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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/planarity.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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1
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1 from collections import defaultdict
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2 import networkx as nx
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3
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4 __all__ = ["check_planarity", "PlanarEmbedding"]
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5
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6
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7 def check_planarity(G, counterexample=False):
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8 """Check if a graph is planar and return a counterexample or an embedding.
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9
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10 A graph is planar iff it can be drawn in a plane without
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11 any edge intersections.
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12
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13 Parameters
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14 ----------
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15 G : NetworkX graph
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16 counterexample : bool
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17 A Kuratowski subgraph (to proof non planarity) is only returned if set
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18 to true.
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19
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20 Returns
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21 -------
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22 (is_planar, certificate) : (bool, NetworkX graph) tuple
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23 is_planar is true if the graph is planar.
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24 If the graph is planar `certificate` is a PlanarEmbedding
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25 otherwise it is a Kuratowski subgraph.
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26
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27 Notes
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28 -----
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29 A (combinatorial) embedding consists of cyclic orderings of the incident
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30 edges at each vertex. Given such an embedding there are multiple approaches
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31 discussed in literature to drawing the graph (subject to various
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32 constraints, e.g. integer coordinates), see e.g. [2].
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33
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34 The planarity check algorithm and extraction of the combinatorial embedding
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35 is based on the Left-Right Planarity Test [1].
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36
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37 A counterexample is only generated if the corresponding parameter is set,
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38 because the complexity of the counterexample generation is higher.
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39
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40 References
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41 ----------
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42 .. [1] Ulrik Brandes:
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43 The Left-Right Planarity Test
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44 2009
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45 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.217.9208
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46 .. [2] Takao Nishizeki, Md Saidur Rahman:
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47 Planar graph drawing
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48 Lecture Notes Series on Computing: Volume 12
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49 2004
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50 """
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51
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52 planarity_state = LRPlanarity(G)
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53 embedding = planarity_state.lr_planarity()
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54 if embedding is None:
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55 # graph is not planar
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56 if counterexample:
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57 return False, get_counterexample(G)
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58 else:
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59 return False, None
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60 else:
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61 # graph is planar
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62 return True, embedding
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63
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64
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65 def check_planarity_recursive(G, counterexample=False):
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66 """Recursive version of :meth:`check_planarity`."""
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67 planarity_state = LRPlanarity(G)
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68 embedding = planarity_state.lr_planarity_recursive()
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69 if embedding is None:
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70 # graph is not planar
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71 if counterexample:
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72 return False, get_counterexample_recursive(G)
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73 else:
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74 return False, None
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75 else:
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76 # graph is planar
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77 return True, embedding
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78
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79
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80 def get_counterexample(G):
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81 """Obtains a Kuratowski subgraph.
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82
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83 Raises nx.NetworkXException if G is planar.
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84
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85 The function removes edges such that the graph is still not planar.
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86 At some point the removal of any edge would make the graph planar.
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87 This subgraph must be a Kuratowski subgraph.
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88
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89 Parameters
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90 ----------
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91 G : NetworkX graph
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92
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93 Returns
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94 -------
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95 subgraph : NetworkX graph
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96 A Kuratowski subgraph that proves that G is not planar.
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97
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98 """
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99 # copy graph
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100 G = nx.Graph(G)
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101
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102 if check_planarity(G)[0]:
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103 raise nx.NetworkXException("G is planar - no counter example.")
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104
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105 # find Kuratowski subgraph
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106 subgraph = nx.Graph()
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107 for u in G:
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108 nbrs = list(G[u])
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109 for v in nbrs:
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110 G.remove_edge(u, v)
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111 if check_planarity(G)[0]:
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112 G.add_edge(u, v)
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113 subgraph.add_edge(u, v)
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114
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115 return subgraph
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116
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117
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118 def get_counterexample_recursive(G):
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119 """Recursive version of :meth:`get_counterexample`.
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120 """
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121
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122 # copy graph
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123 G = nx.Graph(G)
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124
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125 if check_planarity_recursive(G)[0]:
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126 raise nx.NetworkXException("G is planar - no counter example.")
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127
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128 # find Kuratowski subgraph
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129 subgraph = nx.Graph()
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130 for u in G:
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131 nbrs = list(G[u])
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132 for v in nbrs:
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133 G.remove_edge(u, v)
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134 if check_planarity_recursive(G)[0]:
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135 G.add_edge(u, v)
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136 subgraph.add_edge(u, v)
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137
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138 return subgraph
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139
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140
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141 class Interval(object):
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142 """Represents a set of return edges.
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143
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144 All return edges in an interval induce a same constraint on the contained
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145 edges, which means that all edges must either have a left orientation or
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146 all edges must have a right orientation.
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147 """
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148
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149 def __init__(self, low=None, high=None):
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150 self.low = low
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151 self.high = high
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152
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153 def empty(self):
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154 """Check if the interval is empty"""
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155 return self.low is None and self.high is None
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156
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157 def copy(self):
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158 """Returns a copy of this interval"""
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159 return Interval(self.low, self.high)
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160
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161 def conflicting(self, b, planarity_state):
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162 """Returns True if interval I conflicts with edge b"""
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163 return (not self.empty() and
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164 planarity_state.lowpt[self.high] > planarity_state.lowpt[b])
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165
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166
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167 class ConflictPair(object):
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168 """Represents a different constraint between two intervals.
