segmentation / graph_gui

  #!/usr/bin/env python3
  # -*- coding: utf-8 -*-
  """
  Created on Tue Sep  3 13:15:54 2019
  
  @author: pavel
  """
  
  from scipy.spatial import Voronoi, voronoi_plot_2d

  from scipy.spatial import Delaunay, delaunay_plot_2d
  
  from triangle import triangulate
  from triangle import plot as triangle_plot

  from scipy.interpolate import interp1d
  #import matplotlib._cntr as cntr
  from shapely.geometry import Point
  from shapely.geometry import Polygon
  import numpy as np
  import scipy as sp
  import math
  import matplotlib.pyplot as plt
  import sys
  import copy
  
  from skimage import measure
  
  from collections import defaultdict
  
  import network_dep as nwt
  
  class Polygon_mass:
      def __init__(self, G):
          self.G = G

          print(nwt.gt.graph_tool.topology.is_planar(G))

          self.get_aabb()
          self.gen_polygon()
          self.torque = []

          self.forces_r = np.zeros(2)
          self.forces_a = np.zeros(2)

          self.vel = 0.0
          self.aa = 0.0

          self.degree = 0

        
          
      def clear_torques(self):
          self.torque = []        

      def clear_forces(self):
          self.forces_r = np.zeros(2)
          self.forces_a = np.zeros(2)
          
      def set_degree(self, degree):
          self.degree = degree
          

      def add_torque(self, p, f):

          #direction of the torque = cross of (r, f)
          #magnitude = ||r||*||f||*sin(theta)
          #r = level arm vector

          d = self.CoM - p

          #r = np.linalg.norm(self.CoM - p)
          value = np.dot(d, f)/np.dot(d, d)/np.dot(f, f)
          if value < 1.0 and value > -1.0:
              theta = math.acos(value)
              torque = math.sin(theta) * np.sqrt(f[0]*f[0]+f[1]*f[1]) * np.sqrt(d[0]*d[0]+d[1]*d[1])
          else:
              #print("value = ", value)
              torque = 0.0
          

          #if < 0 then clockwise, else counter

          direction = np.cross(d, f)

          if direction < 0:

              self.torque.append([torque, f, p, "counterclock"])

          else:

              self.torque.append([torque, f, p, "clockwise"])
          

      def calculate_moment(self, use_graph=False):

          
          #returns the area of a triangle defined by two points
          def area(t):
              output = 1.0/2.0*abs(t[0,0]*(t[1,1]-t[2,1]) + t[1,0]*(t[2,1]-t[0,1]) + t[2,0]*(t[0,1]-t[1,1]))
              return output
          
          def center(t):
              output = np.asarray([(t[0,0]+t[1,0]+t[2,0])/3.0, (t[0,1]+t[1,1]+t[2,1])/3.0])

              return output

          
          segs = []
          pts = np.asarray(self.polygon.exterior.xy).T
          pts = pts[:-1, :]
          for k in range(pts.shape[0]-1):
              segs.append([k, k+1])
          segs.append([pts.shape[0]-1, 0])

          if use_graph:
              points = self.G.vertex_properties["pos"].get_2d_array(range(2)).T
              segs2 = []
              n_pts = pts.shape[0]
              for e in self.G.edges():
                  segs2.append([int(e.source())+n_pts, int(e.target())+n_pts])
              pts = np.concatenate((pts, points))
              segs = segs + segs2

          mesh = dict(vertices=pts, segments=segs)
          #print(self.polygon.area())

          tri = triangulate(mesh, 'pq20Ds')
          self.mesh = mesh
          self.tri = tri

          moment = 0.0
          #NEED TO ADD MASS maybe?
          for i in range(tri['triangles'].shape[0]):
              t = tri['vertices'][tri['triangles'][i]]
              A = area(t)
              C = center(t)
              Moi = A+A*np.linalg.norm(C-self.CoM)**2
              moment += Moi
              

          self.MoI = abs(math.log(moment))
          #self.MoI = 10
          print(self.MoI)

