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assemble_segments.py
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assemble_segments.py
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#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright (c) 2010.
# SMHI,
# Folkborgsvägen 1,
# Norrköping,
# Sweden
# Author(s):
# Martin Raspaud <martin.raspaud@smhi.se>
# This file is part of mpop.
# mpop is free software: you can redistribute it and/or modify it under the
# terms of the GNU General Public License as published by the Free Software
# Foundation, either version 3 of the License, or (at your option) any later
# version.
# mpop 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 General Public License for more details.
# You should have received a copy of the GNU General Public License along with
# mpop. If not, see <http://www.gnu.org/licenses/>.
"""Spherical geometry module.
"""
import math
import numpy as np
EPSILON = 0.0000001
class Coordinate(object):
"""Point on earth in terms of lat and lon.
"""
lat = None
lon = None
x__ = None
y__ = None
z__ = None
def __init__(self, lat=None, lon=None,
x__=None, y__=None, z__=None, R=1):
self.R = R
if lat is not None and lon is not None:
self.lat = math.radians(lat)
self.lon = math.radians(lon)
self._update_cart()
else:
self.x__ = x__
self.y__ = y__
self.z__ = z__
self._update_lonlat()
def _update_cart(self):
"""Convert lon/lat to cartesian coordinates.
"""
self.x__ = math.cos(self.lat) * math.cos(self.lon)
self.y__ = math.cos(self.lat) * math.sin(self.lon)
self.z__ = math.sin(self.lat)
def _update_lonlat(self):
"""Convert cartesian to lon/lat.
"""
self.lat = math.degrees(math.asin(self.z__ / self.R))
self.lon = math.degrees(math.atan2(self.y__, self.x__))
def __ne__(self, other):
if(abs(self.lat - other.lat) < EPSILON and
abs(self.lon - other.lon) < EPSILON):
return 0
else:
return 1
def __eq__(self, other):
return not self.__ne__(other)
def __str__(self):
return str((math.degrees(self.lat), math.degrees(self.lon)))
def __repr__(self):
return str((math.degrees(self.lat), math.degrees(self.lon)))
def cross2cart(self, point):
"""Compute the cross product, and convert to cartesian coordinates
(assuming radius 1).
"""
lat1 = self.lat
lon1 = self.lon
lat2 = point.lat
lon2 = point.lon
res = Coordinate(
x__=(math.sin(lat1 - lat2) * math.sin((lon1 + lon2) / 2) *
math.cos((lon1 - lon2) / 2) - math.sin(lat1 + lat2) *
math.cos((lon1 + lon2) / 2) * math.sin((lon1 - lon2) / 2)),
y__=(math.sin(lat1 - lat2) * math.cos((lon1 + lon2) / 2) *
math.cos((lon1 - lon2) / 2) + math.sin(lat1 + lat2) *
math.sin((lon1 + lon2) / 2) * math.sin((lon1 - lon2) / 2)),
z__=(math.cos(lat1) * math.cos(lat2) * math.sin(lon1 - lon2)))
return res
def distance(self, point):
"""Vincenty formula.
"""
dlambda = self.lon - point.lon
num = ((math.cos(point.lat) * math.sin(dlambda)) ** 2 +
(math.cos(self.lat) * math.sin(point.lat) -
math.sin(self.lat) * math.cos(point.lat) *
math.cos(dlambda)) ** 2)
den = (math.sin(self.lat) * math.sin(point.lat) +
math.cos(self.lat) * math.cos(point.lat) * math.cos(dlambda))
return math.atan2(math.sqrt(num), den)
def norm(self):
"""Return the norm of the vector.
"""
return math.sqrt(self.x__ ** 2 + self.y__ ** 2 + self.z__ ** 2)
def normalize(self):
"""normalize the vector.
"""
norm = self.norm()
self.x__ /= norm
self.y__ /= norm
self.z__ /= norm
return self
def cross(self, point):
"""cross product with another vector.
