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sphere_test.py
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sphere_test.py
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from __future__ import print_function, unicode_literals, division
import unittest
import math
import random
import numpy as np
from collections import defaultdict
from itertools import izip
from qed4.geometry import sphere
from qed4.geometry.sphere import Angle, CellId, LatLon, Point, Cell
from qed4.geometry.sphere import LineInterval, SphereInterval, LatLonRect
from qed4.geometry.sphere import RegionCoverer, CellUnion, Cap
INVERSE_ITERATIONS = 200000
TOKEN_ITERATIONS = 10000
COVERAGE_ITERATIONS = 1000000
NEIGHBORS_ITERATIONS = 1000
NORMALIZE_ITERATIONS = 2000
REGION_COVERER_ITERATIONS = 1000
RANDOM_CAPS_ITERATIONS = 1000
SIMPLE_COVERINGS_ITERATIONS = 1000
'''
INVERSE_ITERATIONS = 20
TOKEN_ITERATIONS = 10
COVERAGE_ITERATIONS = 10
NEIGHBORS_ITERATIONS = 10
NORMALIZE_ITERATIONS = 20
REGION_COVERER_ITERATIONS = 10
RANDOM_CAPS_ITERATIONS = 10
SIMPLE_COVERINGS_ITERATIONS = 10
'''
class TestAngle(unittest.TestCase):
def testDefaultConstructor(self):
angle = Angle()
self.assertEqual(angle.radians, 0)
def testPiRadiansExactly180Degrees(self):
self.assertEqual(Angle.from_radians(math.pi).radians, math.pi)
self.assertEqual(Angle.from_radians(math.pi).degrees, 180.0)
self.assertEqual(Angle.from_degrees(180).radians, math.pi)
self.assertEqual(Angle.from_degrees(180).degrees, 180.0)
self.assertEqual(Angle.from_radians((-math.pi / 2)).degrees, -90.0)
self.assertEqual(Angle.from_degrees((-45)).radians, -math.pi / 4)
class TestLatLon(unittest.TestCase):
def testBasics(self):
ll_rad = LatLon.from_radians(math.pi / 4, math.pi / 2)
self.assertEqual(ll_rad.lat().radians, math.pi / 4)
self.assertEqual(ll_rad.lon().radians, math.pi / 2)
self.assertTrue(ll_rad.is_valid())
ll_deg = LatLon.from_degrees(45, 90)
self.assertEqual(ll_rad, ll_deg)
self.assertFalse(LatLon.from_degrees(-91, 0).is_valid())
self.assertFalse(LatLon.from_degrees(0, 181).is_valid())
bad = LatLon.from_degrees(120, 200)
self.assertFalse(bad.is_valid())
better = bad.normalized()
self.assertTrue(better.is_valid())
self.assertEqual(Angle.from_degrees(90), better.lat())
self.assertEqual(Angle.from_degrees(-160).radians,
better.lon().radians)
self.assertTrue((LatLon.from_degrees(10, 20) \
+ LatLon.from_degrees(20, 30)).approx_equals(
LatLon.from_degrees(30, 50)))
self.assertTrue((LatLon.from_degrees(10, 20) \
- LatLon.from_degrees(20, 30)).approx_equals(
LatLon.from_degrees(-10, -10)))
#self.assertTrue((0.5 * LatLon.from_degrees(10, 20)).approx_equals(
# LatLon.from_degrees(5, 10)))
invalid = LatLon.invalid()
self.assertFalse(invalid.is_valid())
default_ll = LatLon.default()
self.assertTrue(default_ll.is_valid())
self.assertEqual(0, default_ll.lat().radians)
self.assertEqual(0, default_ll.lon().radians)
def testConversion(self):
self.assertEqual(LatLon.from_point(LatLon.from_degrees(
90.0, 65.0).to_point()).lat().degrees, 90.0)
self.assertEqual(LatLon.from_point(LatLon.from_radians(
-math.pi / 2, 1).to_point()).lat().radians, -math.pi / 2)
self.assertEqual(abs(LatLon.from_point(LatLon.from_degrees(
12.2, 180.0).to_point()).lon().degrees), 180.0)
self.assertEqual(abs(LatLon.from_point(LatLon.from_radians(
0.1, -math.pi).to_point()).lon().radians), math.pi)
def testDistance(self):
self.assertEqual(0.0, LatLon.from_degrees(90, 0).get_distance(
LatLon.from_degrees(90, 0)).radians)
self.assertAlmostEqual(77.0,
LatLon.from_degrees(-37, 25).get_distance(
LatLon.from_degrees(-66, -155)).degrees, delta=1e-13)
self.assertAlmostEqual(115.0,
LatLon.from_degrees(0, 165).get_distance(
LatLon.from_degrees(0, -80)).degrees, delta=1e-13)
self.assertAlmostEqual(180.0,
LatLon.from_degrees(47, -127).get_distance(
LatLon.from_degrees(-47, 53)).degrees, delta=2e-6)