  #        triangle_plot(plt.gca(), **tri)
  #        plt.gca().set_title(str(self.polygon.area))

       
      def translate(self, step):
          d = self.forces_a + self.forces_r
          #print(self.forces_a, self.forces_r)
          d0 = step*d
          self.CoM = self.CoM + d0
          pos = self.G.vertex_properties["pos"].get_2d_array(range(2)).T
          pos = pos + d0
          self.G.vertex_properties["pos"] = self.G.new_vertex_property("vector<double>", vals = pos)
      

      def rotate(self, phi, direction = "counterclock"):
          if("counterclock"):

              for v in self.G.vertices():
                  p_prime = copy.deepcopy(self.G.vertex_properties["pos"][v])
                  p = copy.deepcopy(self.G.vertex_properties["pos"][v])
                  p_prime[0] = self.CoM[0] + math.cos(phi) * (p[0] - self.CoM[0]) - math.sin(phi) * (p[1] - self.CoM[1])
                  p_prime[1] = self.CoM[1] + math.sin(phi) * (p[0] - self.CoM[0]) + math.cos(phi) * (p[1] - self.CoM[1])
                  self.G.vertex_properties["pos"][v] = p_prime
              #rotate points in mesh
              points = copy.deepcopy(self.mesh['vertices'])
              for v in range(points.shape[0]):
                  points[v][0] = self.CoM[0] + math.cos(phi) * (self.mesh['vertices'][v][0] - self.CoM[0]) - math.sin(phi) * (self.mesh['vertices'][v][1] - self.CoM[1])
                  points[v][1] = self.CoM[1] + math.sin(phi) * (self.mesh['vertices'][v][0] - self.CoM[0]) + math.cos(phi) * (self.mesh['vertices'][v][1] - self.CoM[1])
              self.mesh['vertices'] = points

          else:

              for v in self.G.vertices():
                  p_prime = copy.deepcopy(self.G.vertex_properties["pos"][v])
                  p = copy.deepcopy(self.G.vertex_properties["pos"][v])
                  p_prime[0] = self.CoM[0] + math.cos(phi) * (p[0] - self.CoM[0]) + math.sin(phi) * (p[1] - self.CoM[1])
                  p_prime[1] = self.CoM[1] - math.sin(phi) * (p[0] - self.CoM[0]) + math.cos(phi) * (p[1] - self.CoM[1])
                  self.G.vertex_properties["pos"][v] = p_prime
              #rotate points in mesh
              points = copy.deepcopy(self.mesh['vertices'])
              for v in range(points.shape[0]):
                  points[v][0] = self.CoM[0] + math.cos(phi) * (self.mesh['vertices'][v][0] - self.CoM[0]) + math.sin(phi) * (self.mesh['vertices'][v][1] - self.CoM[1])
                  points[v][1] = self.CoM[1] - math.sin(phi) * (self.mesh['vertices'][v][0] - self.CoM[0]) + math.cos(phi) * (self.mesh['vertices'][v][1] - self.CoM[1])
              self.mesh['vertices'] = points

       
      def plot_graph(self, D, x, y):
          plt.figure()
          ext = [self.a[0], self.b[0], self.a[1], self.b[1]]

          #plt.imshow(D, origin = 'lower', extent=ext)

          p = self.G.vertex_properties["pos"].get_2d_array(range(2)).T
          plt.scatter(p[:,0], p[:,1], color='r')
          plt.scatter(self.CoM[0], self.CoM[1], marker='*')
          

          #mesh = dict(vertices=pts, segments=segs)
          #print(self.polygon.area())
          #tri = triangulate(mesh, 'pq20Ds')
          triangle_plot(plt.gca(), **self.mesh)

          #plot polygon
          #plt.plot(*self.polygon.exterior.xy, color = 'r')

  #        for i in range(len(segs)):
  #            plt.plot((pts[segs[i][0]][0], pts[segs[i][1]][0]), (pts[segs[i][0]][1], pts[segs[i][1]][1]), color='b')

          plt.gca().set_title(str(self.polygon.area))
          

          for e in self.torque:
              plt.quiver(e[2][0], e[2][1], e[1][0], e[1][1], color='r')

          #tri = Delaunay(np.asarray(self.polygon.exterior.coords.xy).T)
          #tri = triangulate(mesh, 'pq20a' + str(self.polygon.area/100.0)+'D')
          #delaunay_plot_2d(tri)
          

