def __draw_dual_pivot__(G, pos, width, height, pivot, mapping, node_size, pivot_color, pivot_label):
"""
Given a pivot, annotate it with color and label (handling duplicate if necessary) in dual.
:param G: Graph.
:param pos: position in canvas.
:param pivot: pivot dart.
:param mapping:
:param node_size: size of nodes in drawing.
:param pivot_color: pivot dart color.
:param pivot_label:
:return: Nothing.
"""
# Use different color for pivot dart (Handle boundary duplication if necessary).
pivot_dups = resolve_boundary_darts(
mapping[pivot.dual.tail.name], mapping[pivot.dual.head.name]) if pivot != None else []
pivot_dups = __remove_boundary_to_boundary_darts__(pivot_dups, width, height)
nx.draw_spectral(G,node_size=node_size,edgelist=pivot_dups,width=3,edge_color=pivot_color,node_color='white')
# Label pivot dart with pivot_label.
nx.draw_networkx_edge_labels(G, pos, edge_labels=__pivot_labels__(pivot_dups, pivot_label), label_pos=0.5)
def __draw_primal_pivot__(G, pos, pivot, mapping, node_size, pivot_color, pivot_label):
"""
Given a pivot, annotate it with color and label (handling duplicate if necessary).
:param G: Graph.
:param pos: position in canvas.
:param pivot: pivot dart.
:param mapping:
:param node_size: size of nodes in drawing.
:param pivot_color: pivot dart color.
:param pivot_label:
:return: Nothing.
"""
# Use different color for pivot dart (Handle boundary duplication if necessary).
pivot_in_dups = resolve_boundary_darts(mapping[pivot.tail.name], mapping[pivot.head.name]) if \
pivot is not None else []
nx.draw_spectral(G,node_size=node_size,edgelist=pivot_in_dups,width=3,edge_color=pivot_color,arrows=True)
# Annotate pivot dart label with "in".
nx.draw_networkx_edge_labels(G, pos, edge_labels=__pivot_labels__(pivot_in_dups, pivot_label),
label_pos=0.5,arrows=True)
def draw_dual(grid, blue, red, pred, face_mapping, pivot_in=None, pivot_out=None, file=None):
"""
Draw dual grid. Note that we replicate boundary faces on visualization.
:param grid: Grid graph to draw.
:param blue: Vertices decreasing in distance.
:param red: Vertices increasing in distance.
:param pred: Predecessor pointer dictionary for current holy tree.
:param face_mapping: Mapping of faces to their boundary duplicates. {(i ,j) -> [(i, j), (a, b)], etc}
:param pivot_in: Pivoting in dart.
:param pivot_out: Pivoting out dart.
:param file: File to save the drawing.
:return: Nothing
"""
node_size=200
# Construct the width + 1 by height + 1 grid with directed edges.
(G, pos) = __grid_layout__(grid.width + 1, grid.height + 1)
blue_vertices, red_vertices = Set(blue), Set(red)
if (-1,-1) in blue_vertices:
blue_vertices.remove((-1, -1))
if (-1,-1) in red_vertices:
red_vertices.remove((-1, -1))
core = Set() # keep track of all the edges in the 2-core in the dual.
# blue: both head and tail are blue
# red: both head and tail are red
# green: active darts with blue tail and red head.
blue_darts, red_darts, green_darts = [], [], []
for u in grid.vertices:
for v in u.neighbors:
# u -> v in the primal Holy Tree, skip.
if pred[v] == u or pred[u] == v:
continue
# u -> v is not in original graph (for instance, (-1, -1)), then skip.
if u.name < (0,0) or v.name < (0,0):
continue
# u -> v has no dual defined, should not be the case.
if u.neighbors[v].dual == None:
print("No dual defined: {}".format(u.neighbors[v]))
continue
# Get the dual dart.
dd = u.neighbors[v].dual
core.add((min(dd.head.name, dd.tail.name), max(dd.head.name, dd.tail.name)))
# If both u, v are blue, then dual dart is blue.
if u.name in blue_vertices and v.name in blue_vertices:
blue_darts += resolve_boundary_darts(face_mapping[dd.tail.name], face_mapping[dd.head.name])
# If both u, v are red, then dual dart is blue.
elif u.name in red_vertices and v.name in red_vertices:
red_darts += resolve_boundary_darts(face_mapping[dd.tail.name], face_mapping[dd.head.name])
# If both u blue, v is red, then dual dart is green.
elif u.name in blue_vertices and v.name in red_vertices:
green_darts += resolve_boundary_darts(face_mapping[dd.tail.name], face_mapping[dd.head.name])
############################## Anchor ###########################
# Remove all hairs.
done = False
while not done:
total_removed = 0
for (t1, h1) in core:
count_t1 = 1
count_h1 = 1
for (t2, h2) in core:
if t1 == t2 and h1 == h2:
continue
if t1 == t2 or t1 == h2:
count_t1 += 1
if h1 == t2 or h1 == h2:
count_h1 += 1
if count_t1 == 1 or count_h1 == 1:
core.remove((t1, h1))
total_removed += 1
break
if total_removed == 0:
done = True
# count how many time each vertex appear.
count_vertex = {}
for (t, h) in core:
count_vertex[t] = count_vertex[t] + 1 if t in count_vertex else 1
count_vertex[h] = count_vertex[h] + 1 if h in count_vertex else 1
# Vertices appearing more than 2 are anchor vertices.
anchor_vertices = []
for v in count_vertex:
if count_vertex[v] > 2:
anchor_vertices.append(v)
anchors_points = []
for v in anchor_vertices:
anchors_points += face_mapping[v]
############################## Anchor ###########################
# Draw darts with colored labels. Note that boundary to boundary darts are removed to avoid duplicate boundary
# darts confusion.
nx.draw_spectral(G, node_size=node_size,
edgelist=__remove_boundary_to_boundary_darts__(red_darts, grid.width, grid.height),
width=2, edge_color='red', arrows=False)
nx.draw_spectral(G,node_size=node_size,
edgelist=__remove_boundary_to_boundary_darts__(blue_darts, grid.width, grid.height)
,width=2,edge_color='blue',arrows=False)
nx.draw_spectral(G,node_size=node_size,
edgelist=__remove_boundary_to_boundary_darts__(green_darts, grid.width, grid.height)
,width=2,edge_color='green',arrows=True)
# Override label vertices with boundary.
labels = __boundary_labels__(grid, face_mapping, anchors_points)
nx.draw_networkx_labels(G, pos, labels=labels, font_size=8)
__draw_dual_pivot__(G, pos, grid.width, grid.height, pivot_in, face_mapping, node_size, "purple", "i")
__draw_dual_pivot__(G, pos, grid.width, grid.height, pivot_out, face_mapping, node_size, "black", "o")
__draw_plot__(file)
def draw_primal(grid, sliding_dart, blue, red, pred, vertex_mapping, pivot_in=None, pivot_out=None, file=None):
"""
Draw primal grid. Note that we replicate boundary vertices on visualization.
:param grid: Grid graph to draw.
:param sliding_dart: Current root name -> Next root name.
:param blue: Vertices decreasing in distance.
:param red: Vertices increasing in distance.
:param pred: Predecessor pointer dictionary for current holy tree.
:param vertex_mapping: Mapping of vertex to its boundary duplicates. {(i ,j) -> [(i, j), (a, b)], etc}
:param pivot_in: Pivoting in dart.
:param pivot_out: Pivoting out dart.
:param file: File to save the drawing.
:return: Nothing
"""
node_size = 200
# Construct the width + 1 by height + 1 grid with directed edges.
(G, pos) = __grid_layout__(grid.width, grid.height)
# blue: distance decreasing
blue_vertices = expand_vertices_list(blue, vertex_mapping)
# red: distance increasing
red_vertices = expand_vertices_list(red, vertex_mapping)
blue_vertices, red_vertices = Set(blue_vertices), Set(red_vertices)
if (-1,-1) in blue_vertices:
blue_vertices.remove((-1, -1))
if (-1,-1) in red_vertices:
red_vertices.remove((-1, -1))
# blue: both head and tail are blue
# red: both head and tail are red
# green: active darts with blue tail and red head.
blue_darts, red_darts, green_darts = [], [], []
for v in pred:
u = pred[v]
if u != None and u.name in blue_vertices and v.name in blue_vertices:
blue_darts += resolve_boundary_darts(vertex_mapping[u.name], vertex_mapping[v.name])
if u != None and u.name in red_vertices and v.name in red_vertices:
red_darts += resolve_boundary_darts(vertex_mapping[u.name], vertex_mapping[v.name])
for u in grid.vertices:
for v in u.neighbors:
if u.name >= (0,0) and v.name >= (0,0) and u.name in blue_vertices and v.name in red_vertices:
green_darts += resolve_boundary_darts(vertex_mapping[u.name], vertex_mapping[v.name])
# Draw darts with colored labels.
nx.draw_spectral(G,node_size=node_size,edgelist=red_darts,width=2,edge_color='red',arrows=True)
nx.draw_spectral(G,node_size=node_size,edgelist=blue_darts,width=2,edge_color='blue',arrows=True)
nx.draw_spectral(G,node_size=node_size,edgelist=green_darts,width=2,edge_color='green',arrows=True)
# Override label vertices with boundary.
labels = __boundary_labels__(grid, vertex_mapping)
nx.draw_networkx_labels(G, pos,labels=labels,font_size=8,arrows=False)
# Annotate the sliding dart by dashed line when drawing.
nx.draw_spectral(G,node_size=node_size,
edgelist=resolve_boundary_darts(vertex_mapping[sliding_dart[0]], vertex_mapping[sliding_dart[1]]),
width=3,edge_color='black',style='dashed',arrows=False)
__draw_primal_pivot__(G, pos, pivot_in, vertex_mapping, node_size, "black", "i")
__draw_primal_pivot__(G, pos, pivot_out, vertex_mapping, node_size, "purple", "o")
# Color vertices with labels.
nx.draw_spectral(G,node_size=node_size,nodelist=blue_vertices,node_color='blue',arrows=False)
nx.draw_spectral(G,node_size=node_size,nodelist=red_vertices,node_color='red',arrows=False)
__draw_plot__(file)
