# Source code for openquake.hazardlib.geo.surface.planar

```
# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2017 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
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# 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 <http://www.gnu.org/licenses/>.
"""
Module :mod:`openquake.hazardlib.geo.surface.planar` contains
:class:`PlanarSurface`.
"""
import numpy
from openquake.baselib.node import Node
from openquake.hazardlib.geo import Point
from openquake.hazardlib.geo.surface.base import BaseQuadrilateralSurface
from openquake.hazardlib.geo.mesh import Mesh, RectangularMesh
from openquake.hazardlib.geo import geodetic
from openquake.hazardlib.geo.nodalplane import NodalPlane
from openquake.hazardlib.geo import utils as geo_utils
from openquake.baselib.slots import with_slots
def _corners(array):
# convert a composite array with fields lon, lat, depth into four Points
# [topleft, topright, bottomleft, bottomright]
points = []
for p in array:
points.append(Point(p['lon'], p['lat'], p['depth']))
return points
[docs]@with_slots
class PlanarSurface(BaseQuadrilateralSurface):
"""
Planar rectangular surface with two sides parallel to the Earth surface.
:param mesh_spacing:
The desired distance between two adjacent points in the surface mesh
in both horizontal and vertical directions, in km.
:param strike:
Strike of the surface is the azimuth from ``top_left`` to ``top_right``
points.
:param dip:
Dip is the angle between the surface itself and the earth surface.
Other parameters are points (instances of
:class:`~openquake.hazardlib.geo.point.Point`) defining the surface
corners in clockwise direction starting from top left corner. Top and
bottom edges of the polygon must be parallel to earth surface and to each
other.
See :class:`~openquake.hazardlib.geo.nodalplane.NodalPlane` for more
detailed definition of ``strike`` and ``dip``. Note that these parameters
are supposed to match the factual surface geometry (defined by corner
points), but this is not enforced or even checked.
:raises ValueError:
If either top or bottom points differ in depth or if top edge
is not parallel to the bottom edge, if top edge differs in length
from the bottom one, or if mesh spacing is not positive.
"""
#: Maximum difference in surface's rectangle side lengths, maximum offset
#: of a bottom right corner from a plane that contains other corners,
#: as well as maximum offset of a bottom left corner from a line drawn
#: downdip perpendicular to top edge from top left corner, expressed
#: as a fraction of the surface's area.
IMPERFECT_RECTANGLE_TOLERANCE = 0.002
_slots_ = ('mesh_spacing strike dip width length '
'corner_lons corner_lats corner_depths '
'normal d uv1 uv2 zero_zero').split()
@property
def surface_nodes(self):
"""
A single element list containing a planarSurface node
"""
node = Node('planarSurface')
for name, lon, lat, depth in zip(
'topLeft topRight bottomLeft bottomRight'.split(),
self.corner_lons, self.corner_lats, self.corner_depths):
node.append(Node(name, dict(lon=lon, lat=lat, depth=depth)))
return [node]
def __init__(self, mesh_spacing, strike, dip,
top_left, top_right, bottom_right, bottom_left):
super(PlanarSurface, self).__init__()
if not (top_left.depth == top_right.depth and
bottom_left.depth == bottom_right.depth):
raise ValueError("top and bottom edges must be parallel "
"to the earth surface")
if not mesh_spacing > 0:
raise ValueError("mesh spacing must be positive")
self.mesh_spacing = mesh_spacing
NodalPlane.check_dip(dip)
NodalPlane.check_strike(strike)
self.dip = dip
self.strike = strike
self.corner_lons = numpy.array([
top_left.longitude, top_right.longitude,
bottom_left.longitude, bottom_right.longitude
])
self.corner_lats = numpy.array([
top_left.latitude, top_right.latitude,
bottom_left.latitude, bottom_right.latitude
])
self.corner_depths = numpy.array([
top_left.depth, top_right.depth,
bottom_left.depth, bottom_right.depth
])
# now set the attributes normal, d, uv1, uv2, zero_zero
self._init_plane()
# now we can check surface for validity
dists, xx, yy = self._project(self.corner_lons, self.corner_lats,
self.corner_depths)
# "length" of the rupture is measured along the top edge
length1, length2 = xx[1] - xx[0], xx[3] - xx[2]
# "width" of the rupture is measured along downdip direction
width1, width2 = yy[2] - yy[0], yy[3] - yy[1]
self.width = (width1 + width2) / 2.0
self.length = (length1 + length2) / 2.0
# calculate the imperfect rectangle tolerance
# relative to surface's area
tolerance = (self.width * self.length *
self.IMPERFECT_RECTANGLE_TOLERANCE)
if numpy.max(numpy.abs(dists)) > tolerance:
raise ValueError("corner points do not lie on the same plane")
if length2 < 0:
raise ValueError("corners are in the wrong order")
if abs(length1 - length2) > tolerance:
raise ValueError("top and bottom edges have different lengths")
[docs] @classmethod
def from_corner_points(cls, mesh_spacing, top_left, top_right,
bottom_right, bottom_left):
"""
Create and return a planar surface from four corner points.