  #        for n, contour in enumerate(self.cn):
  #            X = interp1d(np.arange(0, x.shape[0]), x)
  #            Y = interp1d(np.arange(0, y.shape[0]), y)
  #            contour[:, 1] = X(contour[:, 1])
  #            contour[: ,0] = Y(contour[:, 0])
  #            plt.plot(contour[:, 1], contour[:, 0])
  #        mx = np.amax(D)
  #        mn = np.amin(D)
  #        level = (mx-mn)/5.5
  #        cn = plt.contour(x, y, D, levels = [level])
          

  #        for e in self.G.edges():
  #            coord = self.G.vertex_properties["pos"][e.source()]
  #            coord2 = self.G.vertex_properties["pos"][e.target()]
  #            X = [coord[0], coord2[0]]
  #            Y = [coord[1], coord2[1]]
  #            #all_plots.plot(x, y, 'go--', linewidth=1, markersize=1)
  #            plt.plot(X, Y, 'go--', linewidth=1, markersize=1)

  #        

          plt.show()
          
      def get_aabb(self):
          pts = self.G.vertex_properties["pos"].get_2d_array(range(2)).T
          a = np.asarray([100000.0, 100000.0])
          b = np.asarray([-100000.0, -100000.0])
          
          #Find the bounding box based on the vertices.
          for i in pts:
              if(i[0] < a[0]):
                  a[0] = i[0]
              if(i[1] < a[1]):
                  a[1] = i[1]
              if(i[0] > b[0]):
                  b[0] = i[0]
              if(i[1] > b[1]):
                  b[1] = i[1]
          
          #add 50% of the bounding box as padding on each side
          d = 0.5*abs(a-b)
          self.a = a - d
          self.b = b + d
          
      def line(self, p1, p2, step1, step2):
          return list(np.asarray(a) for a in zip(np.linspace(p1[0], p2[0], step1+1), np.linspace(p1[1], p2[1], step2+1)))
      
      def gen_polygon(self):
          D, x, y = self.distancefield()
          mx = np.amax(D)
          mn = np.amin(D)
          level = (mx-mn)/5.5
          cn = measure.find_contours(D, level)
          contour = copy.deepcopy(cn[0])
          X = interp1d(np.arange(0, x.shape[0]), x)
          Y = interp1d(np.arange(0, y.shape[0]), y)
          contour[:, 0] = X(cn[0][:, 1])
          contour[: ,1] = Y(cn[0][:, 0])
          self.polygon = Polygon(contour)
          self.CoM = self.centroid_com(contour)

          self.calculate_moment(True)

          #cn = plt.contour(x, y, D, levels = [level])
          #cn = plt.contour(x, y, D, levels = [level])
  #        plt.close()
          #p = cn.collections[0].get_paths()[0]
  #        for i in range(len(cn.allsegs[0])):
  #            
  #        self.p = p
  #        v = p.vertices
  #        x = v[:, 0]
  #        y = v[:, 1]
  #        pts = np.array(zip(x, y))
  #        #nlist = c.trace(level, level, 0)
  #        #segs = nlist[:len(nlist)//2]
          #self.polygon = Polygon(pts)

          #self.plot_graph(D, x, y)

          
          
      
      def distancefield(self):      

          #generate a meshgrid of the appropriate size and resolution to surround the network
          #get the space occupied by the network
          lower = self.a
          upper = self.b
          R = np.asarray(np.floor(abs(lower-upper)), dtype=np.int)
          if(R[0] < 10):
              R[0] = 10
          if(R[1] < 10):
              R[1] = 10
          x = np.linspace(lower[0], upper[0], R[0])   #get the grid points for uniform sampling of this space
          y = np.linspace(lower[1], upper[1], R[1])
          X, Y = np.meshgrid(x, y)
          #Z = 150 * numpy.ones(X.shape)
                 
          Q = np.stack((X, Y), 2)
          d_x = abs(x[1]-x[0]);
          d_y = abs(y[1]-y[0]);
          dis1 = math.sqrt(pow(d_x,2)+pow(d_y,2))
          #dx = abs(x[1]-x[0])
          