"""
x__ = self.y__ * point.z__ - self.z__ * point.y__
y__ = self.z__ * point.x__ - self.x__ * point.z__
z__ = self.x__ * point.y__ - self.y__ * point.x__
return Coordinate(x__=x__, y__=y__, z__=z__)
def dot(self, point):
"""dot product with another vector.
"""
return (self.x__ * point.x__ +
self.y__ * point.y__ +
self.z__ * point.z__)
class Arc(object):
"""An arc of the great circle between two points.
"""
start = None
end = None
def __init__(self, start, end):
self.start, self.end = start, end
def center_angle(self):
"""Angle of an arc at the center of the sphere.
"""
val = (math.cos(self.start.lat - self.end.lat) +
math.cos(self.start.lon - self.end.lon) - 1)
if val > 1:
val = 1
elif val < -1:
val = -1
return math.acos(val)
def __eq__(self, other):
if(self.start == other.start and self.end == other.end):
return 1
return 0
def __ne__(self, other):
return not self.__eq__(other)
def __str__(self):
return str((str(self.start), str(self.end)))
def angle(self, other_arc):
"""Oriented angle between two arcs.
"""
if self.start == other_arc.start:
a__ = self.start
b__ = self.end
c__ = other_arc.end
elif self.start == other_arc.end:
a__ = self.start
b__ = self.end
c__ = other_arc.start
elif self.end == other_arc.end:
a__ = self.end
b__ = self.start
c__ = other_arc.start
elif self.end == other_arc.start:
a__ = self.end
b__ = self.start
c__ = other_arc.end
else:
raise ValueError("No common point in angle computation.")
ua_ = a__.cross(b__)
ub_ = a__.cross(c__)
val = ua_.dot(ub_) / (ua_.norm() * ub_.norm())
if abs(val - 1) < EPSILON:
angle = 0
elif abs(val + 1) < EPSILON:
angle = math.pi
else:
angle = math.acos(val)
n__ = ua_.normalize()
if n__.dot(c__) > 0:
return -angle
else:
return angle
def intersections(self, other_arc):
"""Gives the two intersections of the greats circles defined by the
current arc and *other_arc*.
"""
if self.end.lon - self.start.lon > math.pi:
self.end.lon -= 2 * math.pi
if other_arc.end.lon - other_arc.start.lon > math.pi:
other_arc.end.lon -= 2 * math.pi
if self.end.lon - self.start.lon < -math.pi:
self.end.lon += 2 * math.pi
if other_arc.end.lon - other_arc.start.lon < -math.pi:
other_arc.end.lon += 2 * math.pi
ea_ = self.start.cross2cart(self.end).normalize()
eb_ = other_arc.start.cross2cart(other_arc.end).normalize()
cross = ea_.cross(eb_)
lat = math.atan2(cross.z__, math.sqrt(cross.x__ ** 2 + cross.y__ ** 2))
lon = math.atan2(-cross.y__, cross.x__)
return (Coordinate(math.degrees(lat), math.degrees(lon)),
Coordinate(math.degrees(-lat),
math.degrees(modpi(lon + math.pi))))
def intersects(self, other_arc):
"""Says if two arcs defined by the current arc and the *other_arc*
intersect. An arc is defined as the shortest tracks between two points.
"""
for i in self.intersections(other_arc):
a__ = self.start
b__ = self.end
c__ = other_arc.start
d__ = other_arc.end
ab_ = a__.distance(b__)
cd_ = c__.distance(d__)
if(abs(a__.distance(i) + b__.distance(i) - ab_) < EPSILON and
abs(c__.distance(i) + d__.distance(i) - cd_) < EPSILON):
return True
return False
def intersection(self, other_arc):
"""Says where, if two arcs defined by the current arc and the
*other_arc* intersect. An arc is defined as the shortest tracks between
two points.