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169
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170 The edges in the left interval must have a different orientation than
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171 the one in the right interval.
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172 """
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173
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174 def __init__(self, left=Interval(), right=Interval()):
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175 self.left = left
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176 self.right = right
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177
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178 def swap(self):
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179 """Swap left and right intervals"""
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180 temp = self.left
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181 self.left = self.right
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182 self.right = temp
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183
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184 def lowest(self, planarity_state):
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185 """Returns the lowest lowpoint of a conflict pair"""
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186 if self.left.empty():
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187 return planarity_state.lowpt[self.right.low]
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188 if self.right.empty():
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189 return planarity_state.lowpt[self.left.low]
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190 return min(planarity_state.lowpt[self.left.low],
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191 planarity_state.lowpt[self.right.low])
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192
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193
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194 def top_of_stack(l):
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195 """Returns the element on top of the stack."""
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196 if not l:
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197 return None
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198 return l[-1]
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199
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200
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201 class LRPlanarity(object):
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202 """A class to maintain the state during planarity check."""
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203 __slots__ = [
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204 'G', 'roots', 'height', 'lowpt', 'lowpt2', 'nesting_depth',
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205 'parent_edge', 'DG', 'adjs', 'ordered_adjs', 'ref', 'side', 'S',
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206 'stack_bottom', 'lowpt_edge', 'left_ref', 'right_ref', 'embedding'
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207 ]
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208
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209 def __init__(self, G):
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210 # copy G without adding self-loops
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211 self.G = nx.Graph()
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212 self.G.add_nodes_from(G.nodes)
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213 for e in G.edges:
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214 if e[0] != e[1]:
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215 self.G.add_edge(e[0], e[1])
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216
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217 self.roots = []
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218
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219 # distance from tree root
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220 self.height = defaultdict(lambda: None)
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221
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222 self.lowpt = {} # height of lowest return point of an edge
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223 self.lowpt2 = {} # height of second lowest return point
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224 self.nesting_depth = {} # for nesting order
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225
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226 # None -> missing edge
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227 self.parent_edge = defaultdict(lambda: None)
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228
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229 # oriented DFS graph
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230 self.DG = nx.DiGraph()
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231 self.DG.add_nodes_from(G.nodes)
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232
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233 self.adjs = {}
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234 self.ordered_adjs = {}
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235
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236 self.ref = defaultdict(lambda: None)
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237 self.side = defaultdict(lambda: 1)
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238
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239 # stack of conflict pairs
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240 self.S = []
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241 self.stack_bottom = {}
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242 self.lowpt_edge = {}
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243
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244 self.left_ref = {}
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245 self.right_ref = {}
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246
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247 self.embedding = PlanarEmbedding()
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248
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249 def lr_planarity(self):
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250 """Execute the LR planarity test.
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251
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252 Returns
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253 -------
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254 embedding : dict
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255 If the graph is planar an embedding is returned. Otherwise None.
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256 """
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257 if self.G.order() > 2 and self.G.size() > 3 * self.G.order() - 6:
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258 # graph is not planar
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259 return None
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260
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261 # make adjacency lists for dfs
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262 for v in self.G:
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263 self.adjs[v] = list(self.G[v])
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264
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265 # orientation of the graph by depth first search traversal
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266 for v in self.G:
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267 if self.height[v] is None:
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268 self.height[v] = 0
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269 self.roots.append(v)
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270 self.dfs_orientation(v)
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271
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272 # Free no longer used variables
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273 self.G = None
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274 self.lowpt2 = None
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275 self.adjs = None
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276
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277 # testing
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278 for v in self.DG: # sort the adjacency lists by nesting depth
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279 # note: this sorting leads to non linear time
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280 self.ordered_adjs[v] = sorted(
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281 self.DG[v], key=lambda x: self.nesting_depth[(v, x)])
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282 for v in self.roots:
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283 if not self.dfs_testing(v):
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284 return None
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285
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286 # Free no longer used variables
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287 self.height = None
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288 self.lowpt = None
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289 self.S = None
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290 self.stack_bottom = None
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291 self.lowpt_edge = None
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292
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293 for e in self.DG.edges:
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294 self.nesting_depth[e] = self.sign(e) * self.nesting_depth[e]
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295
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296 self.embedding.add_nodes_from(self.DG.nodes)
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297 for v in self.DG:
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298 # sort the adjacency lists again
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299 self.ordered_adjs[v] = sorted(
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300 self.DG[v], key=lambda x: self.nesting_depth[(v, x)])
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301 # initialize the embedding
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302 previous_node = None
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303 for w in self.ordered_adjs[v]:
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304 self.embedding.add_half_edge_cw(v, w, previous_node)
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305 previous_node = w
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306
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307 # Free no longer used variables
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308 self.DG = None
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309 self.nesting_depth = None
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310 self.ref = None
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311
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312 # compute the complete embedding
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313 for v in self.roots:
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314 self.dfs_embedding(v)
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315
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316 # Free no longer used variables
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317 self.roots = None
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318 self.parent_edge = None
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319 self.ordered_adjs = None
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320 self.left_ref = None
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321 self.right_ref = None
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322 self.side = None
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323
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324 return self.embedding
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325
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326 def lr_planarity_recursive(self):
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327 """Recursive version of :meth:`lr_planarity`."""