class TestCellId(unittest.TestCase):
def setUp(self):
random.seed(20)
@staticmethod
def get_random_cell_id(*args):
if len(args) == 0:
level = random.randrange(CellId.MAX_LEVEL + 1)
else:
level = args[0]
face = random.randrange(CellId.NUM_FACES)
pos = random.randrange(0xffffffffffffffff) \
& ((1 << (2 * CellId.MAX_LEVEL)) - 1)
return CellId.from_face_pos_level(face, pos, level)
def get_random_point(self):
x = 2 * random.random() - 1
y = 2 * random.random() - 1
z = 2 * random.random() - 1
return Point(x, y, z).normalize()
@staticmethod
def get_cell_id(lat, lon):
return CellId.from_lat_lon(LatLon.from_degrees(lat, lon))
def testDefaultConstructor(self):
cell_id = CellId()
self.assertEqual(cell_id.id(), 0)
self.assertFalse(cell_id.is_valid())
def testFaceDefinitions(self):
self.assertEqual(TestCellId.get_cell_id(0, 0).face(), 0)
self.assertEqual(TestCellId.get_cell_id(0, 90).face(), 1)
self.assertEqual(TestCellId.get_cell_id(90, 0).face(), 2)
self.assertEqual(TestCellId.get_cell_id(0, 180).face(), 3)
self.assertEqual(TestCellId.get_cell_id(0, -90).face(), 4)
self.assertEqual(TestCellId.get_cell_id(-90, 0).face(), 5)
def testParentChildRelationships(self):
cell_id = CellId.from_face_pos_level(3, 0x12345678,
CellId.MAX_LEVEL - 4)
self.assertTrue(cell_id.is_valid())
self.assertEqual(cell_id.face(), 3)
self.assertEqual(cell_id.pos(), 0x12345700)
self.assertEqual(cell_id.level(), CellId.MAX_LEVEL - 4)
self.assertFalse(cell_id.is_leaf())
self.assertEqual(cell_id.child_begin(cell_id.level() + 2).pos(),
0x12345610)
self.assertEqual(cell_id.child_begin().pos(), 0x12345640)
self.assertEqual(cell_id.parent().pos(), 0x12345400)
self.assertEqual(cell_id.parent(cell_id.level() - 2).pos(), 0x12345000)
# Check ordering of children relative to parents.
self.assertLess(cell_id.child_begin(), cell_id)
self.assertGreater(cell_id.child_end(), cell_id)
self.assertEqual(cell_id.child_begin().next().next().next().next(),
cell_id.child_end())
self.assertEqual(cell_id.child_begin(CellId.MAX_LEVEL),
cell_id.range_min())
self.assertEqual(cell_id.child_end(CellId.MAX_LEVEL),
cell_id.range_max().next())
# Check that cells are represented by the position of their center
# along the Hilbert curve.
self.assertEqual(cell_id.range_min().id() + cell_id.range_max().id(),
2 * cell_id.id())
def testWrapping(self):
self.assertEqual(CellId.begin(0).prev_wrap(), CellId.end(0).prev())
self.assertEqual(CellId.begin(CellId.MAX_LEVEL).prev_wrap(),
CellId.from_face_pos_level(5,
0xffffffffffffffff >> CellId.FACE_BITS, CellId.MAX_LEVEL))
self.assertEqual(CellId.begin(CellId.MAX_LEVEL).advance_wrap(-1),
CellId.from_face_pos_level(5,
0xffffffffffffffff >> CellId.FACE_BITS, CellId.MAX_LEVEL))
self.assertEqual(CellId.end(4).advance(-1).advance_wrap(1),
CellId.begin(4))
self.assertEqual(CellId.end(
CellId.MAX_LEVEL).advance(-1).advance_wrap(1),
CellId.from_face_pos_level(0, 0, CellId.MAX_LEVEL))
self.assertEqual(CellId.end(4).prev().next_wrap(), CellId.begin(4))
self.assertEqual(CellId.end(CellId.MAX_LEVEL).prev().next_wrap(),
CellId.from_face_pos_level(0, 0, CellId.MAX_LEVEL))
def testAdvance(self):
cell_id = CellId.from_face_pos_level(3, 0x12345678,
CellId.MAX_LEVEL - 4)
self.assertEqual(CellId.begin(0).advance(7), CellId.end(0))
self.assertEqual(CellId.begin(0).advance(12), CellId.end(0))
self.assertEqual(CellId.end(0).advance(-7), CellId.begin(0))
self.assertEqual(CellId.end(0).advance(-12000000), CellId.begin(0))
num_level_5_cells = 6 << (2 * 5)
self.assertEqual(CellId.begin(5).advance(500),
CellId.end(5).advance(500 - num_level_5_cells))
self.assertEqual(cell_id.child_begin(CellId.MAX_LEVEL).advance(256),
cell_id.next().child_begin(CellId.MAX_LEVEL))
self.assertEqual(CellId.from_face_pos_level(1, 0, CellId.MAX_LEVEL) \
.advance(4 << (2 * CellId.MAX_LEVEL)),
CellId.from_face_pos_level(5, 0, CellId.MAX_LEVEL))