The azimuth of the line connecting the top left and the top right
corners define the surface strike, while the angle between the line
connecting the top left and bottom left corners and a line parallel
to the earth surface defines the surface dip.
:param mesh_spacing:
Distance between two subsequent points in the mesh representing
the planar surface, in km.
:param openquake.hazardlib.geo.point.Point top_left:
Upper left corner
:param openquake.hazardlib.geo.point.Point top_right:
Upper right corner
:param openquake.hazardlib.geo.point.Point bottom_right:
Lower right corner
:param openquake.hazardlib.geo.point.Point bottom_left:
Lower left corner
:returns:
An instance of :class:`PlanarSurface`.
"""
strike = top_left.azimuth(top_right)
dist = top_left.distance(bottom_left)
vert_dist = bottom_left.depth - top_left.depth
dip = numpy.degrees(numpy.arcsin(vert_dist / dist))
return cls(mesh_spacing, strike, dip, top_left, top_right,
bottom_right, bottom_left)
[docs] @classmethod
def from_array(cls, mesh_spacing, array):
"""
:param mesh_spacing: mesh spacing parameter
:param array: a composite array with fields (lon, lat, depth)
:returns: a :class:`PlanarSurface` instance
"""
tl, tr, bl, br = _corners(array)
strike = tl.azimuth(tr)
dip = numpy.degrees(
numpy.arcsin((bl.depth - tl.depth) / tl.distance(bl)))
return cls(mesh_spacing, strike, dip, tl, tr, br, bl)
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
[docs] def translate(self, p1, p2):
"""
Translate the surface for a specific distance along a specific azimuth
direction.
Parameters are two points (instances of
:class:`openquake.hazardlib.geo.point.Point`) representing the
direction and an azimuth for translation. The resulting surface corner
points will be that far along that azimuth from respective corner
points of this surface as ``p2`` is located with respect to ``p1``.
:returns:
A new :class:`PlanarSurface` object with the same mesh spacing,
dip, strike, width, length and depth but with corners longitudes
and latitudes translated.
"""
azimuth = geodetic.azimuth(p1.longitude, p1.latitude,
p2.longitude, p2.latitude)
distance = geodetic.geodetic_distance(p1.longitude, p1.latitude,
p2.longitude, p2.latitude)
# avoid calling PlanarSurface's constructor
nsurf = object.__new__(PlanarSurface)
# but do call BaseQuadrilateralSurface's one
BaseQuadrilateralSurface.__init__(nsurf)
nsurf.mesh_spacing = self.mesh_spacing
nsurf.dip = self.dip
nsurf.strike = self.strike
nsurf.corner_lons, nsurf.corner_lats = geodetic.point_at(
self.corner_lons, self.corner_lats, azimuth, distance
)
nsurf.corner_depths = self.corner_depths.copy()
nsurf._init_plane()
nsurf.width = self.width
nsurf.length = self.length
return nsurf
@property
def top_left(self):
return Point(self.corner_lons[0], self.corner_lats[0],
self.corner_depths[0])
@property
def top_right(self):
return Point(self.corner_lons[1], self.corner_lats[1],
self.corner_depths[1])
@property
def bottom_left(self):
return Point(self.corner_lons[2], self.corner_lats[2],
self.corner_depths[2])
@property
def bottom_right(self):
return Point(self.corner_lons[3], self.corner_lats[3],
self.corner_depths[3])
def _create_mesh(self):
"""
See
:meth:`openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface._create_mesh`.
