def comps_to_nx_planar_embedding(components):
"""Set of connected planar graphs (possibly derived) to nx.PlanarEmbedding."""
res = nx.PlanarEmbedding()
for g in components:
g = g.underive_all()
g = g.to_planar_embedding(relabel=False)
res = nx.PlanarEmbedding(nx.compose(res, g))
# Relabel once all the components are in the same graph.
# relabel_networkx(res)
return res
def test_missing_edge_orientation(self):
with pytest.raises(nx.NetworkXException):
embedding = nx.PlanarEmbedding()
embedding.add_edge(1, 2)
embedding.add_edge(2, 1)
# Invalid structure because the orientation of the edge was not set
embedding.check_structure()
def test_invalid_edge_orientation(self):
with pytest.raises(nx.NetworkXException):
embedding = nx.PlanarEmbedding()
embedding.add_half_edge_first(1, 2)
embedding.add_half_edge_first(2, 1)
embedding.add_edge(1, 3)
embedding.check_structure()
def test_not_fulfilling_euler_formula(self):
embedding = nx.PlanarEmbedding()
for i in range(5):
for j in range(5):
if i != j:
embedding.add_half_edge_first(i, j)
embedding.check_structure()
def test_not_fulfilling_euler_formula(self):
with pytest.raises(nx.NetworkXException):
embedding = nx.PlanarEmbedding()
for i in range(5):
for j in range(5):
if i != j:
embedding.add_half_edge_first(i, j)
embedding.check_structure()
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 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 get_dual(primal):
"""
Returns the dual of a planar embedding.
Parameters
----------
primal: nx.PlanarEmbedding
Returns
-------
primal_faces: dict
A dict whose values are lists representing facial walks of
the primal and whose keys are its dual nodes.
dual: nx.PlanarEmbedding
The dual of the primal.
dual_faces: dict
A dict whose values are lists representing facial walks of
the dual and whose keys are nodes of the primal.
"""
if not isinstance(primal, nx.PlanarEmbedding):
print("'primal' must be a planar embedding.")
# Constracting the dual embedding of 'primal'.
primal_faces = get_faces(primal)
dual = nx.PlanarEmbedding()
for tail, primal_face in primal_faces.items():
# Define a clockwize rotation around tail in dual nodes.
pre_head = None
for i in range(len(primal_face)):
u = primal_face[i]
v = primal_face[(i + 1) % len(primal_face)]
head = primal.edges[v, u]['dual_node']
dual.add_half_edge_cw(tail, head, pre_head)
pre_head = head
primal.edges[v, u]['right_half_edge'] = (tail, head)
dual.edges[tail, head]['dual_node'] = u
dual.edges[tail, head]['right_half_edge'] = (u, v)
# A face of 'dual' can be derived from
# clockwize rotation around a node of 'primal'.
dual.check_structure()
dual_faces = {}
for u in primal.nodes:
dual_face = []
for v in primal.neighbors_cw_order(u):
dual_face.append(primal.edges[u, v]['right_half_edge'][0])
dual_faces[u] = dual_face
return primal_faces, dual, dual_faces
def convert_pos_to_embedding(G, pos):
"""
Only straight line in G.
"""
emd = nx.PlanarEmbedding()
for node in G:
neigh_pos = {
neigh: (pos[neigh][0]-pos[node][0], pos[neigh][1]-pos[node][1]) for neigh in G[node]
}
neighbors_sorted = sorted(G.adj[node], key=lambda v: m.atan2(neigh_pos[v][1], neigh_pos[v][0])) # counter clockwise
last = None
for neigh in neighbors_sorted:
emd.add_half_edge_ccw(node, neigh, last)
last = neigh
emd.check_structure()
return emd
def main():
# Cycle graph
_, embedding = nx.check_planarity(nx.cycle_graph(20))
embedding_fully, _ = nx.triangulate_embedding(embedding, True)
diff_fully = nx.Graph(list(embedding_fully.edges - embedding.edges))
embedding_internal, _ = nx.triangulate_embedding(embedding, False)
diff_internal = nx.Graph(list(embedding_internal.edges - embedding.edges))
pos = nx.combinatorial_embedding_to_pos(embedding_fully)
nx.draw(diff_fully, pos, alpha=0.5, width=1, style="dotted", node_size=30)
nx.draw(embedding, pos, width=2 , node_size=30)
plt.savefig("drawing_cycle_fully_triangulated.png", format="PNG")
