def projection_0(self, kmax=1):
"""Projection of a coarse quad mesh to the closest two-colourable sub-spaces.
Parameters
----------
mesh : CoarseQuadMesh
A coarse quad mesh.
Returns
-------
results : dict
The combination pointing to the its result. If the combination is valid, the result is a tuple of the the two-colourable mesh, the two-colourable network, and the network vertex colors.
References
----------
.. [1] Oval et al., *Topology Finding of Two-Colourable Quad-Mesh Patterns in Structural Design*. Submitted.
"""
mesh = self.quad_mesh
# result for input mesh
vertices, edges = mesh.strip_graph()
if is_adjacency_two_colorable(adjacency_from_edges(edges)) is not None:
self.results = True
return True
results = {}
# guarantee valid kmax
n = mesh.number_of_strips()
if kmax < 1 or kmax > n:
kmax = n
t0 = time.time()
t1 = -float('inf')
t2 = -float('inf')
total_valid = 0
# start iteration
k = 0
discarding_combination = []
discarding_combination_type = {}
while k < kmax:
k += 1
to_continue = False
at_least_one_valid_k = False
# test all combinations of (n k) strips
for combination in itertools.combinations(mesh.strips(), k):
set_combi = set(combination)
# check results from potential previous sub-combinations
for disc_comb in discarding_combination:
if disc_comb.issubset(set_combi):
#if are_items_in_list(previous_combination, combination):
# if a sub-combination yielded an invalid topology do not pursue
if discarding_combination_type[tuple(
disc_comb)] == 'invalid shape topology':
results[
combination] = 'already invalid shape topology'
break
elif discarding_combination_type[tuple(
disc_comb)] == 'two-colourable':
results[combination] = 'already two-colourable'
break
if len(collateral_strip_deletions(mesh, combination)) > 0:
results[combination] = 'collateral deletions'
if len(total_boundary_deletions(mesh, combination)) > 0:
results[combination] = 'invalid shape topology'
discarding_combination.append(set(combination))
discarding_combination_type[tuple(
combination)] = 'invalid shape topology'
if combination in results:
continue
# delete strips in mesh and check validity
copy_mesh = mesh.copy()
#copy_mesh.collect_strips()
delete_strips(copy_mesh, combination, preserve_boundaries=True)
topological_validity = copy_mesh.is_manifold(
) and copy_mesh.euler() == mesh.euler()
if not topological_validity:
results[combination] = 'invalid shape topology'
discarding_combination.append(set(combination))
discarding_combination_type[tuple(
combination)] = 'invalid shape topology'
# delete strip vertices in network and check colourability
else:
#vertices, edges = copy_mesh.strip_graph()
new_vertices = {
vkey: xyz
for vkey, xyz in vertices.items()
if vkey not in combination
}
new_edges = [
(u, v) for u, v in edges
if u not in combination and v not in combination
]
two_colourability = is_adjacency_two_colorable(
adjacency_from_edges(new_edges))
if not two_colourability:
results[combination] = 'not two-colourable'
to_continue = True
else:
results[combination] = (copy_mesh, (new_vertices,
new_edges),
two_colourability)
discarding_combination.append(set(combination))
discarding_combination_type[tuple(
combination)] = 'two-colourable'
at_least_one_valid_k = True
total_valid += 1
if t1 < 0:
t1 = time.time()
if t2 < 0 and total_valid > 0 and not at_least_one_valid_k:
t2 = time.time()
if not to_continue:
break
t3 = time.time()
print(len(discarding_combination))
print(t3 - t0)
self.results = results
self.times = (t1 - t0, t2 - t0, t3 - t0)
def projection_4(self, kmax=1):
"""Projection of a coarse quad mesh to the closest two-colourable sub-spaces.
Parameters
----------
mesh : CoarseQuadMesh
A coarse quad mesh.
Returns
-------
results : dict
The combination pointing to the its result. If the combination is valid, the result is a tuple of the the two-colourable mesh, the two-colourable network, and the network vertex colors.
References
----------
.. [1] Oval et al., *Topology Finding of Two-Colourable Quad-Mesh Patterns in Structural Design*. Submitted.
"""
mesh = self.quad_mesh
vertices, edges = mesh.strip_graph()
if is_adjacency_two_colorable(adjacency_from_edges(edges)) is not None:
self.results = True
return True
results = {}
t0 = time.time()
k = 0
current_pool = [[skey] for skey in mesh.strips()]
while k < kmax:
k += 1
next_pool = []
#print(current_pool)
for combination in current_pool:
if len(combination) > 1:
combination = list(
set([i for item in combination for i in item]))
else:
combination = list(set(combination))
if len(collateral_strip_deletions(mesh, combination)) > 0:
continue
if len(total_boundary_deletions(mesh, combination)) > 0:
continue
# delete strips in mesh and check validity
copy_mesh = mesh.copy()
delete_strips(copy_mesh, combination, preserve_boundaries=True)
topological_validity = copy_mesh.is_manifold(
) and copy_mesh.euler() == mesh.euler()
if not topological_validity:
pass
# delete strip vertices in network and check colourability
else:
new_vertices = {
vkey: xyz
for vkey, xyz in vertices.items()
if vkey not in combination
}
new_edges = [
(u, v) for u, v in edges
if u not in combination and v not in combination
]
two_colourability = is_adjacency_two_colorable(
adjacency_from_edges(new_edges))
if not two_colourability:
next_pool.append(combination)
else:
results[tuple(combination)] = (copy_mesh,
(new_vertices,
new_edges),
two_colourability)
current_pool = itertools.combinations(next_pool, 2)
t1 = time.time()
print(t1 - t0)
self.results = results
def projection(self, kmax=1):
"""Projection of a coarse quad mesh to the closest two-colourable sub-spaces.