"""
llons, llats, ldepths = geodetic.intervals_between(
self.top_left.longitude, self.top_left.latitude,
self.top_left.depth,
self.bottom_left.longitude, self.bottom_left.latitude,
self.bottom_left.depth,
self.mesh_spacing
)
rlons, rlats, rdepths = geodetic.intervals_between(
self.top_right.longitude, self.top_right.latitude,
self.top_right.depth,
self.bottom_right.longitude, self.bottom_right.latitude,
self.bottom_right.depth,
self.mesh_spacing
)
mlons, mlats, mdepths = [], [], []
for i in range(len(llons)):
lons, lats, depths = geodetic.intervals_between(
llons[i], llats[i], ldepths[i], rlons[i], rlats[i], rdepths[i],
self.mesh_spacing
)
mlons.append(lons)
mlats.append(lats)
mdepths.append(depths)
return RectangularMesh(numpy.array(mlons), numpy.array(mlats),
numpy.array(mdepths))
[docs] def get_strike(self):
"""
Return strike value that was provided to the constructor.
"""
return self.strike
[docs] def get_dip(self):
"""
Return dip value that was provided to the constructor.
"""
return self.dip
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 _project_back(self, dists, xx, yy):
"""
Convert coordinates in plane's Cartesian space back to spherical
coordinates.
Parameters are numpy arrays, as returned from :meth:`_project`, which
this method does the opposite to.
:return:
Tuple of longitudes, latitudes and depths numpy arrays.
"""
vectors = (self.zero_zero +
self.uv1 * xx.reshape(xx.shape + (1, )) +
self.uv2 * yy.reshape(yy.shape + (1, )) +
self.normal * dists.reshape(dists.shape + (1, )))
return geo_utils.cartesian_to_spherical(vectors)
[docs] def get_min_distance(self, mesh):
"""
See :meth:`superclass' method
<openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface.get_min_distance>`.
This is an optimized version specific to planar surface that doesn't
make use of the mesh.
"""
# we project all the points of the mesh on a plane that contains
# the surface (translating coordinates of the projections to a local
# 2d space) and at the same time calculate the distance to that
# plane.
dists, xx, yy = self._project(mesh.lons, mesh.lats, mesh.depths)
# the actual resulting distance is a square root of squares
# of a distance from a point to a plane that contains the surface
# and a distance from a projection of that point on that plane
# and a surface rectangle. we have former (``dists``), now we need
# to find latter.
#
# we process separately two coordinate components of the point
# projection. for abscissa we consider three possible cases:
#
# I . III . II
# . .
# 0-----+ → x axis direction
# | |
# +-----+
# . .
# . .
#
mxx = numpy.select(
condlist=[
# case "I": point on the left hand side from the rectangle
xx < 0,
# case "II": point is on the right hand side
xx > self.length
# default -- case "III": point is in between vertical sides
],
choicelist=[
# case "I": we need to consider distance between a point
# and a line containing left side of the rectangle
xx,
# case "II": considering a distance between a point and
# a line containing the right side
xx - self.length
],
# case "III": abscissa doesn't have an effect on a distance
# to the rectangle
default=0
)
# for ordinate we do the same operation (again three cases):
#
# I
# - - - 0---+ - - - ↓ y axis direction
# III | |
# - - - +---+ - - -
# II
#
myy = numpy.select(
condlist=[
# case "I": point is above the rectangle top edge
yy < 0,
# case "II": point is below the rectangle bottom edge
yy > self.width
# default -- case "III": point is in between lines containing
# top and bottom edges
],
choicelist=[
# case "I": considering a distance to a line containing
# a top edge
yy,
# case "II": considering a distance to a line containing
# a bottom edge
yy - self.width
],
# case "III": ordinate doesn't affect the distance
default=0
)
# distance between a point project and a rectangle combines from
# both components
dists2d_squares = mxx ** 2 + myy ** 2
# finding a resulting distance combining a distance on a plane
# with a distance to a plane
return numpy.sqrt(dists ** 2 + dists2d_squares)
[docs] def get_closest_points(self, mesh):
"""
See :meth:`superclass' method
<openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface.get_closest_points>`.
