import math
import pytest
import networkx as nx
from networkx.algorithms.planar_drawing import triangulate_embedding
def test_graph1():
embedding_data = {0: [1, 2, 3], 1: [2, 0], 2: [3, 0, 1], 3: [2, 0]}
check_embedding_data(embedding_data)
def test_graph2():
embedding_data = {
0: [8, 6],
1: [2, 6, 9],
2: [8, 1, 7, 9, 6, 4],
3: [9],
4: [2],
5: [6, 8],
6: [9, 1, 0, 5, 2],
7: [9, 2],
8: [0, 2, 5],
9: [1, 6, 2, 7, 3],
}
check_embedding_data(embedding_data)
def test_circle_graph():
embedding_data = {
0: [1, 9],
1: [0, 2],
2: [1, 3],
3: [2, 4],
4: [3, 5],
5: [4, 6],
6: [5, 7],
7: [6, 8],
8: [7, 9],
9: [8, 0],
}
check_embedding_data(embedding_data)
def test_grid_graph():
embedding_data = {
(0, 1): [(0, 0), (1, 1), (0, 2)],
(1, 2): [(1, 1), (2, 2), (0, 2)],
(0, 0): [(0, 1), (1, 0)],
(2, 1): [(2, 0), (2, 2), (1, 1)],
(1, 1): [(2, 1), (1, 2), (0, 1), (1, 0)],
(2, 0): [(1, 0), (2, 1)],
(2, 2): [(1, 2), (2, 1)],
(1, 0): [(0, 0), (2, 0), (1, 1)],
(0, 2): [(1, 2), (0, 1)],
}
check_embedding_data(embedding_data)
def test_one_node_graph():
embedding_data = {0: []}
check_embedding_data(embedding_data)
def test_two_node_graph():
embedding_data = {0: [1], 1: [0]}
check_embedding_data(embedding_data)
def test_three_node_graph():
embedding_data = {0: [1, 2], 1: [0, 2], 2: [0, 1]}
check_embedding_data(embedding_data)
def test_multiple_component_graph1():
embedding_data = {0: [], 1: []}
check_embedding_data(embedding_data)
def test_multiple_component_graph2():
embedding_data = {0: [1, 2], 1: [0, 2], 2: [0, 1], 3: [4, 5], 4: [3, 5], 5: [3, 4]}
check_embedding_data(embedding_data)
def test_invalid_half_edge():
with pytest.raises(nx.NetworkXException):
embedding_data = {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2, 4], 4: [1, 2, 3]}
embedding = nx.PlanarEmbedding()
embedding.set_data(embedding_data)
nx.combinatorial_embedding_to_pos(embedding)
def test_triangulate_embedding1():
embedding = nx.PlanarEmbedding()
embedding.add_node(1)
expected_embedding = {1: []}
check_triangulation(embedding, expected_embedding)
def test_triangulate_embedding2():
embedding = nx.PlanarEmbedding()
embedding.connect_components(1, 2)
expected_embedding = {1: [2], 2: [1]}
check_triangulation(embedding, expected_embedding)
def check_triangulation(embedding, expected_embedding):
res_embedding, _ = triangulate_embedding(embedding, True)
assert (
res_embedding.get_data() == expected_embedding
), "Expected embedding incorrect"
res_embedding, _ = triangulate_embedding(embedding, False)
assert (
res_embedding.get_data() == expected_embedding
), "Expected embedding incorrect"
def check_embedding_data(embedding_data):
"""Checks that the planar embedding of the input is correct"""
embedding = nx.PlanarEmbedding()
embedding.set_data(embedding_data)
pos_fully = nx.combinatorial_embedding_to_pos(embedding, False)
msg = "Planar drawing does not conform to the embedding (fully triangulation)"
assert planar_drawing_conforms_to_embedding(embedding, pos_fully), msg
check_edge_intersections(embedding, pos_fully)
pos_internally = nx.combinatorial_embedding_to_pos(embedding, True)
msg = "Planar drawing does not conform to the embedding (internal triangulation)"
assert planar_drawing_conforms_to_embedding(embedding, pos_internally), msg
check_edge_intersections(embedding, pos_internally)
def is_close(a, b, rel_tol=1e-09, abs_tol=0.0):
# Check if float numbers are basically equal, for python >=3.5 there is
# function for that in the standard library
return abs(a - b) <= max(rel_tol * max(abs(a), abs(b)), abs_tol)
def point_in_between(a, b, p):
# checks if p is on the line between a and b
x1, y1 = a
x2, y2 = b
px, py = p
dist_1_2 = math.sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2)
dist_1_p = math.sqrt((x1 - px) ** 2 + (y1 - py) ** 2)
dist_2_p = math.sqrt((x2 - px) ** 2 + (y2 - py) ** 2)
return is_close(dist_1_p + dist_2_p, dist_1_2)
def check_edge_intersections(G, pos):
"""Check all edges in G for intersections.