"""
for i in self.intersections(other_arc):
a__ = self.start
b__ = self.end
c__ = other_arc.start
d__ = other_arc.end
ab_ = a__.distance(b__)
cd_ = c__.distance(d__)
if(abs(a__.distance(i) + b__.distance(i) - ab_) < EPSILON and
abs(c__.distance(i) + d__.distance(i) - cd_) < EPSILON):
return i
return None
def modpi(val):
"""Puts *val* between -pi and pi.
"""
return (val + math.pi) % (2 * math.pi) - math.pi
def modpi2(val):
"""Puts *val* between 0 and 2pi.
"""
return val % (2 * math.pi)
def point_inside(point, corners):
"""Is a point inside the 4 corners ? This uses great circle arcs as area
boundaries.
"""
arc1 = Arc(corners[0], corners[1])
arc2 = Arc(corners[1], corners[2])
arc3 = Arc(corners[2], corners[3])
arc4 = Arc(corners[3], corners[0])
arc5 = Arc(corners[1], point)
arc6 = Arc(corners[3], point)
angle1 = modpi(arc1.angle(arc2))
angle1bis = modpi(arc1.angle(arc5))
angle2 = modpi(arc3.angle(arc4))
angle2bis = modpi(arc3.angle(arc6))
return (np.sign(angle1) == np.sign(angle1bis) and
abs(angle1) > abs(angle1bis) and
np.sign(angle2) == np.sign(angle2bis) and
abs(angle2) > abs(angle2bis))
def overlaps(area_corners, segment_corners):
"""Are two areas overlapping ? This uses great circle arcs as area
boundaries.
"""
for i in area_corners:
if point_inside(i, segment_corners):
return True
for i in segment_corners:
if point_inside(i, area_corners):
return True
area_arc1 = Arc(area_corners[0], area_corners[1])
area_arc2 = Arc(area_corners[1], area_corners[2])
area_arc3 = Arc(area_corners[2], area_corners[3])
area_arc4 = Arc(area_corners[3], area_corners[0])
segment_arc1 = Arc(segment_corners[0], segment_corners[1])
segment_arc2 = Arc(segment_corners[1], segment_corners[2])
segment_arc3 = Arc(segment_corners[2], segment_corners[3])
segment_arc4 = Arc(segment_corners[3], segment_corners[0])
for i in (area_arc1, area_arc2, area_arc3, area_arc4):
for j in (segment_arc1, segment_arc2, segment_arc3, segment_arc4):
if i.intersects(j):
return True
return False
def get_intersections(b__, boundaries):
"""Get the intersections of *b__* with *boundaries*.
Returns both the intersection coordinates and the concerned boundaries.
"""
intersections = []
bounds = []
for other_b in boundaries:
inter = b__.intersection(other_b)
if inter is not None:
intersections.append(inter)
bounds.append(other_b)
return intersections, bounds
def get_first_intersection(b__, boundaries):
"""Get the first intersection on *b__* with *boundaries*.
"""
intersections, bounds = get_intersections(b__, boundaries)
del bounds
dists = np.array([b__.start.distance(p__) for p__ in intersections])
indices = dists.argsort()
if len(intersections) > 0:
return intersections[indices[0]]
return None
def get_next_intersection(p__, b__, boundaries):
"""Get the next intersection from the intersection of arcs *p__* and *b__*
along segment *b__* with *boundaries*.
"""
new_b = Arc(p__, b__.end)
intersections, bounds = get_intersections(new_b, boundaries)
dists = np.array([b__.start.distance(p2) for p2 in intersections])
indices = dists.argsort()
if len(intersections) > 0 and intersections[indices[0]] != p__:
return intersections[indices[0]], bounds[indices[0]]
elif len(intersections) > 1:
return intersections[indices[1]], bounds[indices[1]]
return None, None
def polygon(area_corners, segment_corners):
"""Get the intersection polygon between two areas.