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328 if self.G.order() > 2 and self.G.size() > 3 * self.G.order() - 6:
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329 # graph is not planar
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330 return None
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331
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332 # orientation of the graph by depth first search traversal
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333 for v in self.G:
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334 if self.height[v] is None:
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335 self.height[v] = 0
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336 self.roots.append(v)
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337 self.dfs_orientation_recursive(v)
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338
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339 # Free no longer used variable
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340 self.G = None
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341
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342 # testing
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343 for v in self.DG: # sort the adjacency lists by nesting depth
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344 # note: this sorting leads to non linear time
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345 self.ordered_adjs[v] = sorted(
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346 self.DG[v], key=lambda x: self.nesting_depth[(v, x)])
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347 for v in self.roots:
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348 if not self.dfs_testing_recursive(v):
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349 return None
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350
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351 for e in self.DG.edges:
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352 self.nesting_depth[e] = (self.sign_recursive(e) *
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353 self.nesting_depth[e])
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354
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355 self.embedding.add_nodes_from(self.DG.nodes)
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356 for v in self.DG:
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357 # sort the adjacency lists again
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358 self.ordered_adjs[v] = sorted(
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359 self.DG[v], key=lambda x: self.nesting_depth[(v, x)])
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360 # initialize the embedding
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361 previous_node = None
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362 for w in self.ordered_adjs[v]:
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363 self.embedding.add_half_edge_cw(v, w, previous_node)
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364 previous_node = w
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365
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366 # compute the complete embedding
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367 for v in self.roots:
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368 self.dfs_embedding_recursive(v)
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369
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370 return self.embedding
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371
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372 def dfs_orientation(self, v):
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373 """Orient the graph by DFS, compute lowpoints and nesting order.
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374 """
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375 # the recursion stack
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376 dfs_stack = [v]
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377 # index of next edge to handle in adjacency list of each node
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378 ind = defaultdict(lambda: 0)
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379 # boolean to indicate whether to skip the initial work for an edge
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380 skip_init = defaultdict(lambda: False)
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381
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382 while dfs_stack:
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383 v = dfs_stack.pop()
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384 e = self.parent_edge[v]
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385
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386 for w in self.adjs[v][ind[v]:]:
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387 vw = (v, w)
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388
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389 if not skip_init[vw]:
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390 if (v, w) in self.DG.edges or (w, v) in self.DG.edges:
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391 ind[v] += 1
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diff changeset
392 continue # the edge was already oriented
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
393
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
394 self.DG.add_edge(v, w) # orient the edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
395
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
396 self.lowpt[vw] = self.height[v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
397 self.lowpt2[vw] = self.height[v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
398 if self.height[w] is None: # (v, w) is a tree edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
399 self.parent_edge[w] = vw
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
400 self.height[w] = self.height[v] + 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
401
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
402 dfs_stack.append(v) # revisit v after finishing w
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
403 dfs_stack.append(w) # visit w next
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
404 skip_init[vw] = True # don't redo this block
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
405 break # handle next node in dfs_stack (i.e. w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
406 else: # (v, w) is a back edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
407 self.lowpt[vw] = self.height[w]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
408
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
409 # determine nesting graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
410 self.nesting_depth[vw] = 2 * self.lowpt[vw]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
411 if self.lowpt2[vw] < self.height[v]: # chordal
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
412 self.nesting_depth[vw] += 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
413
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
414 # update lowpoints of parent edge e
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
415 if e is not None:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
416 if self.lowpt[vw] < self.lowpt[e]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
417 self.lowpt2[e] = min(self.lowpt[e], self.lowpt2[vw])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
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418 self.lowpt[e] = self.lowpt[vw]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
419 elif self.lowpt[vw] > self.lowpt[e]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
420 self.lowpt2[e] = min(self.lowpt2[e], self.lowpt[vw])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
421 else:
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parents:
diff changeset
422 self.lowpt2[e] = min(self.lowpt2[e], self.lowpt2[vw])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
423
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
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424 ind[v] += 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
425
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parents:
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426 def dfs_orientation_recursive(self, v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
427 """Recursive version of :meth:`dfs_orientation`."""
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guerler
parents:
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428 e = self.parent_edge[v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
429 for w in self.G[v]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
430 if (v, w) in self.DG.edges or (w, v) in self.DG.edges:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
431 continue # the edge was already oriented
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parents:
diff changeset
432 vw = (v, w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
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433 self.DG.add_edge(v, w) # orient the edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
434
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
435 self.lowpt[vw] = self.height[v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
436 self.lowpt2[vw] = self.height[v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
437 if self.height[w] is None: # (v, w) is a tree edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
438 self.parent_edge[w] = vw
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
439 self.height[w] = self.height[v] + 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
440 self.dfs_orientation_recursive(w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
441 else: # (v, w) is a back edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
442 self.lowpt[vw] = self.height[w]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
443
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
444 # determine nesting graph
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
445 self.nesting_depth[vw] = 2 * self.lowpt[vw]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
446 if self.lowpt2[vw] < self.height[v]: # chordal
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guerler
parents:
diff changeset
447 self.nesting_depth[vw] += 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
448
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
449 # update lowpoints of parent edge e
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
450 if e is not None:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
451 if self.lowpt[vw] < self.lowpt[e]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
452 self.lowpt2[e] = min(self.lowpt[e], self.lowpt2[vw])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
453 self.lowpt[e] = self.lowpt[vw]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
454 elif self.lowpt[vw] > self.lowpt[e]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
455 self.lowpt2[e] = min(self.lowpt2[e], self.lowpt[vw])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
456 else:
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parents:
diff changeset
457 self.lowpt2[e] = min(self.lowpt2[e], self.lowpt2[vw])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
458
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
459 def dfs_testing(self, v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
460 """Test for LR partition."""