plt.show()
pos = nx.combinatorial_embedding_to_pos(embedding_internal)
nx.draw(diff_internal, pos, alpha=0.5, width=1, style="dotted", node_size=30)
nx.draw(embedding, pos, width=2, node_size=30)
plt.savefig("drawing_cycle_internally_triangulated.png", format="PNG")
plt.show()
# Other graph
G = nx.Graph([(1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (1, 4), (4, 3)])
is_planar, embedding = nx.check_planarity(G)
print(is_planar)
embedding_fully, _ = nx.triangulate_embedding(embedding, True)
diff_fully = nx.Graph(list(embedding_fully.edges - embedding.edges))
embedding_internal, _ = nx.triangulate_embedding(embedding, False)
diff_internal = nx.Graph(list(embedding_internal.edges - embedding.edges))
pos = nx.combinatorial_embedding_to_pos(embedding_fully)
nx.draw(diff_fully, pos, alpha=0.5, width=1, style="dotted", node_size=30)
nx.draw(embedding, pos, width=2, node_size=30)
plt.savefig("drawing_other_fully_triangulated.png", format="PNG")
plt.show()
pos = nx.combinatorial_embedding_to_pos(embedding_internal)
nx.draw(diff_internal, pos, alpha=0.5, width=1, style="dotted", node_size=30)
nx.draw(embedding, pos, width=2, node_size=30)
plt.savefig("drawing_other_internally_triangulated.png", format="PNG")
plt.show()
embedding_data = {0: [36, 42], 1: [], 2: [23, 16], 3: [19], 4: [23, 17], 5: [45, 18], 6: [42, 29, 40], 7: [48, 26, 32], 8: [15, 44, 23], 9: [11, 27], 10: [39, 11, 32, 47, 26, 15], 11: [10, 9], 12: [41, 34, 35], 13: [48], 14: [28, 45], 15: [34, 8, 10], 16: [2, 39, 21], 17: [4], 18: [5], 19: [22, 3], 20: [], 21: [16, 49], 22: [26, 47, 19], 23: [8, 2, 4], 24: [46], 25: [], 26: [7, 34, 10, 22, 38], 27: [9, 48], 28: [36, 41, 14], 29: [6], 30: [48], 31: [], 32: [7, 10, 46], 33: [48], 34: [12, 15, 26], 35: [12, 41], 36: [0, 28, 43], 37: [47], 38: [26], 39: [16, 10], 40: [6], 41: [28, 12, 35], 42: [44, 0, 6], 43: [36], 44: [8, 42], 45: [14, 5], 46: [32, 24], 47: [22, 10, 37], 48: [27, 7, 13, 30, 33], 49: [21]}
embedding = nx.PlanarEmbedding()
embedding.set_data(embedding_data)
pos = nx.combinatorial_embedding_to_pos(embedding, fully_triangulate=False)
nx.draw(embedding, pos, node_size=30)
plt.savefig("drawing_large_graph_internally_triangulated.png", format="PNG")
plt.show()
def get_planar_embedding(self):
"""only straight line in G."""
emd = nx.PlanarEmbedding()
for node in self.g:
neigh_pos = {
neigh: (self.pos[neigh][0] - self.pos[node][0],
self.pos[neigh][1] - self.pos[node][1])
for neigh in self.g[node]
}
neighes_sorted = sorted(
self.g.adj[node],
key=lambda v: math.atan2(neigh_pos[v][1], neigh_pos[v][0]
)) # counter clockwise
last = None
for neigh in neighes_sorted:
emd.add_half_edge_ccw(node, neigh, last)
last = neigh
emd.check_structure()
return emd
def get_radial(primal):
"""
Returns the dual and the radial of a planar embedding.
The radial graph of a planar embedding G is also known as the vertex-face map
whose vertices are the vertices of G together with the faces of G,
and whose edges correspond to the vertex-face incidence in G.
Parameters
----------
primal: nx.PlanarEmbedding
Returns
-------
dual: nx.PlanarEmbedding
The dual of the primal.
radial: nx.PlanarEmbedding
The radial of the primal.
"""
primal_faces, dual, dual_faces = get_dual(primal)
radial = nx.PlanarEmbedding()
for p in primal.nodes:
p_name = 'p' + str(p)
pre_d_name = None
for d in dual_faces[p]:
d_name = 'd' + str(d)
radial.add_half_edge_cw(p_name, d_name, pre_d_name)
pre_d_name = d_name
radial.nodes[p_name]['primal'] = True
radial.nodes[p_name]['original'] = p
for d in dual.nodes:
d_name = 'd' + str(d)
pre_p_name = None
for p in primal_faces[d]:
p_name = 'p' + str(p)
radial.add_half_edge_cw(d_name, p_name, pre_p_name)
pre_p_name = p_name
radial.nodes[d_name]['primal'] = False
radial.nodes[d_name]['original'] = d
radial.check_structure()
return dual, radial
def to_planar_embedding(self, relabel=True):
"""Converts to nx.PlanarEmbedding.