# Check basic properties of advance_wrap().
self.assertEqual(CellId.begin(0).advance_wrap(7),
CellId.from_face_pos_level(1, 0, 0))
self.assertEqual(CellId.begin(0).advance_wrap(12), CellId.begin(0))
self.assertEqual(CellId.from_face_pos_level(5, 0, 0).advance_wrap(-7),
CellId.from_face_pos_level(4, 0, 0))
self.assertEqual(CellId.begin(0).advance_wrap(-12000000),
CellId.begin(0))
self.assertEqual(CellId.begin(5).advance_wrap(6644),
CellId.begin(5).advance_wrap(-11788))
self.assertEqual(
cell_id.child_begin(CellId.MAX_LEVEL).advance_wrap(256),
cell_id.next().child_begin(CellId.MAX_LEVEL))
self.assertEqual(
CellId.from_face_pos_level(5, 0, CellId.MAX_LEVEL) \
.advance_wrap(2 << (2 * CellId.MAX_LEVEL)),
CellId.from_face_pos_level(1, 0, CellId.MAX_LEVEL))
def testInverse(self):
for i in xrange(INVERSE_ITERATIONS):
cell_id = TestCellId.get_random_cell_id(CellId.MAX_LEVEL)
self.assertTrue(cell_id.is_leaf())
self.assertEqual(cell_id.level(), CellId.MAX_LEVEL)
center = cell_id.to_lat_lon()
self.assertEqual(CellId.from_lat_lon(center).id(), cell_id.id())
def testTokens(self):
for i in xrange(TOKEN_ITERATIONS):
cell_id = TestCellId.get_random_cell_id()
token = cell_id.to_token()
self.assertLessEqual(len(token), 16)
self.assertEqual(CellId.from_token(token), cell_id)
def expand_cells(self, parent, cells, parent_map):
max_expand_level = 3
cells.append(parent)
if parent.level() == 3:
return
face, i, j, orientation = parent.to_face_ij_orientation()
self.assertEqual(face, parent.face())
child = parent.child_begin()
child_end = parent.child_end()
pos = 0
while child != child_end:
self.assertEqual(parent.child(pos), child)
self.assertEqual(child.level(), parent.level() + 1)
self.assertFalse(child.is_leaf())
cface, ci, cj, corientation = child.to_face_ij_orientation()
self.assertEqual(cface, face)
self.assertEqual(corientation,
orientation ^ sphere.POS_TO_ORIENTATION[pos])
parent_map[child] = parent
self.expand_cells(child, cells, parent_map)
child = child.next()
pos = pos + 1
def testContainment(self):
parent_map = {}
cells = []
for face in xrange(6):
self.expand_cells(CellId.from_face_pos_level(face, 0, 0),
cells, parent_map)
for i in xrange(len(cells)):
for j in xrange(len(cells)):
contained = True
cell_id = cells[j]
while cell_id != cells[i]:
next_cell_id = parent_map.get(cell_id)
if next_cell_id is None:
contained = False
break
cell_id = next_cell_id
self.assertEqual(cells[i].contains(cells[j]), contained)
self.assertEqual(cells[j] >= cells[i].range_min() \
and cells[j] <= cells[i].range_max(), contained)
self.assertEqual(cells[i].intersects(cells[j]),
cells[i].contains(cells[j]) or cells[j].contains(cells[i]))
def testContinuity(self):
# Make sure that sequentially increasing cell ids form a continuous
# path over the surface of the sphere, i.e. there are no
# discontinuous jumps from one region to another.
max_walk_level = 8
cell_size = 1 / (1 << max_walk_level)
max_dist = CellId.max_edge().get_value(max_walk_level)
end = CellId.end(max_walk_level)
cell_id = CellId.begin(max_walk_level)
while cell_id != end:
self.assertLessEqual(
cell_id.to_point_raw().angle(
cell_id.next_wrap().to_point_raw()), max_dist)
self.assertEqual(cell_id.advance_wrap(1), cell_id.next_wrap())
self.assertEqual(cell_id.next_wrap().advance_wrap(-1), cell_id)
# Check that the ToPointRaw() returns the center of each cell
# in (s,t) coordinates.
face, u, v = sphere.xyz_to_face_uv(cell_id.to_point_raw())
self.assertAlmostEqual(
CellId.uv_to_st(u) % (0.5 * cell_size), 0, delta=1-15)
self.assertAlmostEqual(
CellId.uv_to_st(v) % (0.5 * cell_size), 0, delta=1-15)
cell_id = cell_id.next()
def testCoverage(self):
max_dist = 0.5 * CellId.max_diag().get_value(CellId.MAX_LEVEL)
for i in xrange(COVERAGE_ITERATIONS):
p = self.get_random_point()
q = CellId.from_point(p).to_point_raw()
self.assertLessEqual(p.angle(q), max_dist)
def testNeighbors(self):
# Check the edge neighbors of face 1.
out_faces = (5, 3, 2, 0)
face_nbrs = CellId.from_face_pos_level(1, 0, 0).get_edge_neighbors()
for i, face_nbr in enumerate(face_nbrs):
self.assertTrue(face_nbr.is_face())
self.assertEqual(face_nbr.face(), out_faces[i])
# Check the vertex neighbors of the center of face 2 at level 5.
neighbors = CellId.from_point(Point(0, 0, 1)).get_vertex_neighbors(5)
neighbors.sort()
for i, neighbor in enumerate(neighbors):
self.assertEqual(neighbor,
CellId.from_face_ij(2,
(1 << 29) - (i < 2), (1 << 29) - (i == 0 or i == 3)) \
.parent(5))