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
461 # the recursion stack
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
462 dfs_stack = [v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
463 # index of next edge to handle in adjacency list of each node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
464 ind = defaultdict(lambda: 0)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
465 # boolean to indicate whether to skip the initial work for an edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
466 skip_init = defaultdict(lambda: False)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
467
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
468 while dfs_stack:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
469 v = dfs_stack.pop()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
470 e = self.parent_edge[v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
471 # to indicate whether to skip the final block after the for loop
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
472 skip_final = False
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
473
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
474 for w in self.ordered_adjs[v][ind[v]:]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
475 ei = (v, w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
476
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
477 if not skip_init[ei]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
478 self.stack_bottom[ei] = top_of_stack(self.S)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
479
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
480 if ei == self.parent_edge[w]: # tree edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
481 dfs_stack.append(v) # revisit v after finishing w
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
482 dfs_stack.append(w) # visit w next
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
483 skip_init[ei] = True # don't redo this block
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
484 skip_final = True # skip final work after breaking
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
485 break # handle next node in dfs_stack (i.e. w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
486 else: # back edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
487 self.lowpt_edge[ei] = ei
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
488 self.S.append(ConflictPair(right=Interval(ei, ei)))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
489
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
490 # integrate new return edges
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
491 if self.lowpt[ei] < self.height[v]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
492 if w == self.ordered_adjs[v][0]: # e_i has return edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
493 self.lowpt_edge[e] = self.lowpt_edge[ei]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
494 else: # add constraints of e_i
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
495 if not self.add_constraints(ei, e):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
496 # graph is not planar
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
497 return False
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
498
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
499 ind[v] += 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
500
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
501 if not skip_final:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
502 # remove back edges returning to parent
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
503 if e is not None: # v isn't root
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
504 self.remove_back_edges(e)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
505
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
506 return True
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
507
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
508 def dfs_testing_recursive(self, v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
509 """Recursive version of :meth:`dfs_testing`."""
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
510 e = self.parent_edge[v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
511 for w in self.ordered_adjs[v]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
512 ei = (v, w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
513 self.stack_bottom[ei] = top_of_stack(self.S)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
514 if ei == self.parent_edge[w]: # tree edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
515 if not self.dfs_testing_recursive(w):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
516 return False
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
517 else: # back edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
518 self.lowpt_edge[ei] = ei
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
519 self.S.append(ConflictPair(right=Interval(ei, ei)))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
520
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
521 # integrate new return edges
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
522 if self.lowpt[ei] < self.height[v]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
523 if w == self.ordered_adjs[v][0]: # e_i has return edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
524 self.lowpt_edge[e] = self.lowpt_edge[ei]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
525 else: # add constraints of e_i
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
526 if not self.add_constraints(ei, e):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
527 # graph is not planar
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
528 return False
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
529
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
530 # remove back edges returning to parent
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
531 if e is not None: # v isn't root
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
532 self.remove_back_edges(e)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
533 return True
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
534
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
535 def add_constraints(self, ei, e):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
536 P = ConflictPair()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
537 # merge return edges of e_i into P.right
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
538 while True:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
539 Q = self.S.pop()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
540 if not Q.left.empty():
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
541 Q.swap()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
542 if not Q.left.empty(): # not planar
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
543 return False
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
544 if self.lowpt[Q.right.low] > self.lowpt[e]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
545 # merge intervals
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
546 if P.right.empty(): # topmost interval
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
547 P.right = Q.right.copy()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
548 else:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
549 self.ref[P.right.low] = Q.right.high
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
550 P.right.low = Q.right.low
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
551 else: # align
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
552 self.ref[Q.right.low] = self.lowpt_edge[e]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
553 if top_of_stack(self.S) == self.stack_bottom[ei]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
554 break
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
555 # merge conflicting return edges of e_1,...,e_i-1 into P.L
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
556 while (top_of_stack(self.S).left.conflicting(ei, self) or
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
557 top_of_stack(self.S).right.conflicting(ei, self)):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
558 Q = self.S.pop()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
559 if Q.right.conflicting(ei, self):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
560 Q.swap()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
561 if Q.right.conflicting(ei, self): # not planar
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
562 return False
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
563 # merge interval below lowpt(e_i) into P.R
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
564 self.ref[P.right.low] = Q.right.high
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
565 if Q.right.low is not None:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
566 P.right.low = Q.right.low
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
567
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
568 if P.left.empty(): # topmost interval
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
569 P.left = Q.left.copy()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
570 else:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
571 self.ref[P.left.low] = Q.left.high
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
572 P.left.low = Q.left.low
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
573
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
574 if not (P.left.empty() and P.right.empty()):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
575 self.S.append(P)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
576 return True
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
577
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
578 def remove_back_edges(self, e):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
579 u = e[0]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
580 # trim back edges ending at parent u
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
581 # drop entire conflict pairs
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
582 while self.S and top_of_stack(self.S).lowest(self) == self.height[u]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
583 P = self.S.pop()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
584 if P.left.low is not None:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
585 self.side[P.left.low] = -1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