"""
area_boundaries = [Arc(area_corners[0], area_corners[1]),
Arc(area_corners[1], area_corners[2]),
Arc(area_corners[2], area_corners[3]),
Arc(area_corners[3], area_corners[0])]
segment_boundaries = [Arc(segment_corners[0], segment_corners[1]),
Arc(segment_corners[1], segment_corners[2]),
Arc(segment_corners[2], segment_corners[3]),
Arc(segment_corners[3], segment_corners[0])]
angle1 = area_boundaries[0].angle(area_boundaries[1])
angle2 = segment_boundaries[0].angle(segment_boundaries[1])
if np.sign(angle1) != np.sign(angle2):
segment_corners.reverse()
segment_boundaries = [Arc(segment_corners[0], segment_corners[1]),
Arc(segment_corners[1], segment_corners[2]),
Arc(segment_corners[2], segment_corners[3]),
Arc(segment_corners[3], segment_corners[0])]
poly = []
boundaries = area_boundaries
other_boundaries = segment_boundaries
b__ = None
for b__ in boundaries:
if point_inside(b__.start, segment_corners):
poly.append(b__.start)
break
else:
inter = get_first_intersection(b__, other_boundaries)
if inter is not None:
poly.append(inter)
break
if len(poly) == 0:
return None
while len(poly) < 2 or poly[0] != poly[-1]:
inter, b2_ = get_next_intersection(poly[-1], b__, other_boundaries)
if inter is None:
poly.append(b__.end)
idx = (boundaries.index(b__) + 1) % len(boundaries)
b__ = boundaries[idx]
else:
poly.append(inter)
b__ = b2_
boundaries, other_boundaries = other_boundaries, boundaries
return poly[:-1]
R = 1
def get_area(corners):
"""Get the area of the convex area defined by *corners*.
"""
c1_ = corners[0]
area = 0
for idx in range(1, len(corners) - 1):
b1_ = Arc(c1_, corners[idx])
b2_ = Arc(c1_, corners[idx + 1])
b3_ = Arc(corners[idx], corners[idx + 1])
e__ = (abs(b1_.angle(b2_)) +
abs(b2_.angle(b3_)) +
abs(b3_.angle(b1_)))
area += R ** 2 * e__ - math.pi
return area
def overlap_rate(swath_corners, area_corners):
"""Get how much a swath overlaps an area.
"""
area_area = get_area(area_corners)
inter_area = get_area(polygon(area_corners, swath_corners))
return inter_area / area_area
def min_distances(area_corners, segment_corners):
"""Min distances between each corner of *area_corners* and
*segment_corners*.
"""
dists = np.ones(4) * np.infty
for i, ic_ in enumerate(area_corners):
for jc_ in segment_corners:
dist = ic_.distance(jc_)
if dists[i] > dist:
dists[i] = dist
return dists
def should_wait(area_corners, segment_corners, previous_segment_corners):
"""Are the newest cornest still inside the area ? is the last segment
boundary overlapping any boundary of the area ? In this case we should wait
for the next segment to arrive.
"""
dists = min_distances(segment_corners, previous_segment_corners)
indices = np.argsort(dists)
new_corners = np.array(segment_corners)[indices[2:]]
if len(new_corners) != 2:
raise ValueError("More than 2 corners differ from previous segment...")
new_arc = Arc(new_corners[0], new_corners[1])
for i in new_corners:
if point_inside(i, area_corners):
return True
area_arc1 = Arc(area_corners[0], area_corners[1])
area_arc2 = Arc(area_corners[1], area_corners[2])
area_arc3 = Arc(area_corners[2], area_corners[3])
area_arc4 = Arc(area_corners[3], area_corners[0])
for i in (area_arc1, area_arc2, area_arc3, area_arc4):
if i.intersects(new_arc):
return True
return False
import unittest
class TestSphereGeometry(unittest.TestCase):
"""Testing sphere geometry from this module.