Parameters
----------
mesh : CoarseQuadMesh
A coarse quad mesh.
Returns
-------
results : dict
The combination pointing to the its result. If the combination is valid, the result is a tuple of the the two-colourable mesh, the two-colourable network, and the network vertex colors.
References
----------
.. [1] Oval et al., *Topology Finding of Two-Colourable Quad-Mesh Patterns in Structural Design*. Submitted.
"""
mesh = self.quad_mesh
# result for input mesh
vertices, edges = mesh.strip_graph()
if is_adjacency_two_colorable(adjacency_from_edges(edges)) is not None:
self.results = True
return True
results = {}
# guarantee valid kmax
n = mesh.number_of_strips()
if kmax < 1 or kmax > n:
kmax = n
t0 = time.time()
# start iteration
k = 0
while k < kmax:
k += 1
to_continue = False
# test all combinations of (n k) strips
for combination in itertools.combinations(mesh.strips(), k):
# check results from potential previous sub-combinations
for previous_combination in results:
if are_items_in_list(previous_combination, combination):
# if a sub-combination yielded an invalid topology do not pursue
if results[
previous_combination] == 'invalid shape topology':
results[
combination] = 'already invalid shape topology'
break
elif type(results[previous_combination]) == tuple:
results[combination] = 'already two-colourable'
break
if combination in results:
continue
if len(collateral_strip_deletions(mesh, combination)) > 0:
to_continue = True
continue
if len(total_boundary_deletions(mesh, combination)) > 0:
results[combination] = 'invalid shape topology'
continue
# delete strips in mesh and check validity
copy_mesh = mesh.copy()
copy_mesh.collect_strips()
delete_strips(copy_mesh, combination, preserve_boundaries=True)
topological_validity = copy_mesh.is_manifold(
) and copy_mesh.euler() == mesh.euler()
if not topological_validity:
results[combination] = 'invalid shape topology'
# delete strip vertices in network and check colourability
else:
vertices, edges = copy_mesh.strip_graph()
two_colourability = is_adjacency_two_colorable(
adjacency_from_edges(edges))
if not two_colourability:
results[combination] = 'not two-colourable'
to_continue = True
else:
results[combination] = (copy_mesh, (vertices, edges),
two_colourability)
if not to_continue:
break
t1 = time.time()
self.results = results
self.time = t1 - t0
def projection_2(self, kmax=1):
"""Projection of a coarse quad mesh to the closest two-colourable sub-spaces.
Parameters
----------
mesh : CoarseQuadMesh
A coarse quad mesh.
Returns
-------
results : dict
The combination pointing to the its result. If the combination is valid, the result is a tuple of the the two-colourable mesh, the two-colourable network, and the network vertex colors.
References
----------
.. [1] Oval et al., *Topology Finding of Two-Colourable Quad-Mesh Patterns in Structural Design*. Submitted.
"""
mesh = self.quad_mesh
# result for input mesh
vertices, edges = mesh.strip_graph()
if is_adjacency_two_colorable(adjacency_from_edges(edges)) is not None:
self.results = True
return True
results = {}
# guarantee valid kmax
n = mesh.number_of_strips()
if kmax < 1 or kmax > n:
kmax = n
t0 = time.time()
# start iteration
k = 0
discarding_combination = []
while k < kmax:
k += 1
to_continue = False
at_least_one_valid_k = False
# test all combinations of (n k) strips
for combination in itertools.combinations(mesh.strips(), k):
set_combi = set(combination)
# check results from potential previous sub-combinations
for disc_comb in discarding_combination:
if disc_comb.issubset(set_combi):
break
if len(collateral_strip_deletions(mesh, combination)) > 0:
to_continue = True
continue
if len(total_boundary_deletions(mesh, combination)) > 0:
discarding_combination.append(set(combination))
continue
# delete strips in mesh and check validity
copy_mesh = mesh.copy()
delete_strips(copy_mesh, combination, preserve_boundaries=True)
topological_validity = copy_mesh.is_manifold(
) and copy_mesh.euler() == mesh.euler()
if not topological_validity:
discarding_combination.append(set(combination))
# delete strip vertices in network and check colourability
else:
new_vertices = {
vkey: xyz
for vkey, xyz in vertices.items()
if vkey not in combination
}
new_edges = [
(u, v) for u, v in edges
if u not in combination and v not in combination
]
two_colourability = is_adjacency_two_colorable(
adjacency_from_edges(new_edges))
if not two_colourability:
to_continue = True
else:
results[combination] = (copy_mesh, (new_vertices,
new_edges),
two_colourability)
discarding_combination.append(set(combination))
if not to_continue:
break
t1 = time.time()
print(t1 - t0)
#print(results)
self.results = results