          #dy = abs(y[1]-y[0])
          #dz = abs(z[1]-z[0])
           #get a list of all node positions in the network
          P = []
        
          for e in self.G.edges():    #12-17
              start = self.G.vertex_properties["pos"][e.source()]
              end = self.G.vertex_properties["pos"][e.target()]
              l = self.line(start, end, 10, 10)
              P = P + l
                 
              for j in range(len(l)-1):
                  d_t = l[j+1]-l[j]
                  dis2 = math.sqrt(pow(d_t[0],2)+pow(d_t[1],2))
                  ins = max(int(d_t[0]/d_x), int(d_t[1]/d_y))
                  if(ins > 0):  
                      ins = ins+1
                      for k in range(ins):
                          p_ins =l[j]+(k+1)*(l[j+1]-l[j])/ins
                          P.append(p_ins)
          #turn that list into a Numpy array so that we can create a KD tree
          P = np.array(P)
        
          #generate a KD-Tree out of the network point array
          tree = sp.spatial.cKDTree(P)
          
          #specify the resolution of the ouput grid
          # R = (200, 200, 200)
  
          D, I = tree.query(Q)

          self.D = D
          self.x = x
          self.y = y

          
          return D, x, y
      
      def centroid_com(self, vertices):
      # Polygon's signed area
          A = 0
          # Centroid's x
          C_x = 0
          # Centroid's y
          C_y = 0
          for i in range(0, len(vertices) - 1):
              s = (vertices[i, 0] * vertices[i + 1, 1] - vertices[i + 1, 0] * vertices[i, 1])
              A = A + s
              C_x = C_x + (vertices[i, 0] + vertices[i + 1, 0]) * s
              C_y = C_y + (vertices[i, 1] + vertices[i + 1, 1]) * s
          A = 0.5 * A
          C_x = (1.0 / (6.0 * A)) * C_x
          C_y = (1.0 / (6.0 * A)) * C_y
          

          return np.array([C_x, C_y])  
      
  #Graph G
  #List of Polygonmass objects with the same cluster index.
  def get_torques(G, masses):
      for i in masses:
          i.clear_torques()
      for e in G.edges():
          #if the source and target cluster is not equal to each other
          #add an inter subgraph edge.
          if(G.vertex_properties["clusters"][e.source()] != G.vertex_properties["clusters"][e.target()]):

              #index of the cluster
              t0 = G.vertex_properties["clusters"][e.target()]
              t1 = G.vertex_properties["clusters"][e.source()]
              #index of the vertex outside of the subgraph
              v0_index = G.vertex_properties["idx"][e.target()]
              v1_index = G.vertex_properties["idx"][e.source()]
              #location of torque arm in the subgraph
              p0 = masses[t0].G.vertex_properties["pos"][np.argwhere(masses[t0].G.vertex_properties["idx"].get_array() == v0_index)]
              p1 = masses[t1].G.vertex_properties["pos"][np.argwhere(masses[t1].G.vertex_properties["idx"].get_array() == v1_index)]

              f0 = np.subtract(p0, p1)
              f1 = np.subtract(p1, p0)
              masses[t0].add_torque(p0, f1)
              masses[t1].add_torque(p1, f0)
  '''
      c1 scales the attractive force before log.
      c2 scales the attractive force inside log.
      c3 scales the repulsive force.
  '''
  def get_forces(G, masses, c1 = 50.0, c2 = 1.0, c3 = 1.0):
      for i in range(len(masses)):
          masses[i].clear_forces()
          f_total = np.zeros(2)
          for j in range(len(masses)):
              if i != j:
                  f0 = np.subtract(masses[i].CoM, masses[j].CoM)
                  f1 = np.power(f0, 3.0)
                  f1[0] = c3/f1[0]*np.sign(f0[0])
                  f1[1] = c3/f1[1]*np.sign(f0[1])
                  f_total = np.add(f_total, f1)
          masses[i].forces_r = f_total