# Check the vertex neighbors of the corner of faces 0, 4, and 5.
cell_id = CellId.from_face_pos_level(0, 0, CellId.MAX_LEVEL)
neighbors = cell_id.get_vertex_neighbors(0)
neighbors.sort()
self.assertEqual(len(neighbors), 3)
self.assertEqual(neighbors[0], CellId.from_face_pos_level(0, 0, 0))
self.assertEqual(neighbors[1], CellId.from_face_pos_level(4, 0, 0))
self.assertEqual(neighbors[2], CellId.from_face_pos_level(5, 0, 0))
for i in xrange(NEIGHBORS_ITERATIONS):
cell_id = TestCellId.get_random_cell_id()
if cell_id.is_leaf():
cell_id = cell_id.parent()
max_diff = min(6, CellId.MAX_LEVEL - cell_id.level() - 1)
if max_diff == 0:
level = cell_id.level()
else:
level = cell_id.level() + random.randrange(max_diff)
self.check_all_neighbors(cell_id, level)
def check_all_neighbors(self, cell_id, level):
self.assertGreaterEqual(level, cell_id.level())
self.assertLess(level, CellId.MAX_LEVEL)
all, expected = set(), set()
neighbors = cell_id.get_all_neighbors(level)
all.update(neighbors)
for c in cell_id.children(level + 1):
all.add(c.parent())
expected.update(c.get_vertex_neighbors(level))
self.assertEqual(expected, all)
class LevelStats(object):
def __init__(self):
self.count = 0
self.min_area = 100
self.max_area = 0
self.avg_area = 0
self.min_width = 100
self.max_width = 0
self.avg_width = 0
self.min_edge = 100
self.max_edge = 0
self.avg_edge = 0
self.max_edge_aspect = 0
self.min_diag = 100
self.max_diag = 0
self.avg_diag = 0
self.max_diag_aspect = 0
self.min_angle_span = 100
self.max_angle_span = 0
self.avg_angle_span = 0
self.min_approx_ratio = 100
self.max_approx_ratio = 0
class TestCell(unittest.TestCase):
def setUp(self):
random.seed(20)
self.level_stats = [LevelStats()] * (CellId.MAX_LEVEL + 1)
def tearDown(self):
del self.level_stats
def testFaces(self):
edge_counts, vertex_counts = defaultdict(int), defaultdict(int)
for face in xrange(6):
cell_id = CellId.from_face_pos_level(face, 0, 0)
cell = Cell(cell_id)
self.assertEqual(cell_id, cell.id())
self.assertEqual(face, cell.face())
self.assertEqual(0, cell.level())
# Top-level faces have alternating orientations to get RHS
# coordinates.
self.assertEqual(face & sphere.SWAP_MASK, cell.orientation())
self.assertFalse(cell.is_leaf())
for k in xrange(4):
edge_counts[cell.get_edge_raw(k)] += 1
vertex_counts[cell.get_vertex_raw(k)] += 1
self.assertEqual(
cell.get_vertex_raw(k).dot_prod(cell.get_edge_raw(k)), 0.0)
self.assertEqual(
cell.get_vertex_raw((k + 1) & 3).dot_prod(
cell.get_edge_raw(k)), 0.0)
# this is assertEqual in C++ code
self.assertAlmostEqual(
cell.get_vertex_raw(k).cross_prod(
cell.get_vertex_raw((k + 1) & 3)) \
.normalize().dot_prod(cell.get_edge(k)), 1.0)
# Check that edges have multiplicity 2 and vertices have multiplicity 3.
for count in edge_counts.itervalues():
self.assertEqual(count, 2)
for count in vertex_counts.itervalues():
self.assertEqual(count, 3)
def gather_stats(self, cell):
s = self.level_stats[cell.level()]
exact_area = cell.exact_area()
approx_area = cell.approx_area()
min_edge = 100
max_edge = 0
avg_edge = 0
min_diag = 100
max_diag = 0
min_width = 100
max_width = 0
min_angle_span = 100
max_angle_span = 0
for i in xrange(4):
edge = cell.get_vertex_raw(i).angle(
cell.get_vertex_raw((i + 1) & 3))
min_edge = min(edge, min_edge)
max_edge = max(edge, max_edge)
# this could be wrong
avg_edge += 0.25 * edge
mid = cell.get_vertex_raw(i) + cell.get_vertex_raw((i + 1) & 3)
width = math.pi / 2.0 - mid.angle(cell.get_edge_raw(i ^ 2))
min_width = min(width, min_width)
max_width = max(width, max_width)
if i < 2:
diag = cell.get_vertex_raw(i).angle(cell.get_vertex_raw(i ^ 2))
min_diag = min(diag, min_diag)
max_diag = max(diag, max_diag)
angle_span = cell.get_edge_raw(i).angle(
-cell.get_edge_raw(i ^ 2))
min_angle_span = min(angle_span, min_angle_span)
max_angle_span = max(angle_span, max_angle_span)
s.count += 1
s.min_area = min(exact_area, s.min_area)
s.max_area = max(exact_area, s.max_area)
s.avg_area += exact_area
s.min_width = min(min_width, s.min_width)
s.max_width = max(max_width, s.max_width)
s.avg_width += 0.5 * (min_width + max_width)
s.min_edge = min(min_edge, s.min_edge)
s.max_edge = max(max_edge, s.max_edge)
s.avg_edge += avg_edge
s.max_edge_aspect = max(max_edge / min_edge, s.max_edge_aspect)
s.min_diag = min(min_diag, s.min_diag)
s.max_diag = max(max_diag, s.max_diag)
s.avg_diag += 0.5 * (min_diag + max_diag)
s.max_diag_aspect = max(max_diag /min_diag, s.max_diag_aspect)
s.min_angle_span = min(min_angle_span, s.min_angle_span)
s.max_angle_span = max(max_angle_span, s.max_angle_span)
s.avg_angle_span += 0.5 * (min_angle_span + max_angle_span)
approx_ratio = approx_area / exact_area
s.min_approx_ratio = min(approx_ratio, s.min_approx_ratio)
s.max_approx_ratio = max(approx_ratio, s.max_approx_ratio)
def check_subdivide(self, cell):
self.gather_stats(cell)
if cell.is_leaf():
return
children = tuple(cell.subdivide())
exact_area = 0
approx_area = 0
average_area = 0
for i, (child, child_id) \
in enumerate(izip(children, cell.id().children())):
exact_area += child.exact_area()
approx_area += child.approx_area()
average_area += child.average_area()
self.assertEqual(child.id(), child_id)
self.assertLess(
child.get_center().angle(child_id.to_point()), 1e-15)
direct = Cell(child_id)
self.assertEqual(direct.face(), child.face())
self.assertEqual(direct.level(), child.level())
self.assertEqual(direct.orientation(), child.orientation())
self.assertEqual(direct.get_center_raw(), child.get_center_raw())
for k in xrange(4):
self.assertEqual(direct.get_vertex_raw(k),
child.get_vertex_raw(k))
self.assertEqual(direct.get_edge_raw(k),
child.get_edge_raw(k))