"""
def test_angle(self):
"""Testing the angle value between two arcs.
"""
base = 0
p0_ = Coordinate(base, base)
p1_ = Coordinate(base + 1, base)
p2_ = Coordinate(base, base + 1)
p3_ = Coordinate(base - 1, base)
p4_ = Coordinate(base, base - 1)
arc1 = Arc(p0_, p1_)
arc2 = Arc(p0_, p2_)
arc3 = Arc(p0_, p3_)
arc4 = Arc(p0_, p4_)
self.assertAlmostEqual(arc1.angle(arc2), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc2.angle(arc3), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc3.angle(arc4), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc4.angle(arc1), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc1.angle(arc4), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc4.angle(arc3), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc3.angle(arc2), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc2.angle(arc1), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc1.angle(arc3), math.pi,
msg="this should be pi")
self.assertAlmostEqual(arc3.angle(arc1), math.pi,
msg="this should be pi")
self.assertAlmostEqual(arc2.angle(arc4), math.pi,
msg="this should be pi")
self.assertAlmostEqual(arc4.angle(arc2), math.pi,
msg="this should be pi")
p5_ = Coordinate(base + 1, base + 1)
p6_ = Coordinate(base - 1, base + 1)
p7_ = Coordinate(base - 1, base - 1)
p8_ = Coordinate(base + 1, base - 1)
arc5 = Arc(p0_, p5_)
arc6 = Arc(p0_, p6_)
arc7 = Arc(p0_, p7_)
arc8 = Arc(p0_, p8_)
self.assertAlmostEqual(arc1.angle(arc5), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc5.angle(arc2), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc2.angle(arc6), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc6.angle(arc3), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc3.angle(arc7), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc7.angle(arc4), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc4.angle(arc8), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc8.angle(arc1), math.pi / 4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(arc1.angle(arc6), 3 * math.pi / 4, 3,
msg="this should be 3pi/4")
c0_ = Coordinate(0, 180)
c1_ = Coordinate(1, 180)
c2_ = Coordinate(0, -179)
c3_ = Coordinate(-1, -180)
c4_ = Coordinate(0, 179)
arc1 = Arc(c0_, c1_)
arc2 = Arc(c0_, c2_)
arc3 = Arc(c0_, c3_)
arc4 = Arc(c0_, c4_)
self.assertAlmostEqual(arc1.angle(arc2), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc2.angle(arc3), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc3.angle(arc4), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc4.angle(arc1), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc1.angle(arc4), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc4.angle(arc3), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc3.angle(arc2), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc2.angle(arc1), -math.pi / 2,
msg="this should be -pi/2")
# case of the north pole
c0_ = Coordinate(90, 0)
c1_ = Coordinate(89, 0)
c2_ = Coordinate(89, -90)
c3_ = Coordinate(89, 180)
c4_ = Coordinate(89, 90)
arc1 = Arc(c0_, c1_)
arc2 = Arc(c0_, c2_)
arc3 = Arc(c0_, c3_)
arc4 = Arc(c0_, c4_)
self.assertAlmostEqual(arc1.angle(arc2), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc2.angle(arc3), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc3.angle(arc4), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc4.angle(arc1), math.pi / 2,
msg="this should be pi/2")
self.assertAlmostEqual(arc1.angle(arc4), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc4.angle(arc3), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc3.angle(arc2), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(arc2.angle(arc1), -math.pi / 2,
msg="this should be -pi/2")
self.assertAlmostEqual(Arc(c1_, c2_).angle(arc1), math.pi/4, 3,
msg="this should be pi/4")
self.assertAlmostEqual(Arc(c4_, c3_).angle(arc4), -math.pi/4, 3,
msg="this should be -pi/4")
self.assertAlmostEqual(Arc(c1_, c4_).angle(arc1), -math.pi/4, 3,
msg="this should be -pi/4")
def test_inside(self):
"""Testing if a point is inside for other points.