Raises an exception if an intersection is found.
Parameters
----------
G : NetworkX graph
pos : dict
Maps every node to a tuple (x, y) representing its position
"""
for a, b in G.edges():
for c, d in G.edges():
# Check if end points are different
if a != c and b != d and b != c and a != d:
x1, y1 = pos[a]
x2, y2 = pos[b]
x3, y3 = pos[c]
x4, y4 = pos[d]
determinant = (x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4)
if determinant != 0: # the lines are not parallel
# calculate intersection point, see:
# https://en.wikipedia.org/wiki/Line%E2%80%93line_intersection
px = (x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (
x3 * y4 - y3 * x4
) / determinant
py = (x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (
x3 * y4 - y3 * x4
) / determinant
# Check if intersection lies between the points
if point_in_between(pos[a], pos[b], (px, py)) and point_in_between(
pos[c], pos[d], (px, py)
):
msg = f"There is an intersection at {px},{py}"
raise nx.NetworkXException(msg)
# Check overlap
msg = "A node lies on a edge connecting two other nodes"
if (
point_in_between(pos[a], pos[b], pos[c])
or point_in_between(pos[a], pos[b], pos[d])
or point_in_between(pos[c], pos[d], pos[a])
or point_in_between(pos[c], pos[d], pos[b])
):
raise nx.NetworkXException(msg)
# No edge intersection found
class Vector:
"""Compare vectors by their angle without loss of precision
All vectors in direction [0, 1] are the smallest.
The vectors grow in clockwise direction.
"""
__slots__ = ["x", "y", "node", "quadrant"]
def __init__(self, x, y, node):
self.x = x
self.y = y
self.node = node
if self.x >= 0 and self.y > 0:
self.quadrant = 1
elif self.x > 0 and self.y <= 0:
self.quadrant = 2
elif self.x <= 0 and self.y < 0:
self.quadrant = 3
else:
self.quadrant = 4
def __eq__(self, other):
return self.quadrant == other.quadrant and self.x * other.y == self.y * other.x
def __lt__(self, other):
if self.quadrant < other.quadrant:
return True
elif self.quadrant > other.quadrant:
return False
else:
return self.x * other.y < self.y * other.x
def __ne__(self, other):
return self != other
def __le__(self, other):
return not other < self
def __gt__(self, other):
return other < self
def __ge__(self, other):
return not self < other
def planar_drawing_conforms_to_embedding(embedding, pos):
"""Checks if pos conforms to the planar embedding
Returns true iff the neighbors are actually oriented in the orientation
specified of the embedding
"""
for v in embedding:
nbr_vectors = []
v_pos = pos[v]
for nbr in embedding[v]:
new_vector = Vector(pos[nbr][0] - v_pos[0], pos[nbr][1] - v_pos[1], nbr)
nbr_vectors.append(new_vector)
# Sort neighbors according to their phi angle
nbr_vectors.sort()
for idx, nbr_vector in enumerate(nbr_vectors):
cw_vector = nbr_vectors[(idx + 1) % len(nbr_vectors)]
ccw_vector = nbr_vectors[idx - 1]
if (
embedding[v][nbr_vector.node]["cw"] != cw_vector.node
or embedding[v][nbr_vector.node]["ccw"] != ccw_vector.node
):
return False
if cw_vector.node != nbr_vector.node and cw_vector == nbr_vector:
# Lines overlap
return False
if ccw_vector.node != nbr_vector.node and ccw_vector == nbr_vector:
# Lines overlap
return False
return True