Returns
-------
PlanarEmbedding
"""
nodes = self.half_edge.node_dict()
embedding = nx.PlanarEmbedding()
# Loop over all nodes in the graph (node_nr).
for node in nodes:
embedding.add_node(node)
# Loop over all half-edges incident the the current node, in ccw order around the node.
reference_neighbour = None
for he in nodes[node]:
if he.opposite is None:
continue
embedding.add_half_edge_ccw(node, he.opposite.node_nr,
reference_neighbour)
reference_neighbour = he.opposite.node_nr
if relabel:
relabel_networkx(embedding)
return embedding
def test_unsuccessful_face_traversal(self):
with pytest.raises(nx.NetworkXException):
embedding = nx.PlanarEmbedding()
embedding.add_edge(1, 2, ccw=2, cw=3)
embedding.add_edge(2, 1, ccw=1, cw=3)
embedding.traverse_face(1, 2)
def test_successful_face_traversal(self):
embedding = nx.PlanarEmbedding()
embedding.add_half_edge_first(1, 2)
embedding.add_half_edge_first(2, 1)
face = embedding.traverse_face(1, 2)
assert face == [1, 2]
def test_connect_components(self):
embedding = nx.PlanarEmbedding()
embedding.connect_components(1, 2)
def test_missing_reference(self):
with pytest.raises(nx.NetworkXException):
embedding = nx.PlanarEmbedding()
embedding.add_half_edge_cw(1, 2, 3)
def test_missing_half_edge(self):
with pytest.raises(nx.NetworkXException):
embedding = nx.PlanarEmbedding()
embedding.add_half_edge_first(1, 2)
# Invalid structure because other half edge is missing
embedding.check_structure()
def triangulate_embedding(embedding, fully_triangulate=True):
"""Triangulates the embedding.
Traverses faces of the embedding and adds edges to a copy of the
embedding to triangulate it.
The method also ensures that the resulting graph is 2-connected by adding
edges if the same vertex is contained twice on a path around a face.
Parameters
----------
embedding : nx.PlanarEmbedding
The input graph must contain at least 3 nodes.
fully_triangulate : bool
If set to False the face with the most nodes is chooses as outer face.
This outer face does not get triangulated.
Returns
-------
(embedding, outer_face) : (nx.PlanarEmbedding, list) tuple
The element `embedding` is a new embedding containing all edges from
the input embedding and the additional edges to triangulate the graph.
The element `outer_face` is a list of nodes that lie on the outer face.
If the graph is fully triangulated these are three arbitrary connected
nodes.
"""
if len(embedding.nodes) <= 1:
return embedding, list(embedding.nodes)
embedding = nx.PlanarEmbedding(embedding)
# Get a list with a node for each connected component
component_nodes = [next(iter(x)) for x in nx.connected_components(embedding)]
# 1. Make graph a single component (add edge between components)
for i in range(len(component_nodes) - 1):
v1 = component_nodes[i]
v2 = component_nodes[i + 1]
embedding.connect_components(v1, v2)
# 2. Calculate faces, ensure 2-connectedness and determine outer face
outer_face = [] # A face with the most number of nodes
face_list = []
edges_visited = set() # Used to keep track of already visited faces
for v in embedding.nodes():
for w in embedding.neighbors_cw_order(v):
new_face = make_bi_connected(embedding, v, w, edges_visited)
if new_face:
# Found a new face
face_list.append(new_face)
if len(new_face) > len(outer_face):
# The face is a candidate to be the outer face
outer_face = new_face
# 3. Triangulate (internal) faces
for face in face_list:
if face is not outer_face or fully_triangulate:
# Triangulate this face
triangulate_face(embedding, face[0], face[1])
if fully_triangulate:
v1 = outer_face[0]
v2 = outer_face[1]
v3 = embedding[v2][v1]["ccw"]
outer_face = [v1, v2, v3]
return embedding, outer_face
def test_smoke_planar_layout_embedding_input(self):
embedding = nx.PlanarEmbedding()
embedding.set_data({0: [1, 2], 1: [0, 2], 2: [0, 1]})
nx.planar_layout(embedding)
def test_missing_edge_orientation(self):
embedding = nx.PlanarEmbedding()
embedding.add_edge(1, 2)
embedding.add_edge(2, 1)
# Invalid structure because the orientation of the edge was not set
embedding.check_structure()
def test_invalid_half_edge():
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 get_star_embedding(n):
embedding = nx.PlanarEmbedding()
for i in range(1, n):
embedding.add_half_edge_first(0, i)
embedding.add_half_edge_first(i, 0)
return embedding
def test_missing_half_edge(self):
embedding = nx.PlanarEmbedding()
embedding.add_half_edge_first(1, 2)
# Invalid structure because other half edge is missing
embedding.check_structure()
def test_invalid_edge_orientation(self):
embedding = nx.PlanarEmbedding()
embedding.add_half_edge_first(1, 2)
embedding.add_half_edge_first(2, 1)
embedding.add_edge(1, 3)
embedding.check_structure()
def test_triangulate_embedding2():
embedding = nx.PlanarEmbedding()
embedding.connect_components(1, 2)
expected_embedding = {1: [2], 2: [1]}
check_triangulation(embedding, expected_embedding)
def test_missing_reference(self):
embedding = nx.PlanarEmbedding()
embedding.add_half_edge_cw(1, 2, 3)
def test_triangulate_embedding1():
embedding = nx.PlanarEmbedding()
embedding.add_node(1)
expected_embedding = {1: []}
check_triangulation(embedding, expected_embedding)
def test_unsuccessful_face_traversal(self):
embedding = nx.PlanarEmbedding()
embedding.add_edge(1, 2, ccw=2, cw=3)
embedding.add_edge(2, 1, ccw=1, cw=3)
embedding.traverse_face(1, 2)