"""
c1_ = Coordinate(-11, -11)
c2_ = Coordinate(11, -11)
c3_ = Coordinate(11, 11)
c4_ = Coordinate(-11, 11)
corners = [c1_, c2_, c3_, c4_]
point = Coordinate(0, 0)
self.assertTrue(point_inside(point, corners))
point = Coordinate(0, 12)
self.assertFalse(point_inside(point, corners))
c1_ = Coordinate(-1, 180)
c2_ = Coordinate(1, 179)
c3_ = Coordinate(1, -179)
c4_ = Coordinate(-1, -179)
corners = [c1_, c2_, c3_, c4_]
point = Coordinate(0, 180)
self.assertTrue(point_inside(point, corners))
point = Coordinate(12, 180)
self.assertFalse(point_inside(point, corners))
point = Coordinate(-12, 180)
self.assertFalse(point_inside(point, corners))
point = Coordinate(0, 192)
self.assertFalse(point_inside(point, corners))
point = Coordinate(0, -192)
self.assertFalse(point_inside(point, corners))
# case of the north pole
c1_ = Coordinate(89, 0)
c2_ = Coordinate(89, 90)
c3_ = Coordinate(89, 180)
c4_ = Coordinate(89, -90)
corners = [c1_, c2_, c3_, c4_]
point = Coordinate(90, 90)
self.assertTrue(point_inside(point, corners))
def test_intersects(self):
"""Test if two arcs intersect.
"""
p0_ = Coordinate(0, 0)
p1_ = Coordinate(1, 0)
p2_ = Coordinate(0, 1)
p3_ = Coordinate(-1, 0)
p4_ = Coordinate(0, -1)
p5_ = Coordinate(1, 1)
p6_ = Coordinate(-1, 1)
arc13 = Arc(p1_, p3_)
arc24 = Arc(p2_, p4_)
arc32 = Arc(p3_, p2_)
arc41 = Arc(p4_, p1_)
arc40 = Arc(p4_, p0_)
arc56 = Arc(p5_, p6_)
arc45 = Arc(p4_, p5_)
arc02 = Arc(p0_, p2_)
arc35 = Arc(p3_, p5_)
self.assertTrue(arc13.intersects(arc24))
self.assertFalse(arc32.intersects(arc41))
self.assertFalse(arc56.intersects(arc40))
self.assertFalse(arc56.intersects(arc40))
self.assertFalse(arc45.intersects(arc02))
self.assertTrue(arc35.intersects(arc24))
p0_ = Coordinate(0, 180)
p1_ = Coordinate(1, 180)
p2_ = Coordinate(0, -179)
p3_ = Coordinate(-1, -180)
p4_ = Coordinate(0, 179)
p5_ = Coordinate(1, -179)
p6_ = Coordinate(-1, -179)
arc13 = Arc(p1_, p3_)
arc24 = Arc(p2_, p4_)
arc32 = Arc(p3_, p2_)
arc41 = Arc(p4_, p1_)
arc40 = Arc(p4_, p0_)
arc56 = Arc(p5_, p6_)
arc45 = Arc(p4_, p5_)
arc02 = Arc(p0_, p2_)
arc35 = Arc(p3_, p5_)
self.assertTrue(arc13.intersects(arc24))
self.assertFalse(arc32.intersects(arc41))
self.assertFalse(arc56.intersects(arc40))
self.assertFalse(arc56.intersects(arc40))
self.assertFalse(arc45.intersects(arc02))
self.assertTrue(arc35.intersects(arc24))
# case of the north pole
p0_ = Coordinate(90, 0)
p1_ = Coordinate(89, 0)
p2_ = Coordinate(89, 90)
p3_ = Coordinate(89, 180)
p4_ = Coordinate(89, -90)
p5_ = Coordinate(89, 45)
p6_ = Coordinate(89, 135)
arc13 = Arc(p1_, p3_)
arc24 = Arc(p2_, p4_)
arc32 = Arc(p3_, p2_)
arc41 = Arc(p4_, p1_)
arc40 = Arc(p4_, p0_)
arc56 = Arc(p5_, p6_)
arc45 = Arc(p4_, p5_)
arc02 = Arc(p0_, p2_)
arc35 = Arc(p3_, p5_)
self.assertTrue(arc13.intersects(arc24))
self.assertFalse(arc32.intersects(arc41))
self.assertFalse(arc56.intersects(arc40))
self.assertFalse(arc56.intersects(arc40))
self.assertFalse(arc45.intersects(arc02))
self.assertTrue(arc35.intersects(arc24))
def test_overlaps(self):
"""Test if two areas overlap.
