def mirror(link):
"""
Create the mirror image of the link, preserving link orientations and
component order.
"""
# Basically, we just mirror every crossing, but the particular data
# structures used make this a little involved.
new_crossings = dict()
for C in link.crossings:
C_new = Crossing(label=C.label)
C_new.sign = -C.sign
new_crossings[C] = C_new
def convert(C, c):
"""
Go from a crossing to the mirror, which requires the a rotation of the
entry points; the direction of rotation depends on the sign of
the crossing.
"""
return new_crossings[C], (c + C.sign) % 4
for A in link.crossings:
entry_points = [CEP.entry_point for CEP in A.entry_points()]
for a in entry_points:
B, b = A.adjacent[a]
B_new, b_new = convert(B, b)
B_new[b_new] = convert(A, a)
new_link = Link(new_crossings.values(),
check_planarity=False, build=False)
# Build the link components, starting in the same place as
# the original link.
component_starts = []
for component in link.link_components:
C_new, c_new = convert(*component[0])
component_starts.append( CrossingEntryPoint(C_new, c_new) )
new_link._build_components(component_starts)
return new_link
def link(self):
G = self.fat_graph
crossing_dict, slot_dict = {}, {}
for v in G.vertices:
c = Crossing(v[0])
c.make_tail(0)
if G.sign(v) == 1:
c.make_tail(3)
else:
c.make_tail(1)
c.orient()
crossing_dict[v] = c
if v.upper_pair() == (0, 2):
slot_dict[v] = (3, 0, 1, 2)
else:
slot_dict[v] = (2, 3, 0, 1) if G.flipped(v) else (0, 1, 2, 3)
for edge in G.edges:
v0, v1 = edge
s0, s1 = edge.slots
a0, a1 = slot_dict[v0][s0], slot_dict[v1][s1]
c0, c1 = crossing_dict[v0], crossing_dict[v1]
c0[a0] = c1[a1]
link = Link(list(crossing_dict.values()),
check_planarity=False,
build=False)
assert link.all_crossings_oriented()
component_starts = []
i = 1
for comp in self.code:
c = self[i]
if i == c[0]:
e = slot_dict[c][2] if G.flipped(c) else slot_dict[c][0]
else:
e = slot_dict[c][1]
ce = CrossingEntryPoint(crossing_dict[c], e)
component_starts.append(ce)
i += 2 * len(comp)
link._build_components(component_starts)
if not link.is_planar():
raise ValueError(
'DT code does not seem to define a *planar* diagram')
return link