# Test contains() and may_intersect().
self.assertTrue(cell.contains(child))
self.assertTrue(cell.may_intersect(child))
self.assertFalse(child.contains(cell))
self.assertTrue(cell.contains(child.get_center_raw()))
for j in xrange(4):
self.assertTrue(cell.contains(child.get_vertex_raw(j)))
if i != j:
# cannot get to pass test
self.assertFalse(
child.contains(children[j].get_center_raw()))
self.assertFalse(child.may_intersect(children[j]))
# Test get_cap_bound and get_rect_bound
parent_cap = cell.get_cap_bound()
parent_rect = cell.get_rect_bound()
if cell.contains(Point(0, 0, 1)) \
or cell.contains(Point(0, 0, -1)):
self.assertTrue(parent_rect.lon().is_full())
child_cap = children[i].get_cap_bound()
child_rect = children[i].get_rect_bound()
self.assertTrue(child_cap.contains(children[i].get_center()))
self.assertTrue(child_rect.contains(children[i].get_center_raw()))
self.assertTrue(parent_cap.contains(children[i].get_center()))
self.assertTrue(parent_rect.contains(children[i].get_center_raw()))
for j in xrange(4):
self.assertTrue(child_cap.contains(children[i].get_vertex(j)))
self.assertTrue(child_rect.contains(children[i].get_vertex(j)))
self.assertTrue(
child_rect.contains(children[i].get_vertex_raw(j)))
self.assertTrue(parent_cap.contains(children[i].get_vertex(j)))
self.assertTrue(parent_rect.contains(children[i].get_vertex(j)))
self.assertTrue(
parent_rect.contains(children[i].get_vertex_raw(j)))
if j != i:
# The bounding caps and rectangles should be tight
# enough so that they exclude at least two vertices of
# each adjacent cell.
cap_count = 0
rect_count = 0
for k in xrange(4):
if child_cap.contains(children[j].get_vertex(k)):
++cap_count
if child_rect.contains(children[j].get_vertex_raw(k)):
++rect_count
self.assertLessEqual(cap_count, 2)
if child_rect.lat_lo().radians > -math.pi / 2.0 \
and child_rect.lat_hi().radians < math.pi / 2.0:
# Bounding rectangles may be too large at the poles
# because the pole itself has an arb fixed longitude.
self.assertLessEqual(rect_count, 2)
force_subdivide = False
center = sphere.get_norm(children[i].face())
edge = center + sphere.get_u_axis(children[i].face())
corner = edge + sphere.get_v_axis(children[i].face())
for j in xrange(4):
p = children[i].get_vertex_raw(j)
if p == center or p == edge or p == corner:
force_subdivide = True
if force_subdivide or cell.level() < 5 or random.randrange(5) == 0:
self.check_subdivide(children[i])
self.assertLessEqual(
math.fabs(math.log(exact_area / cell.exact_area())),
math.fabs(math.log(1 + 1e-6)))
self.assertLessEqual(
math.fabs(math.log(approx_area / cell.approx_area())),
math.fabs(math.log(1.03)))
self.assertLessEqual(
math.fabs(math.log(average_area / cell.average_area())),
math.fabs(math.log(1 + 1e-15)))
def testSubdivide(self):
for face in xrange(6):
self.check_subdivide(Cell.from_face_pos_level(face, 0, 0))
class TestLineInterval(unittest.TestCase):
def check_interval_ops(self, x, y, expected):
self.assertEqual(expected[0] == 'T', x.contains(y))
self.assertEqual(expected[1] == 'T', x.interior_contains(y))
self.assertEqual(expected[2] == 'T', x.intersects(y))
self.assertEqual(expected[3] == 'T', x.interior_intersects(y))
def testBasic(self):
unit = LineInterval(0, 1)
negunit = LineInterval(-1, 0)
self.assertEqual(0, unit.lo())
self.assertEqual(1, unit.hi())
self.assertEqual(-1, negunit.bound(0))
self.assertEqual(0, negunit.bound(1))
# Keep immutable for now
#ten = LineInterval(0, 0)
#ten.set_hi(10)
#self.assertEqual(10, ten.hi())
half = LineInterval(0.5, 0.5)
self.assertFalse(unit.is_empty())
self.assertFalse(half.is_empty())
empty = LineInterval.empty()
self.assertTrue(empty.is_empty())
default_empty = LineInterval()
self.assertTrue(default_empty.is_empty())
self.assertEqual(empty.lo(), default_empty.lo())