586
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
587 if self.S: # one more conflict pair to consider
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
588 P = self.S.pop()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
589 # trim left interval
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
590 while P.left.high is not None and P.left.high[1] == u:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
591 P.left.high = self.ref[P.left.high]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
592 if P.left.high is None and P.left.low is not None:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
593 # just emptied
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
594 self.ref[P.left.low] = P.right.low
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
595 self.side[P.left.low] = -1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
596 P.left.low = None
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
597 # trim right interval
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
598 while P.right.high is not None and P.right.high[1] == u:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
599 P.right.high = self.ref[P.right.high]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
600 if P.right.high is None and P.right.low is not None:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
601 # just emptied
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
602 self.ref[P.right.low] = P.left.low
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
603 self.side[P.right.low] = -1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
604 P.right.low = None
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
605 self.S.append(P)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
606
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
607 # side of e is side of a highest return edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
608 if self.lowpt[e] < self.height[u]: # e has return edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
609 hl = top_of_stack(self.S).left.high
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
610 hr = top_of_stack(self.S).right.high
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
611
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
612 if hl is not None and (
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
613 hr is None or self.lowpt[hl] > self.lowpt[hr]):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
614 self.ref[e] = hl
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
615 else:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
616 self.ref[e] = hr
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
617
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
618 def dfs_embedding(self, v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
619 """Completes the embedding."""
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
620 # the recursion stack
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
621 dfs_stack = [v]
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
622 # index of next edge to handle in adjacency list of each node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
623 ind = defaultdict(lambda: 0)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
624
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
625 while dfs_stack:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
626 v = dfs_stack.pop()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
627
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
628 for w in self.ordered_adjs[v][ind[v]:]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
629 ind[v] += 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
630 ei = (v, w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
631
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
632 if ei == self.parent_edge[w]: # tree edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
633 self.embedding.add_half_edge_first(w, v)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
634 self.left_ref[v] = w
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
635 self.right_ref[v] = w
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
636
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
637 dfs_stack.append(v) # revisit v after finishing w
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
638 dfs_stack.append(w) # visit w next
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
639 break # handle next node in dfs_stack (i.e. w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
640 else: # back edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
641 if self.side[ei] == 1:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
642 self.embedding.add_half_edge_cw(w, v,
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643 self.right_ref[w])
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644 else:
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645 self.embedding.add_half_edge_ccw(w, v,
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646 self.left_ref[w])
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647 self.left_ref[w] = v
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648
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649 def dfs_embedding_recursive(self, v):
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650 """Recursive version of :meth:`dfs_embedding`."""
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651 for w in self.ordered_adjs[v]:
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652 ei = (v, w)
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653 if ei == self.parent_edge[w]: # tree edge
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654 self.embedding.add_half_edge_first(w, v)
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655 self.left_ref[v] = w
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656 self.right_ref[v] = w
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657 self.dfs_embedding_recursive(w)
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658 else: # back edge
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659 if self.side[ei] == 1:
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660 # place v directly after right_ref[w] in embed. list of w
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661 self.embedding.add_half_edge_cw(w, v, self.right_ref[w])
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662 else:
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663 # place v directly before left_ref[w] in embed. list of w
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664 self.embedding.add_half_edge_ccw(w, v, self.left_ref[w])
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665 self.left_ref[w] = v
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666
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667 def sign(self, e):
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668 """Resolve the relative side of an edge to the absolute side."""
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669 # the recursion stack
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670 dfs_stack = [e]
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671 # dict to remember reference edges
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672 old_ref = defaultdict(lambda: None)
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673
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674 while dfs_stack:
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675 e = dfs_stack.pop()
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676
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677 if self.ref[e] is not None:
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678 dfs_stack.append(e) # revisit e after finishing self.ref[e]
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679 dfs_stack.append(self.ref[e]) # visit self.ref[e] next
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680 old_ref[e] = self.ref[e] # remember value of self.ref[e]
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681 self.ref[e] = None
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682 else:
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683 self.side[e] *= self.side[old_ref[e]]
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684
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685 return self.side[e]
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686
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687 def sign_recursive(self, e):
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688 """Recursive version of :meth:`sign`."""
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689 if self.ref[e] is not None:
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690 self.side[e] = self.side[e] * self.sign_recursive(self.ref[e])
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691 self.ref[e] = None
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692 return self.side[e]
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693
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694
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695 class PlanarEmbedding(nx.DiGraph):
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696 """Represents a planar graph with its planar embedding.
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697
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698 The planar embedding is given by a `combinatorial embedding
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699 <https://en.wikipedia.org/wiki/Graph_embedding#Combinatorial_embedding>`_.
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700
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701 **Neighbor ordering:**
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702
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703 In comparison to a usual graph structure, the embedding also stores the
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704 order of all neighbors for every vertex.
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705 The order of the neighbors can be given in clockwise (cw) direction or
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706 counterclockwise (ccw) direction. This order is stored as edge attributes
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707 in the underlying directed graph. For the edge (u, v) the edge attribute
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708 'cw' is set to the neighbor of u that follows immediately after v in
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709 clockwise direction.
