# -*- coding: utf-8 -*-
# vim: tabstop=4 shiftwidth=4 softtabstop=4
#
# Copyright (C) 2012-2018 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.line` defines :class:`Line`.
"""
import numpy
from openquake.hazardlib.geo import geodetic
from openquake.hazardlib.geo import utils
[docs]class Line(object):
"""
This class represents a geographical line, which is basically
a sequence of geographical points.
A line is defined by at least one point.
:param points:
The sequence of points defining this line.
:type points:
list of :class:`~openquake.hazardlib.geo.point.Point` instances
"""
def __init__(self, points):
self.points = utils.clean_points(points)
if len(self.points) < 1:
raise ValueError("One point needed to create a line!")
def __eq__(self, other):
"""
>>> from openquake.hazardlib.geo.point import Point
>>> points = [Point(1, 2), Point(3, 4)]; Line(points) == Line(points)
True
>>> Line(points) == Line(list(reversed(points)))
False
"""
return self.points == other.points
def __ne__(self, other):
"""
>>> from openquake.hazardlib.geo.point import Point
>>> Line([Point(1, 2)]) != Line([Point(1, 2)])
False
>>> Line([Point(1, 2)]) != Line([Point(2, 1)])
True
"""
return not self.__eq__(other)
def __len__(self):
return len(self.points)
def __getitem__(self, key):
return self.points.__getitem__(key)
[docs] def on_surface(self):
"""
Check if this line is defined on the surface (i.e. all points
are on the surfance, depth=0.0).
:returns bool:
True if this line is on the surface, false otherwise.
"""
return all(point.on_surface() for point in self.points)
[docs] def horizontal(self):
"""
Check if this line is horizontal (i.e. all depths of points
are equal).
:returns bool:
True if this line is horizontal, false otherwise.
"""
return all(p.depth == self[0].depth for p in self)
[docs] def average_azimuth(self):
"""
Calculate and return weighted average azimuth of all line's segments
in decimal degrees.
Uses formula from
http://en.wikipedia.org/wiki/Mean_of_circular_quantities
>>> from openquake.hazardlib.geo.point import Point as P
>>> '%.1f' % Line([P(0, 0), P(1e-5, 1e-5)]).average_azimuth()
'45.0'
>>> '%.1f' % Line([P(0, 0), P(0, 1e-5), P(1e-5, 1e-5)]).average_azimuth()
'45.0'
>>> line = Line([P(0, 0), P(-2e-5, 0), P(-2e-5, 1.154e-5)])
>>> '%.1f' % line.average_azimuth()
'300.0'
"""
if len(self.points) == 2:
return self.points[0].azimuth(self.points[1])
lons = numpy.array([point.longitude for point in self.points])
lats = numpy.array([point.latitude for point in self.points])
azimuths = geodetic.azimuth(lons[:-1], lats[:-1], lons[1:], lats[1:])
distances = geodetic.geodetic_distance(lons[:-1], lats[:-1],
lons[1:], lats[1:])
azimuths = numpy.radians(azimuths)
# convert polar coordinates to Cartesian ones and calculate
# the average coordinate of each component
avg_x = numpy.mean(distances * numpy.sin(azimuths))
avg_y = numpy.mean(distances * numpy.cos(azimuths))
# find the mean azimuth from that mean vector
azimuth = numpy.degrees(numpy.arctan2(avg_x, avg_y))
if azimuth < 0:
azimuth += 360
return azimuth
[docs] def resample(self, section_length):
"""
Resample this line into sections.
The first point in the resampled line corresponds
to the first point in the original line.
Starting from the first point in the original line, a line
segment is defined as the line connecting the last point in the
resampled line and the next point in the original line.
The line segment is then split into sections of length equal to
``section_length``. The resampled line is obtained
by concatenating all sections.
The number of sections in a line segment is calculated as follows:
``round(segment_length / section_length)``.
Note that the resulting line has a length that is an exact multiple of
``section_length``, therefore its length is in general smaller
or greater (depending on the rounding) than the length
of the original line.
For a straight line, the difference between the resulting length
and the original length is at maximum half of the ``section_length``.
For a curved line, the difference my be larger,
because of corners getting cut.
:param section_length:
The length of the section, in km.
:type section_length:
float
:returns:
A new line resampled into sections based on the given length.
:rtype:
An instance of :class:`Line`
"""
if len(self.points) < 2:
return Line(self.points)
resampled_points = []
# 1. Resample the first section. 2. Loop over the remaining points
# in the line and resample the remaining sections.
# 3. Extend the list with the resampled points, except the first one
# (because it's already contained in the previous set of
# resampled points).
resampled_points.extend(
self.points[0].equally_spaced_points(self.points[1],
section_length)
)
# Skip the first point, it's already resampled
for i in range(2, len(self.points)):
points = resampled_points[-1].equally_spaced_points(
self.points[i], section_length
)
resampled_points.extend(points[1:])
return Line(resampled_points)
[docs] def get_length(self):
"""
Calculate and return the length of the line as a sum of lengths
of all its segments.
:returns:
Total length in km.
"""
length = 0
for i, point in enumerate(self.points):
if i != 0:
length += point.distance(self.points[i - 1])
return length
[docs] def resample_to_num_points(self, num_points):
"""
Resample the line to a specified number of points.
:param num_points:
Integer number of points the resulting line should have.
:returns:
A new line with that many points as requested.
"""
assert len(self.points) > 1, "can not resample the line of one point"
section_length = self.get_length() / (num_points - 1)
resampled_points = [self.points[0]]
segment = 0
acc_length = 0
last_segment_length = 0
for i in range(num_points - 1):
tot_length = (i + 1) * section_length
while tot_length > acc_length and segment < len(self.points) - 1:
last_segment_length = self.points[segment].distance(
self.points[segment + 1]
)
acc_length += last_segment_length
segment += 1
p1, p2 = self.points[segment - 1:segment + 1]
offset = tot_length - (acc_length - last_segment_length)
if offset < 1e-5:
# forward geodetic transformations for very small distances
# are very inefficient (and also unneeded). if target point
# is just 1 cm away from original (non-resampled) line vertex,
# don't even bother doing geodetic calculations.
resampled = p1
else:
resampled = p1.equally_spaced_points(p2, offset)[1]
resampled_points.append(resampled)
return Line(resampled_points)