self.assertEqual(empty.hi(), default_empty.hi())
self.assertEqual(unit.get_center(), 0.5)
self.assertEqual(half.get_center(), 0.5)
self.assertEqual(negunit.get_length(), 1.0)
self.assertLess(empty.get_length(), 0)
# Contains(double), InteriorContains(double)
self.assertTrue(unit.contains(0.5))
self.assertTrue(unit.interior_contains(0.5))
self.assertTrue(unit.contains(0))
self.assertFalse(unit.interior_contains(0))
self.assertTrue(unit.contains(1))
self.assertFalse(unit.interior_contains(1))
self.check_interval_ops(empty, empty, 'TTFF')
self.check_interval_ops(empty, unit, 'FFFF')
self.check_interval_ops(unit, half, 'TTTT')
self.check_interval_ops(unit, unit, 'TFTT')
self.check_interval_ops(unit, empty, 'TTFF')
self.check_interval_ops(unit, negunit, 'FFTF')
self.check_interval_ops(unit, LineInterval(0, 0.5), 'TFTT')
self.check_interval_ops(half, LineInterval(0, 0.5), 'FFTF')
# AddPont() should go here but trying to keep class immutable
# from_point_pair
self.assertEqual(LineInterval(4, 4), LineInterval.from_point_pair(4, 4))
self.assertEqual(LineInterval(-2, -1),
LineInterval.from_point_pair(-1, -2))
self.assertEqual(LineInterval(-5, 3),
LineInterval.from_point_pair(-5, 3))
# expanded
self.assertEqual(empty, empty.expanded(0.45))
self.assertEqual(LineInterval(-0.5, 1.5), unit.expanded(0.5))
# union, intersection
self.assertEqual(LineInterval(99, 100),
LineInterval(99, 100).union(empty))
self.assertEqual(LineInterval(99, 100),
empty.union(LineInterval(99, 100)))
self.assertTrue(
LineInterval(5, 3).union(LineInterval(0, -2).is_empty()))
self.assertTrue(
LineInterval(0, -2).union(LineInterval(5, 3)).is_empty())
self.assertEqual(unit, unit.union(unit))
self.assertEqual(LineInterval(-1, 1), unit.union(negunit))
self.assertEqual(LineInterval(-1, 1), negunit.union(unit))
self.assertEqual(unit, half.union(unit))
self.assertEqual(half, unit.intersection(half))
self.assertTrue(negunit.intersection(half).is_empty())
self.assertTrue(unit.intersection(empty).is_empty())
self.assertTrue(empty.intersection(unit).is_empty())
class TestSphereInterval(unittest.TestCase):
def setUp(self):
self.empty = SphereInterval.empty()
self.full = SphereInterval.full()
self.zero = SphereInterval(0, 0)
self.pi2 = SphereInterval(math.pi / 2.0, math.pi / 2.0)
self.pi = SphereInterval(math.pi, math.pi)
self.mipi = SphereInterval(-math.pi, -math.pi)
self.mipi2 = SphereInterval(-math.pi / 2.0, -math.pi / 2.0)
# Single quadrants:
self.quad1 = SphereInterval(0, math.pi / 2.0)
self.quad2 = SphereInterval(math.pi / 2.0, -math.pi)
self.quad3 = SphereInterval(math.pi, -math.pi / 2.0)
self.quad4 = SphereInterval(-math.pi / 2.0, 0)
# Quadrant pairs:
self.quad12 = SphereInterval(0, -math.pi)
self.quad23 = SphereInterval(math.pi / 2.0, -math.pi / 2.0)
self.quad34 = SphereInterval(-math.pi, 0)
self.quad41 = SphereInterval(-math.pi / 2.0, math.pi / 2.0)
# Quadrant triples:
self.quad123 = SphereInterval(0, -math.pi / 2.0)
self.quad234 = SphereInterval(math.pi / 2.0, 0)
self.quad341 = SphereInterval(math.pi, math.pi / 2.0)
self.quad412 = SphereInterval(-math.pi / 2.0, -math.pi)
# Small intervals around the midpoints between quadrants, such that
# the center of each interval is offset slightly CCW from the midpoint.
self.mid12 = SphereInterval(math.pi / 2 - 0.01, math.pi / 2 + 0.02)
self.mid23 = SphereInterval(math.pi - 0.01, -math.pi + 0.02)
self.mid34 = SphereInterval(-math.pi / 2.0 - 0.01,
-math.pi / 2.0 + 0.02)
self.mid41 = SphereInterval(-0.01, 0.02)
def testConstructorsAndAccessors(self):
self.assertEqual(self.quad12.lo(), 0)
self.assertEqual(self.quad12.hi(), math.pi)
self.assertEqual(self.quad34.bound(0), math.pi)
self.assertEqual(self.quad34.bound(1), 0)
self.assertEqual(self.pi.lo(), math.pi)
self.assertEqual(self.pi.hi(), math.pi)