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710
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711 In order for a PlanarEmbedding to be valid it must fulfill multiple
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712 conditions. It is possible to check if these conditions are fulfilled with
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713 the method :meth:`check_structure`.
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714 The conditions are:
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715
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716 * Edges must go in both directions (because the edge attributes differ)
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717 * Every edge must have a 'cw' and 'ccw' attribute which corresponds to a
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diff changeset
718 correct planar embedding.
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719 * A node with non zero degree must have a node attribute 'first_nbr'.
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720
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721 As long as a PlanarEmbedding is invalid only the following methods should
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722 be called:
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723
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724 * :meth:`add_half_edge_ccw`
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725 * :meth:`add_half_edge_cw`
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726 * :meth:`connect_components`
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727 * :meth:`add_half_edge_first`
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diff changeset
728
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729 Even though the graph is a subclass of nx.DiGraph, it can still be used
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730 for algorithms that require undirected graphs, because the method
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diff changeset
731 :meth:`is_directed` is overridden. This is possible, because a valid
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732 PlanarGraph must have edges in both directions.
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diff changeset
733
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734 **Half edges:**
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735
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736 In methods like `add_half_edge_ccw` the term "half-edge" is used, which is
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737 a term that is used in `doubly connected edge lists
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738 <https://en.wikipedia.org/wiki/Doubly_connected_edge_list>`_. It is used
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diff changeset
739 to emphasize that the edge is only in one direction and there exists
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740 another half-edge in the opposite direction.
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741 While conventional edges always have two faces (including outer face) next
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742 to them, it is possible to assign each half-edge *exactly one* face.
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743 For a half-edge (u, v) that is orientated such that u is below v then the
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diff changeset
744 face that belongs to (u, v) is to the right of this half-edge.
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745
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746 Examples
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747 --------
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748
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749 Create an embedding of a star graph (compare `nx.star_graph(3)`):
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750
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751 >>> G = nx.PlanarEmbedding()
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752 >>> G.add_half_edge_cw(0, 1, None)
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753 >>> G.add_half_edge_cw(0, 2, 1)
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754 >>> G.add_half_edge_cw(0, 3, 2)
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755 >>> G.add_half_edge_cw(1, 0, None)
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756 >>> G.add_half_edge_cw(2, 0, None)
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757 >>> G.add_half_edge_cw(3, 0, None)
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diff changeset
758
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759 Alternatively the same embedding can also be defined in counterclockwise
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diff changeset
760 orientation. The following results in exactly the same PlanarEmbedding:
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761
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762 >>> G = nx.PlanarEmbedding()
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763 >>> G.add_half_edge_ccw(0, 1, None)
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diff changeset
764 >>> G.add_half_edge_ccw(0, 3, 1)
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765 >>> G.add_half_edge_ccw(0, 2, 3)
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diff changeset
766 >>> G.add_half_edge_ccw(1, 0, None)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
767 >>> G.add_half_edge_ccw(2, 0, None)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
768 >>> G.add_half_edge_ccw(3, 0, None)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
769
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
770 After creating a graph, it is possible to validate that the PlanarEmbedding
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
771 object is correct:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
772
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
773 >>> G.check_structure()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
774
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
775 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
776
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
777 def get_data(self):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
778 """Converts the adjacency structure into a better readable structure.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
779
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
780 Returns
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
781 -------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
782 embedding : dict
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
783 A dict mapping all nodes to a list of neighbors sorted in
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
784 clockwise order.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
785
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
786 See Also
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
787 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
788 set_data
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
789
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
790 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
791 embedding = dict()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
792 for v in self:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
793 embedding[v] = list(self.neighbors_cw_order(v))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
794 return embedding
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
795
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
796 def set_data(self, data):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
797 """Inserts edges according to given sorted neighbor list.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
798
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
799 The input format is the same as the output format of get_data().
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
800
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
801 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
802 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
803 data : dict
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
804 A dict mapping all nodes to a list of neighbors sorted in
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
805 clockwise order.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
806
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
807 See Also
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
808 --------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
809 get_data
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
810
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
811 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
812 for v in data:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
813 for w in reversed(data[v]):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
814 self.add_half_edge_first(v, w)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
815
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
816 def neighbors_cw_order(self, v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
817 """Generator for the neighbors of v in clockwise order.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
818
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
819 Parameters
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
820 ----------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
821 v : node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
822
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
823 Yields
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
824 ------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
825 node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
826
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
827 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
828 if len(self[v]) == 0:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
829 # v has no neighbors
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
830 return
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
831 start_node = self.nodes[v]['first_nbr']
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
832 yield start_node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
833 current_node = self[v][start_node]['cw']
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
834 while start_node != current_node:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
835 yield current_node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
836 current_node = self[v][current_node]['cw']
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
837
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
838 def check_structure(self):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
839 """Runs without exceptions if this object is valid.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
840
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
841 Checks that the following properties are fulfilled:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
842
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
843 * Edges go in both directions (because the edge attributes differ).
