def embedded_torus(nw, nh, stop=None, coord_gen=None):
assert nw > 2 and nh > 2
# Build dcel
mD, t1, b1 = embedded_cylinder(nw, nh, coord_gen=coord_gen)
if stop is None:
dcel.glue_boundary(mD, b1, t1)
else:
t1stop = t1.boundary_forward(stop)
dcel.glue_boundary(mD, t1, b1, t1stop)
# return:
# DCEL (mD, t1: starting edge)
return mD, t1
def embedded_torus(nw, nh, stop=None, coord_gen=None):
assert nw > 2 and nh > 2
# Build dcel
mD, t1, b1 = embedded_cylinder(nw, nh, coord_gen=coord_gen)
if stop is None:
dcel.glue_boundary(mD, b1, t1)
else:
t1stop = t1.boundary_forward(stop)
dcel.glue_boundary(mD, t1, b1, t1stop)
# return:
# DCEL (mD, t1: starting edge)
return mD, t1
def cylinder(w,h):
"""Generate DCEL for a triangulated cylinder of height h and circumference w"""
tops = []
bottoms = []
D = dcel.DCEL()
# Create h separate rings of height 1
for i in range(h):
RD,t,b = ring(w)
tops.append(t)
bottoms.append(b)
D |= RD
# Glue the rings top-to-bottom
for i in range(h-1):
dcel.glue_boundary(D, bottoms[i], tops[i + 1])
return D,tops[0],bottoms[-1]
def embedded_cylinder(nw, nh, coord_gen):
"""Generate DCEL for a triangulated cylinder of height h and circumference w"""
tops = []
bottoms = []
D = dcel.DCEL()
# Create h separate rings of height 1
for i in range(nh):
RD, t, b = embedded_ring(nw, i, coord_gen=coord_gen)
tops.append(t)
bottoms.append(b)
D |= RD
# Glue the rings top-to-bottom
for i in range(nh - 1):
dcel.glue_boundary(D, bottoms[i], tops[i + 1])
return D, tops[0], bottoms[-1]
def embedded_cylinder(nw, nh, coord_gen):
"""Generate DCEL for a triangulated cylinder of height h and circumference w"""
tops = []
bottoms = []
D = dcel.DCEL()
# Create h separate rings of height 1
for i in range(nh):
RD,t,b = embedded_ring(nw, i, coord_gen=coord_gen)
tops.append(t)
bottoms.append(b)
D |= RD
# Glue the rings top-to-bottom
for i in range(nh-1):
dcel.glue_boundary(D, bottoms[i], tops[i + 1])
return D,tops[0],bottoms[-1]
# \-D2-/ \-D5-/
D1,T1,B1 = cylinder(5,10)
D2,T2,B2 = cylinder(5,10)
D3,T3,B3 = cylinder(4,10)
D4,T4,B4 = cylinder(5,10)
D5,T5,B5 = cylinder(5,10)
D = D1 | D2 | D3 | D4 | D5
new_bdry_edge_12 = B1.boundary_forward(3)
new_bdry_edge_45 = B4.boundary_forward(3)
dcel.glue_boundary(D, B1, T2, new_bdry_edge_12) # a -> D1,D2 form pair of pants
dcel.glue_boundary(D, T1, B2) # b -> Now punctured torus
dcel.glue_boundary(D, B4, T5, new_bdry_edge_45) # c -> D4,D5 form pair of pants
dcel.glue_boundary(D, T4, B5) # d -> Now punctured torus
# Join the two punctured tori along cylinder D3
dcel.glue_boundary(D, new_bdry_edge_12, T3) # e
dcel.glue_boundary(D, B3, new_bdry_edge_45) # f
print('verts',len(D.V))
print('hedges',len(D.E))
print('faces',len(D.F))
topo = dcel.oriented_manifold_type(D)
for k in topo:
return np.real(M)
def hol_around_vertices(self, X):
return [self.hol_around_vertex(X, v) for v in self.V]
if __name__ == "__main__":
"""Find a KAT point for a one-holed torus with mirror boundary"""
import triangulations
import lsons
from collections import defaultdict
np.set_printoptions(suppress=True)
D, t, b = triangulations.cylinder(5, 5)
t2 = t.boundary_forward(2)
dcel.glue_boundary(D, t, b, t2)
chain_down = [t]
while True:
e = chain_down[-1]
a = e.tri_cw
b = a.vert_ccw
c = b.vert_ccw
chain_down += [a, b, c]
if c == t:
break
chain_right = [t]
while True:
e = chain_right[-1]
a = e.vert_ccw
return np.real(M)
def hol_around_vertices(self,X):
return [ self.hol_around_vertex(X,v) for v in self.V ]
if __name__=="__main__":
"""Find a KAT point for a one-holed torus with mirror boundary"""
import triangulations
import lsons
from collections import defaultdict
np.set_printoptions(suppress=True)
D,t,b = triangulations.cylinder(5,5)
t2 = t.boundary_forward(2)
dcel.glue_boundary(D, t, b, t2)
chain_down = [t]
while True:
e = chain_down[-1]
a = e.tri_cw
b = a.vert_ccw
c = b.vert_ccw
chain_down += [a,b,c]
if c == t:
break
chain_right = [t]
while True:
e = chain_right[-1]
a = e.vert_ccw