining the polygon vertices. The points are connected by great circle arcs in order of appearance. Polygon segment should not cross another polygon segment. At least three points must be defined. :raises ValueError: If ``points`` contains less than three unique points or if polygon perimeter intersects itself. """ _bbox = None def __init__(self, points): points = utils.clean_points(points) if len(points) < 3: raise ValueError('polygon must have at least 3 unique vertices') self.lons = numpy.array([float(point.longitude) for point in points]) self.lats = numpy.array([float(point.latitude) for point in points]) if utils.line_intersects_itself(self.lons, self.lats, closed_shape=1): raise ValueError('polygon perimeter intersects itself') self._projection = None self._polygon2d = None @property def coords(self): """ Coordinates of the polygon as a linear ring, rounded to 5 digits """ lons = numpy.round(self.lons, 5) lats = numpy.round(self.lats, 5) pairs = list(zip(lons, lats)) return pairs + [pairs[0]] @property def wkt(self): """ Generate WKT (Well-Known Text) to represent this polygon. """ pairs = ['%.5f %.5f' % (lon, lat) for lon, lat in zip(self.lons, self.lats)] # the polygon must form a closed loop; first and last coord pairs # are the same pairs.append(pairs[0]) return 'POLYGON((%s))' % ', '.join(pairs)
[docs] @classmethod def from_wkt(cls, wkt_string): """ Create a polygon object from a WKT (Well-Known Text) string. :param wkt_string: A standard WKT polygon string. :returns: New :class:`Polygon` object. """ # Avoid calling class' constructor polygon = object.__new__(cls) # Read WKT polygon and extract coordinates wkt_poly = shapely.wkt.loads(wkt_string) xx, yy = numpy.transpose(wkt_poly.exterior.coords) # Inflate polygon object polygon.lons = xx[:-1] polygon.lats = yy[:-1] polygon._projection = None polygon._polygon2d = None return polygon
@classmethod def _from_2d(cls, polygon2d, proj): """ Create a polygon object from a 2d polygon and a projection. :param polygon2d: Instance of ``shapely.geometry.Polygon``. :param proj: Projection object created by :class:`~openquake.hazardlib.geo.utils.OrthographicProjection` that was used to project ``polygon2d``. That projection will be used for projecting it back to get spherical coordinates from Cartesian ones. :returns: New :class:`Polygon` object. Note that spherical coordinates of that polygon do not get upsampled even for longer edges. """ # avoid calling class' constructor polygon = object.__new__(cls) # project polygon2d back on the sphere # NOTE(LB): We use 'exterior' here in case the `polygon2d` has # interiors (holes) defined. In our use cases, we don't care about # polygon interiors, so we simply discard these exteriors. xx, yy = numpy.transpose(polygon2d.exterior.coords) # need to cut off the last point -- it repeats the first one polygon.lons, polygon.lats = proj(xx[:-1], yy[:-1], reverse=True) # initialize the instance (as constructor would do) polygon._bbox = utils.get_spherical_bounding_box( polygon.lons, polygon.lats) polygon._polygon2d = polygon2d polygon._projection = proj return polygon
[docs] def get_bbox(self): """ Returns a simple 2D bounding box from the extrema of lons and lats """ min_lon, max_lon = self.lons.min(), self.lons.max() if utils.cross_idl(min_lon, max_lon): lons = self.lons % 360 min_lon, max_lon = lons.min(), lons.max() return (min_lon, self.lats.min(), max_lon, self.lats.max())
def _init_polygon2d(self): """ Spherical bounding box, projection, and Cartesian polygon are all cached to prevent redundant computations. If any of them are `None`, recalculate all of them. """ if (self._polygon2d is None or self._projection is None or self._bbox is None): # resample polygon line segments: lons, lats = get_resampled_coordinates(self.lons, self.lats) # find the bounding box of a polygon in spherical coordinates: self._bbox = utils.get_spherical_bounding_box(lons, lats) # create a projection that is centered in a polygon center: self._projection = utils.OrthographicProjection(*self._bbox) # project polygon vertices to the Cartesian space and create # a shapely polygon object: xx, yy = self._projection(lons, lats) self._polygon2d = shapely.geometry.Polygon(list(zip(xx, yy)))