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
844 * Every edge has a 'cw' and 'ccw' attribute which corresponds to a
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
845 correct planar embedding.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
846 * A node with a degree larger than 0 has a node attribute 'first_nbr'.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
847
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
848 Running this method verifies that the underlying Graph must be planar.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
849
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
850 Raises
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
851 ------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
852 nx.NetworkXException
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
853 This exception is raised with a short explanation if the
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
854 PlanarEmbedding is invalid.
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
855 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
856 # Check fundamental structure
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
857 for v in self:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
858 try:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
859 sorted_nbrs = set(self.neighbors_cw_order(v))
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
860 except KeyError:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
861 msg = "Bad embedding. " \
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
862 "Missing orientation for a neighbor of {}".format(v)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
863 raise nx.NetworkXException(msg)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
864
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
865 unsorted_nbrs = set(self[v])
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
866 if sorted_nbrs != unsorted_nbrs:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
867 msg = "Bad embedding. Edge orientations not set correctly."
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
868 raise nx.NetworkXException(msg)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
869 for w in self[v]:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
870 # Check if opposite half-edge exists
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
871 if not self.has_edge(w, v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
872 msg = "Bad embedding. Opposite half-edge is missing."
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
873 raise nx.NetworkXException(msg)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
874
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
875 # Check planarity
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
876 counted_half_edges = set()
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
877 for component in nx.connected_components(self):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
878 if len(component) == 1:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
879 # Don't need to check single node component
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
880 continue
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
881 num_nodes = len(component)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
882 num_half_edges = 0
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
883 num_faces = 0
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
884 for v in component:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
885 for w in self.neighbors_cw_order(v):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
886 num_half_edges += 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
887 if (v, w) not in counted_half_edges:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
888 # We encountered a new face
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
889 num_faces += 1
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
890 # Mark all half-edges belonging to this face
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
891 self.traverse_face(v, w, counted_half_edges)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
892 num_edges = num_half_edges // 2 # num_half_edges is even
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
893 if num_nodes - num_edges + num_faces != 2:
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
894 # The result does not match Euler's formula
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
895 msg = "Bad embedding. The graph does not match Euler's formula"
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
896 raise nx.NetworkXException(msg)
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
897
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
898 def add_half_edge_ccw(self, start_node, end_node, reference_neighbor):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
899 """Adds a half-edge from start_node to end_node.
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parents:
diff changeset
900
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parents:
diff changeset
901 The half-edge is added counter clockwise next to the existing half-edge
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guerler
parents:
diff changeset
902 (start_node, reference_neighbor).
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parents:
diff changeset
903
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parents:
diff changeset
904 Parameters
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parents:
diff changeset
905 ----------
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parents:
diff changeset
906 start_node : node
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parents:
diff changeset
907 Start node of inserted edge.
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parents:
diff changeset
908 end_node : node
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parents:
diff changeset
909 End node of inserted edge.
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diff changeset
910 reference_neighbor: node
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diff changeset
911 End node of reference edge.
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diff changeset
912
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diff changeset
913 Raises
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diff changeset
914 ------
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parents:
diff changeset
915 nx.NetworkXException
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
916 If the reference_neighbor does not exist.
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diff changeset
917
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diff changeset
918 See Also
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diff changeset
919 --------
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diff changeset
920 add_half_edge_cw
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diff changeset
921 connect_components
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
922 add_half_edge_first
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diff changeset
923
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diff changeset
924 """
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diff changeset
925 if reference_neighbor is None:
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diff changeset
926 # The start node has no neighbors
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parents:
diff changeset
927 self.add_edge(start_node, end_node) # Add edge to graph
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parents:
diff changeset
928 self[start_node][end_node]['cw'] = end_node
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guerler
parents:
diff changeset
929 self[start_node][end_node]['ccw'] = end_node
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parents:
diff changeset
930 self.nodes[start_node]['first_nbr'] = end_node
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diff changeset
931 else:
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diff changeset
932 ccw_reference = self[start_node][reference_neighbor]['ccw']
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diff changeset
933 self.add_half_edge_cw(start_node, end_node, ccw_reference)
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diff changeset
934
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parents:
diff changeset
935 if reference_neighbor == self.nodes[start_node].get('first_nbr',
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diff changeset
936 None):
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parents:
diff changeset
937 # Update first neighbor
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parents:
diff changeset
938 self.nodes[start_node]['first_nbr'] = end_node
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diff changeset
939
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diff changeset
940 def add_half_edge_cw(self, start_node, end_node, reference_neighbor):
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
941 """Adds a half-edge from start_node to end_node.
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diff changeset
942
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parents:
diff changeset
943 The half-edge is added clockwise next to the existing half-edge
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
guerler
parents:
diff changeset
944 (start_node, reference_neighbor).
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diff changeset
945
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diff changeset
946 Parameters
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diff changeset
947 ----------
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parents:
diff changeset
948 start_node : node
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parents:
diff changeset
949 Start node of inserted edge.
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diff changeset
950 end_node : node
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diff changeset
951 End node of inserted edge.
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diff changeset
952 reference_neighbor: node
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diff changeset
953 End node of reference edge.
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diff changeset
954
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diff changeset
955 Raises
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diff changeset
956 ------
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
957 nx.NetworkXException
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
958 If the reference_neighbor does not exist.
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diff changeset
959
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diff changeset
960 See Also
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diff changeset
961 --------
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diff changeset
962 add_half_edge_ccw
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diff changeset
963 connect_components
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diff changeset
964 add_half_edge_first
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diff changeset
965 """
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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diff changeset
966 self.add_edge(start_node, end_node) # Add edge to graph
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diff changeset
967
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diff changeset
968 if reference_neighbor is None:
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diff changeset
969 # The start node has no neighbors
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parents:
diff changeset
970 self[start_node][end_node]['cw'] = end_node
56ad4e20f292 "planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
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parents:
diff changeset
971 self[start_node][end_node]['ccw'] = end_node
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parents:
diff changeset
972 self.nodes[start_node]['first_nbr'] = end_node
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guerler
parents:
diff changeset
973 return
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diff changeset
974
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diff changeset
975 if reference_neighbor not in self[start_node]:
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parents:
diff changeset
976 raise nx.NetworkXException(
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diff changeset
977 "Cannot add edge. Reference neighbor does not exist")
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978
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979 # Get half-edge at the other side
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980 cw_reference = self[start_node][reference_neighbor]['cw']
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981 # Alter half-edge data structures
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diff changeset
982 self[start_node][reference_neighbor]['cw'] = end_node
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parents:
diff changeset
983 self[start_node][end_node]['cw'] = cw_reference
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diff changeset
984 self[start_node][cw_reference]['ccw'] = end_node
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diff changeset
985 self[start_node][end_node]['ccw'] = reference_neighbor
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diff changeset
986
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987 def connect_components(self, v, w):
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diff changeset
988 """Adds half-edges for (v, w) and (w, v) at some position.
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diff changeset
989
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diff changeset
990 This method should only be called if v and w are in different
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diff changeset
991 components, or it might break the embedding.
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diff changeset
992 This especially means that if `connect_components(v, w)`
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diff changeset
993 is called it is not allowed to call `connect_components(w, v)`
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diff changeset
994 afterwards. The neighbor orientations in both directions are
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diff changeset
995 all set correctly after the first call.
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diff changeset
996
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997 Parameters
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998 ----------
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999 v : node
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1000 w : node
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1001
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1002 See Also
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1003 --------
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1004 add_half_edge_ccw
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diff changeset
1005 add_half_edge_cw
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1006 add_half_edge_first
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diff changeset
1007 """
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diff changeset
1008 self.add_half_edge_first(v, w)
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diff changeset
1009 self.add_half_edge_first(w, v)
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diff changeset
1010
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1011 def add_half_edge_first(self, start_node, end_node):
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parents:
diff changeset
1012 """The added half-edge is inserted at the first position in the order.
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diff changeset
1013
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1014 Parameters
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1015 ----------
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diff changeset
1016 start_node : node
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1017 end_node : node
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1018
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1019 See Also
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1020 --------
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1021 add_half_edge_ccw
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diff changeset
1022 add_half_edge_cw
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diff changeset
1023 connect_components
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1024 """
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diff changeset
1025 if start_node in self and 'first_nbr' in self.nodes[start_node]:
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diff changeset
1026 reference = self.nodes[start_node]['first_nbr']
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diff changeset
1027 else:
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1028 reference = None
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1029 self.add_half_edge_ccw(start_node, end_node, reference)
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1030
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1031 def next_face_half_edge(self, v, w):
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1032 """Returns the following half-edge left of a face.
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1033
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1034 Parameters
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1035 ----------
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1036 v : node
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1037 w : node
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1038
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1039 Returns
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1040 -------
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1041 half-edge : tuple
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1042 """
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1043 new_node = self[w][v]['ccw']
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1044 return w, new_node
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1045
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1046 def traverse_face(self, v, w, mark_half_edges=None):
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1047 """Returns nodes on the face that belong to the half-edge (v, w).
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1048
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1049 The face that is traversed lies to the right of the half-edge (in an
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1050 orientation where v is below w).
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1051
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1052 Optionally it is possible to pass a set to which all encountered half
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1053 edges are added. Before calling this method, this set must not include
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1054 any half-edges that belong to the face.
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1055
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1056 Parameters
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1057 ----------
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1058 v : node
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1059 Start node of half-edge.
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1060 w : node
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1061 End node of half-edge.
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1062 mark_half_edges: set, optional
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1063 Set to which all encountered half-edges are added.
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1064
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1065 Returns
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1066 -------
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1067 face : list
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1068 A list of nodes that lie on this face.
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1069 """
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1070 if mark_half_edges is None:
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1071 mark_half_edges = set()
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1072
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1073 face_nodes = [v]
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1074 mark_half_edges.add((v, w))
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1075 prev_node = v
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1076 cur_node = w
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1077 # Last half-edge is (incoming_node, v)
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1078 incoming_node = self[v][w]['cw']
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1079
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1080 while cur_node != v or prev_node != incoming_node:
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1081 face_nodes.append(cur_node)
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1082 prev_node, cur_node = self.next_face_half_edge(prev_node, cur_node)
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1083 if (prev_node, cur_node) in mark_half_edges:
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1084 raise nx.NetworkXException(
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1085 "Bad planar embedding. Impossible face.")
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1086 mark_half_edges.add((prev_node, cur_node))
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1087
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1088 return face_nodes
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1089
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1090 def is_directed(self):
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1091 """A valid PlanarEmbedding is undirected.
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1092
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1093 All reverse edges are contained, i.e. for every existing
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1094 half-edge (v, w) the half-edge in the opposite direction (w, v) is also
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1095 contained.
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1096 """
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1097 return False