This is an optimized version specific to planar surface that doesn't
make use of the mesh.
"""
dists, xx, yy = self._project(mesh.lons, mesh.lats, mesh.depths)
mxx = xx.clip(0, self.length)
myy = yy.clip(0, self.width)
dists.fill(0)
lons, lats, depths = self._project_back(dists, mxx, myy)
return Mesh(lons, lats, depths)
def _get_top_edge_centroid(self):
"""
Overrides :meth:`superclass' method
<openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface._get_top_edge_centroid>`
in order to avoid creating a mesh.
"""
lon, lat = geo_utils.get_middle_point(
self.corner_lons[0], self.corner_lats[0],
self.corner_lons[1], self.corner_lats[1]
)
return Point(lon, lat, self.corner_depths[0])
[docs] def get_top_edge_depth(self):
"""
Overrides :meth:`superclass' method
<openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface.get_top_edge_depth>`
in order to avoid creating a mesh.
"""
return self.corner_depths[0]
[docs] def get_joyner_boore_distance(self, mesh):
"""
See :meth:`superclass' method
<openquake.hazardlib.geo.surface.base.BaseQuadrilateralSurface.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.flatten(), mesh.lats.flatten()
)
# 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)
jb_dists = 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
)
return jb_dists.reshape(mesh.lons.shape)
[docs] def get_rx_distance(self, mesh):
"""
See :meth:`superclass method
<.base.BaseQuadrilateralSurface.get_rx_distance>`
for spec of input and result values.
This is an optimized version specific to planar surface that doesn't
make use of the mesh.
"""
return geodetic.distance_to_arc(
self.corner_lons[0], self.corner_lats[0], self.strike, mesh.lons,
mesh.lats
)
[docs] def get_ry0_distance(self, mesh):
"""
:param mesh:
:class:`~openquake.hazardlib.geo.mesh.Mesh` of points to calculate
Ry0-distance to.
:returns:
Numpy array of distances in km.
See also :meth:`superclass method <.base.BaseSurface.get_ry0_distance>`
for spec of input and result values.
This is version specific to the planar surface doesn't make use of the
mesh
"""
dst1 = geodetic.distance_to_arc(self.top_left.longitude,
self.top_left.latitude,
(self.strike + 90.) % 360,
mesh.lons, mesh.lats)
dst2 = geodetic.distance_to_arc(self.top_right.longitude,
self.top_right.latitude,
(self.strike + 90.) % 360,
mesh.lons, mesh.lats)
# Find the points on the rupture
# Get the shortest distance from the two lines
idx = numpy.sign(dst1) == numpy.sign(dst2)
dst = numpy.zeros_like(dst1)
dst[idx] = numpy.fmin(numpy.abs(dst1[idx]), numpy.abs(dst2[idx]))
return dst
[docs] def get_width(self):
"""
Return surface's width value (in km) as computed in the constructor
(that is mean value of left and right surface sides).
"""
return self.width
[docs] def get_area(self):
"""
Return surface's area value (in squared km) obtained as the product
of surface lenght and width.
"""
return self.width * self.length
[docs] def get_bounding_box(self):
"""
Compute surface bounding box from plane's corners coordinates. Calls
:meth:`openquake.hazardlib.geo.utils.get_spherical_bounding_box`
: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.
"""
return geo_utils.get_spherical_bounding_box(self.corner_lons,
self.corner_lats)
[docs] def get_middle_point(self):
"""
Compute middle point from surface's corners coordinates. Calls
:meth:`openquake.hazardlib.geo.utils.get_middle_point`
"""
# compute middle point between upper left and bottom right corners
lon, lat = geo_utils.get_middle_point(self.corner_lons[0],
self.corner_lats[0],
self.corner_lons[3],
self.corner_lats[3])
depth = (self.corner_depths[0] + self.corner_depths[3]) / 2.
return Point(lon, lat, depth)
[docs] def get_surface_boundaries(self):
"""
The corners lons/lats in WKT-friendly order (clockwise)
"""
return [self.corner_lons.take([0, 1, 3, 2, 0])], \
[self.corner_lats.take([0, 1, 3, 2, 0])]
```