def components(self):
"""
Returns a list of the connected components of the multicurve
corresponding to the 1-cycle, each given as a OneCycle.
Assumes for simplicity that the weights are at most one and
the support of the cycle is a simple multicurve.
"""
assert all(abs(w) <= 1 for w in self.weights)
D = self.cellulation
G = Graph(multiedges=True)
for edge in D.edges:
if self.weights[edge.index] != 0:
i, j = [v.index for v in edge.vertices]
G.add_edge(i, j, edge.index)
assert G.num_verts() == G.num_edges()
ans = []
for H in G.connected_components_subgraphs():
weights = len(self.weights) * [0]
for i in H.edge_labels():
weights[i] = self.weights[i]
ans.append(OneCycle(self.cellulation, weights))
return ans
def check_orthogonal_diagonals(self, motion_types, active_NACs, extra_cycles_orthog_diag=[]):
r"""
Check the necessary conditions for orthogonal diagonals.
TODO:
return orthogonality_graph
"""
perp_by_NAC = [cycle for delta in active_NACs for cycle in self._orthogonal_diagonals[delta]]
deltoids = [cycle for cycle, t in motion_types.items() if t in ['e','o']]
orthogonalLines = []
for perpCycle in perp_by_NAC + deltoids + extra_cycles_orthog_diag:
orthogonalLines.append(Set([Set([perpCycle[0],perpCycle[2]]), Set([perpCycle[1],perpCycle[3]])]))
orthogonalityGraph = Graph(orthogonalLines, format='list_of_edges', multiedges=False)
n_edges = -1
while n_edges != orthogonalityGraph.num_edges():
n_edges = orthogonalityGraph.num_edges()
for perp_subgraph in orthogonalityGraph.connected_components_subgraphs():
isBipartite, partition = perp_subgraph.is_bipartite(certificate=True)
if isBipartite:
graph_0 = Graph([v.list() for v in partition if partition[v]==0])
graph_1 = Graph([v.list() for v in partition if partition[v]==1])
for comp_0 in graph_0.connected_components():
for comp_1 in graph_1.connected_components():
for e0 in Subsets(comp_0,2):
for e1 in Subsets(comp_1,2):
orthogonalityGraph.add_edge([Set(e0), Set(e1)])
else:
raise exceptions.RuntimeError('A component of the orthogonality graph is not bipartite!')
self._orthogonality_graph = orthogonalityGraph
check_again = False
H = {self._edge_ordered(u,v):None for u,v in self._graph.edges(labels=False)}
self._set_same_lengths(H, motion_types)
for c in motion_types:
if not orthogonalityGraph.has_edge(Set([c[0],c[2]]),Set([c[1],c[3]])):
continue
if motion_types[c]=='a': # inconsistent since antiparallel motion cannot have orthogonal diagonals
return False
elif motion_types[c]=='p': # this cycle must be rhombus
self._set_two_edge_same_lengths(H, c[0], c[1], c[2], c[3], 0)
self._set_two_edge_same_lengths(H, c[0], c[1], c[1], c[2], 0)
self._set_two_edge_same_lengths(H, c[0], c[1], c[0], c[3], 0)
check_again = True
for c in motion_types:
if motion_types[c]=='g':
labels = [H[self._edge_ordered(c[i-1],c[i])] for i in range(0,4)]
if (not None in labels
and ((len(Set(labels))==2 and labels.count(labels[0])==2)
or len(Set(labels))==1)):
return False
if (orthogonalityGraph.has_edge(Set([c[0],c[2]]),Set([c[1],c[3]]))
and True in [(H[self._edge_ordered(c[i-1], c[i])]==H[self._edge_ordered(c[i-2], c[i-1])]
and H[self._edge_ordered(c[i-1],c[i])]!= None) for i in range(0,4)]):
return False
if check_again:
for K23_edges in [Graph(self._graph).subgraph(k23_ver).edges(labels=False) for k23_ver in self._graph.induced_K23s()]:
if MotionClassifier._same_edge_lengths(H, K23_edges):
return False
return True