# Check that [-Pi, -Pi] is normalized to [Pi, Pi].
self.assertEqual(self.mipi.lo(), math.pi)
self.assertEqual(self.mipi.hi(), math.pi)
self.assertEqual(self.quad23.lo(), math.pi / 2.0)
self.assertEqual(self.quad23.hi(), -math.pi / 2.0)
default_empty = SphereInterval()
self.assertTrue(default_empty.is_valid())
self.assertTrue(default_empty.is_empty())
self.assertEqual(self.empty.lo(), default_empty.lo())
self.assertEqual(self.empty.hi(), default_empty.hi())
# Should check intervals can be modified here
def testSimplePredicates(self):
# is_valid(), is_empty(), is_full(), is_inverted()
self.assertTrue(self.zero.is_valid() and not self.zero.is_empty() \
and not self.zero.is_full())
self.assertTrue(self.empty.is_valid() and self.empty.is_empty() \
and not self.empty.is_full())
self.assertTrue(self.empty.is_inverted());
self.assertTrue(self.full.is_valid() and not self.full.is_empty() \
and self.full.is_full())
self.assertTrue(not self.quad12.is_empty() \
and not self.quad12.is_full() and not self.quad12.is_inverted())
self.assertTrue(not self.quad23.is_empty() \
and not self.quad23.is_full() and self.quad23.is_inverted())
self.assertTrue(self.pi.is_valid() and not self.pi.is_empty() \
and not self.pi.is_inverted())
self.assertTrue(self.mipi.is_valid() and not self.mipi.is_empty() \
and not self.mipi.is_inverted())
def testGetCenter(self):
self.assertEqual(self.quad12.get_center(), math.pi / 2.0)
self.assertEqual(SphereInterval(3.1, 2.9).get_center(), 3.0 - math.pi)
self.assertEqual(SphereInterval(-2.9, -3.1).get_center(), math.pi - 3.0)
self.assertEqual(SphereInterval(2.1, -2.1).get_center(), math.pi)
self.assertEqual(self.pi.get_center(), math.pi)
self.assertEqual(self.mipi.get_center(), math.pi)
self.assertEqual(self.quad123.get_center(), 0.75 * math.pi)
def testGetLength(self):
self.assertEqual(self.quad12.get_length(), math.pi)
self.assertEqual(self.pi.get_length(), 0)
self.assertEqual(self.mipi.get_length(), 0)
self.assertEqual(self.quad123.get_length(), 1.5 * math.pi)
self.assertEqual(math.fabs(self.quad23.get_length()), math.pi)
self.assertEqual(self.full.get_length(), 2 * math.pi)
self.assertLess(self.empty.get_length(), 0)
def testComplement(self):
self.assertTrue(self.empty.complement().is_full());
self.assertTrue(self.full.complement().is_empty());
self.assertTrue(self.pi.complement().is_full());
self.assertTrue(self.mipi.complement().is_full());
self.assertTrue(self.zero.complement().is_full());
self.assertTrue(self.quad12.complement().approx_equals(self.quad34));
self.assertTrue(self.quad34.complement().approx_equals(self.quad12));
self.assertTrue(self.quad123.complement().approx_equals(self.quad4));
def testContains(self):
self.assertTrue(not self.empty.contains(0) \
and not self.empty.contains(math.pi) \
and not self.empty.contains(-math.pi))
self.assertTrue(not self.empty.interior_contains(math.pi) \
and not self.empty.interior_contains(-math.pi))
self.assertTrue(self.full.contains(0) and self.full.contains(math.pi) \
and self.full.contains(-math.pi))
self.assertTrue(self.full.interior_contains(math.pi) \
and self.full.interior_contains(-math.pi))
self.assertTrue(self.quad12.contains(0) \
and self.quad12.contains(math.pi) \
and self.quad12.contains(-math.pi))
self.assertTrue(self.quad12.interior_contains(math.pi / 2.0) \
and not self.quad12.interior_contains(0))
self.assertTrue(not self.quad12.interior_contains(math.pi) and
not self.quad12.interior_contains(-math.pi))
self.assertTrue(self.quad23.contains(math.pi / 2.0) \
and self.quad23.contains(-math.pi / 2.0))
self.assertTrue(self.quad23.contains(math.pi) \
and self.quad23.contains(-math.pi))
self.assertTrue(not self.quad23.contains(0))
self.assertTrue(not self.quad23.interior_contains(math.pi / 2.0) and \
not self.quad23.interior_contains(-math.pi / 2.0))
self.assertTrue(self.quad23.interior_contains(math.pi) \
and self.quad23.interior_contains(-math.pi))
self.assertTrue(not self.quad23.interior_contains(0))
self.assertTrue(self.pi.contains(math.pi) \
and self.pi.contains(-math.pi) and not self.pi.contains(0))
self.assertTrue(not self.pi.interior_contains(math.pi) \
and not self.pi.interior_contains(-math.pi))
self.assertTrue(self.mipi.contains(math.pi) \
and self.mipi.contains(-math.pi) and not self.mipi.contains(0))
self.assertTrue(not self.mipi.interior_contains(math.pi) \
and not self.mipi.interior_contains(-math.pi))
self.assertTrue(self.zero.contains(0) \
and not self.zero.interior_contains(0))
def check_interval_ops(self, x, y, expected_relation,
expected_union,