"""
p1_ = Coordinate(89, 0)
p2_ = Coordinate(89, 90)
p3_ = Coordinate(89, 180)
p4_ = Coordinate(89, -90)
p5_ = Coordinate(89, 45)
p6_ = Coordinate(89, 135)
p7_ = Coordinate(89, -135)
p8_ = Coordinate(89, -45)
self.assertTrue(overlaps([p1_, p2_, p3_, p4_],
[p5_, p6_, p7_, p8_]))
self.assertFalse(overlaps([p1_, p5_, p2_, p6_],
[p3_, p7_, p4_, p8_]))
p1_ = Coordinate(1, -1)
p2_ = Coordinate(1, 1)
p3_ = Coordinate(-1, 1)
p4_ = Coordinate(-1, -1)
p5_ = Coordinate(0, 0)
p6_ = Coordinate(0, 2)
p7_ = Coordinate(2, 2)
p8_ = Coordinate(2, 0)
self.assertTrue(overlaps([p1_, p2_, p3_, p4_], [p5_, p6_, p7_, p8_]))
self.assertFalse(overlaps([p1_, p8_, p5_, p4_], [p2_, p3_, p6_, p7_]))
def test_overlap_rate(self):
"""Test how much two areas overlap.
"""
p1_ = Coordinate(1, -1)
p2_ = Coordinate(1, 1)
p3_ = Coordinate(-1, 1)
p4_ = Coordinate(-1, -1)
p5_ = Coordinate(0, 0)
p6_ = Coordinate(0, 2)
p7_ = Coordinate(2, 2)
p8_ = Coordinate(2, 0)
self.assertAlmostEqual(overlap_rate([p1_, p2_, p3_, p4_],
[p5_, p6_, p7_, p8_]), 0.25, 3)
c1_ = [(60.5944, 82.829699999999974),
(52.859999999999999, 36.888300000000001),
(66.7547, 2.8773),
(80.395899999999997, 98.145499999999984)]
c2_ = [(62.953206630716465, 7.8098183315148422),
(62.953206630716465, 26.189349044600252),
(53.301561187195546, 26.189349044600252),
(53.301561187195546, 7.8098183315148422)]
cor1 = [Coordinate(t[0], t[1]) for t in c1_]
cor2 = [Coordinate(t[0], t[1]) for t in c2_]
self.assertAlmostEqual(overlap_rate(cor1, cor2), 0.07, 2)
c1_ = [(60.5944, 82.829699999999974),
(52.859999999999999, 36.888300000000001),
(66.7547, 2.8773),
(80.395899999999997, 98.145499999999984)]
c2_ = [(65.98228561983025, 12.108984194981202),
(65.98228561983025, 30.490647126520301),
(57.304862819933433, 30.490647126520301),
(57.304862819933433, 12.108984194981202)]
cor1 = [Coordinate(t[0], t[1]) for t in c1_]
cor2 = [Coordinate(t[0], t[1]) for t in c2_]
self.assertAlmostEqual(overlap_rate(cor1, cor2), 0.5, 2)
if __name__ == '__main__':
unittest.main()