[docs] def dilate(self, dilation): """ Extend the polygon to a specified buffer distance. .. note:: In extreme cases where dilation of a polygon creates holes, thus resulting in a multi-polygon, we discard the holes and simply return the 'exterior' of the shape. :param dilation: Distance in km to extend polygon borders to. :returns: New :class:`Polygon` object with (in general) more vertices and border that is approximately ``dilation`` km far (measured perpendicularly to edges and circularly to vertices) from the border of original polygon. """ assert dilation > 0, dilation self._init_polygon2d() newpoly2d = self._polygon2d.buffer(dilation) return self.__class__._from_2d(newpoly2d, self._projection)
[docs] def intersects(self, mesh): """ Check for intersection with each point of the ``mesh``. Mesh coordinate values are in decimal degrees. :param mesh: :class:`openquake.hazardlib.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
[docs] def discretize(self, mesh_spacing): """ Get a mesh of uniformly spaced points inside the polygon area with distance of ``mesh_spacing`` km between. :returns: An instance of :class:`~openquake.hazardlib.geo.mesh.Mesh` that holds the points data. Mesh is created with no depth information (all the points are on the Earth surface). """ self._init_polygon2d() west, east, north, south = self._bbox lons, lats = [], [] # we cover the bounding box (in spherical coordinates) from highest # to lowest latitude and from left to right by longitude. we step # by mesh spacing distance (linear measure). we check each point # if it is inside the polygon and yield the point object, if so. # this way we produce an uniformly-spaced mesh regardless of the # latitude. latitude = north while latitude > south: longitude = west while utils.get_longitudinal_extent(longitude, east) > 0: # we use Cartesian space just for checking if a point # is inside of the polygon. x, y = self._projection(longitude, latitude) if self._polygon2d.contains(shapely.geometry.Point(x, y)): lons.append(longitude) lats.append(latitude) # move by mesh spacing along parallel... longitude, _, = geodetic.point_at(longitude, latitude, 90, mesh_spacing) # ... and by the same distance along meridian in outer one _, latitude = geodetic.point_at(west, latitude, 180, mesh_spacing) return Mesh(numpy.array(lons), numpy.array(lats), depths=None)
[docs]def get_resampled_coordinates(lons, lats): """ Resample polygon line segments and return the coordinates of the new vertices. This limits distortions when projecting a polygon onto a spherical surface. Parameters define longitudes and latitudes of a point collection in the form of lists or numpy arrays. :return: A tuple of two numpy arrays: longitudes and latitudes of resampled vertices. """ num_coords = len(lons) assert num_coords == len(lats) lons1 = numpy.array(lons) lats1 = numpy.array(lats) lons2 = numpy.concatenate((lons1[1:], lons1[:1])) lats2 = numpy.concatenate((lats1[1:], lats1[:1])) distances = geodetic.geodetic_distance(lons1, lats1, lons2, lats2) resampled_lons = [lons[0]] resampled_lats = [lats[0]] for i in range(num_coords): next_point = (i + 1) % num_coords lon1, lat1 = lons[i], lats[i] lon2, lat2 = lons[next_point], lats[next_point] distance = distances[i] num_points = int(distance / UPSAMPLING_STEP_KM) + 1 if num_points >= 2: # We need to increase the resolution of this arc by adding new # points. new_lons, new_lats, _ = geodetic.npoints_between( lon1, lat1, 0, lon2, lat2, 0, num_points) resampled_lons.extend(new_lons[1:]) resampled_lats.extend(new_lats[1:]) else: resampled_lons.append(lon2) resampled_lats.append(lat2) # NB: we cut off the last point because it repeats the first one return numpy.array(resampled_lons[:-1]), numpy.array(resampled_lats[:-1])