expected_intersection):
self.assertEqual(x.contains(y), expected_relation[0] == 'T')
self.assertEqual(x.interior_contains(y), expected_relation[1] == 'T')
self.assertEqual(x.intersects(y), expected_relation[2] == 'T')
self.assertEqual(x.interior_intersects(y), expected_relation[3] == 'T')
self.assertEqual(x.union(y).bounds(), expected_union.bounds())
self.assertEqual(x.intersection(y).bounds(),
expected_intersection.bounds())
self.assertEqual(x.contains(y), x.union(y) == x)
self.assertEqual(x.intersects(y), not x.intersection(y).is_empty())
#if y.lo() == y.hi():
# S1Interval r = x
# r.AddPoint(y.lo())
# self.assertEqual(r.bounds(), expected_union.bounds())
def testIntervalOps(self):
self.check_interval_ops(self.empty, self.empty,
"TTFF", self.empty, self.empty)
self.check_interval_ops(self.empty, self.full,
"FFFF", self.full, self.empty)
self.check_interval_ops(self.empty, self.zero,
"FFFF", self.zero, self.empty)
self.check_interval_ops(self.empty, self.pi,
"FFFF", self.pi, self.empty)
self.check_interval_ops(self.empty, self.mipi,
"FFFF", self.mipi, self.empty)
self.check_interval_ops(self.full, self.empty,
"TTFF", self.full, self.empty)
self.check_interval_ops(self.full, self.full,
"TTTT", self.full, self.full)
self.check_interval_ops(self.full, self.zero,
"TTTT", self.full, self.zero)
self.check_interval_ops(self.full, self.pi,
"TTTT", self.full, self.pi)
self.check_interval_ops(self.full, self.mipi,
"TTTT", self.full, self.mipi)
self.check_interval_ops(self.full, self.quad12,
"TTTT", self.full, self.quad12)
self.check_interval_ops(self.full, self.quad23,
"TTTT", self.full, self.quad23)
self.check_interval_ops(self.zero, self.empty,
"TTFF", self.zero, self.empty)
self.check_interval_ops(self.zero, self.full,
"FFTF", self.full, self.zero)
self.check_interval_ops(self.zero, self.zero,
"TFTF", self.zero, self.zero)
self.check_interval_ops(self.zero, self.pi,
"FFFF", SphereInterval(0, math.pi), self.empty)
self.check_interval_ops(self.zero, self.pi2,
"FFFF", self.quad1, self.empty)
self.check_interval_ops(self.zero, self.mipi,
"FFFF", self.quad12, self.empty)
self.check_interval_ops(self.zero, self.mipi2,
"FFFF", self.quad4, self.empty)
self.check_interval_ops(self.zero, self.quad12,
"FFTF", self.quad12, self.zero)
self.check_interval_ops(self.zero, self.quad23,
"FFFF", self.quad123, self.empty)
self.check_interval_ops(self.pi2, self.empty,
"TTFF", self.pi2, self.empty)
self.check_interval_ops(self.pi2, self.full,
"FFTF", self.full, self.pi2)
self.check_interval_ops(self.pi2, self.zero,
"FFFF", self.quad1, self.empty)
self.check_interval_ops(self.pi2, self.pi,
"FFFF", SphereInterval(math.pi / 2.0, math.pi), self.empty)
self.check_interval_ops(self.pi2, self.pi2,
"TFTF", self.pi2, self.pi2)
self.check_interval_ops(self.pi2, self.mipi,
"FFFF", self.quad2, self.empty)
self.check_interval_ops(self.pi2, self.mipi2,
"FFFF", self.quad23, self.empty)
self.check_interval_ops(self.pi2, self.quad12,
"FFTF", self.quad12, self.pi2)
self.check_interval_ops(self.pi2, self.quad23,
"FFTF", self.quad23, self.pi2)
self.check_interval_ops(self.pi, self.empty,
"TTFF", self.pi, self.empty)
self.check_interval_ops(self.pi, self.full,
"FFTF", self.full, self.pi)
self.check_interval_ops(self.pi, self.zero,
"FFFF", SphereInterval(math.pi, 0), self.empty)
self.check_interval_ops(self.pi, self.pi,
"TFTF", self.pi, self.pi)
self.check_interval_ops(self.pi, self.pi2,
"FFFF", SphereInterval(math.pi / 2.0, math.pi), self.empty)
self.check_interval_ops(self.pi, self.mipi,
"TFTF", self.pi, self.pi)
self.check_interval_ops(self.pi, self.mipi2,
"FFFF", self.quad3, self.empty)
self.check_interval_ops(self.pi, self.quad12,
"FFTF", SphereInterval(0, math.pi), self.pi)
self.check_interval_ops(self.pi, self.quad23,
"FFTF", self.quad23, self.pi)
self.check_interval_ops(self.mipi, self.empty,
"TTFF", self.mipi, self.empty)
self.check_interval_ops(self.mipi, self.full,
"FFTF", self.full, self.mipi)
self.check_interval_ops(self.mipi, self.zero,
"FFFF", self.quad34, self.empty)
self.check_interval_ops(self.mipi, self.pi,
"TFTF", self.mipi, self.mipi)
self.check_interval_ops(self.mipi, self.pi2,
"FFFF", self.quad2, self.empty)
self.check_interval_ops(self.mipi, self.mipi,
"TFTF", self.mipi, self.mipi)
self.check_interval_ops(self.mipi, self.mipi2,
"FFFF", SphereInterval(-math.pi, -math.pi / 2.0), self.empty)
self.check_interval_ops(self.mipi, self.quad12,
"FFTF", self.quad12, self.mipi)
self.check_interval_ops(self.mipi, self.quad23,
"FFTF", self.quad23, self.mipi)