      for e in G.edges():
                  #if the source and target cluster is not equal to each other
          #add an inter subgraph edge.
          if(G.vertex_properties["clusters"][e.source()] != G.vertex_properties["clusters"][e.target()]):
              #index of the cluster
              t0 = G.vertex_properties["clusters"][e.target()]
              t1 = G.vertex_properties["clusters"][e.source()]
              #index of the vertex outside of the subgraph
              v0_index = G.vertex_properties["idx"][e.target()]
              v1_index = G.vertex_properties["idx"][e.source()]
              #location of torque arm in the subgraph
              p0 = masses[t0].G.vertex_properties["pos"][np.argwhere(masses[t0].G.vertex_properties["idx"].get_array() == v0_index)]
              p1 = masses[t1].G.vertex_properties["pos"][np.argwhere(masses[t1].G.vertex_properties["idx"].get_array() == v1_index)]

              f0 = np.subtract(p1, p0)
              f0_1 = abs(f0)
              f0_1 = c1*np.log(f0_1/c2)/masses[t0].degree
              f0_1 = f0_1*np.sign(f0)
              f1 = np.subtract(p0, p1)
              f1_1 = abs(f1)
              f1_1 = c1*np.log(f1_1/c2)/masses[t1].degree
              f1_1 = f1_1*np.sign(f1)
              masses[t0].forces_a = np.add(masses[t0].forces_a, f1_1)
              masses[t1].forces_a = np.add(masses[t1].forces_a, f0_1)

  
  def voronoi_polygons(voronoi, diameter):
      """Generate shapely.geometry.Polygon objects corresponding to the
      regions of a scipy.spatial.Voronoi object, in the order of the
      input points. The polygons for the infinite regions are large
      enough that all points within a distance 'diameter' of a Voronoi
      vertex are contained in one of the infinite polygons.
  
      """
      centroid = voronoi.points.mean(axis=0)
  
      # Mapping from (input point index, Voronoi point index) to list of
      # unit vectors in the directions of the infinite ridges starting
      # at the Voronoi point and neighbouring the input point.
      ridge_direction = defaultdict(list)
      for (p, q), rv in zip(voronoi.ridge_points, voronoi.ridge_vertices):
          u, v = sorted(rv)
          if u == -1:
              # Infinite ridge starting at ridge point with index v,
              # equidistant from input points with indexes p and q.
              t = voronoi.points[q] - voronoi.points[p] # tangent
              n = np.array([-t[1], t[0]]) / np.linalg.norm(t) # normal
              midpoint = voronoi.points[[p, q]].mean(axis=0)
              direction = np.sign(np.dot(midpoint - centroid, n)) * n
              ridge_direction[p, v].append(direction)
              ridge_direction[q, v].append(direction)
  
      for i, r in enumerate(voronoi.point_region):
          region = voronoi.regions[r]
          if -1 not in region:
              # Finite region.
              yield Polygon(voronoi.vertices[region])
              continue
          # Infinite region.
          inf = region.index(-1)              # Index of vertex at infinity.
          j = region[(inf - 1) % len(region)] # Index of previous vertex.
          k = region[(inf + 1) % len(region)] # Index of next vertex.
          if j == k:
              # Region has one Voronoi vertex with two ridges.
              dir_j, dir_k = ridge_direction[i, j]
          else:
              # Region has two Voronoi vertices, each with one ridge.
              dir_j, = ridge_direction[i, j]
              dir_k, = ridge_direction[i, k]
  
          # Length of ridges needed for the extra edge to lie at least
          # 'diameter' away from all Voronoi vertices.
          length = 2 * diameter / np.linalg.norm(dir_j + dir_k)
  
          # Polygon consists of finite part plus an extra edge.
          finite_part = voronoi.vertices[region[inf + 1:] + region[:inf]]
          extra_edge = [voronoi.vertices[j] + dir_j * length,
                        voronoi.vertices[k] + dir_k * length]
          yield Polygon(np.concatenate((finite_part, extra_edge)))
  
  
  def load_nwt(filepath):
      net = nwt.Network(filepath)
      G = net.createFullGraph_gt()
      G = net.filterDisconnected(G)
      color = np.zeros(4, dtype = np.double)
      color = [0.0, 1.0, 0.0, 1.0]
      G.edge_properties["RGBA"] = G.new_edge_property("vector<double>", val=color)
      color = [1.0, 0.0, 0.0, 0.9]
      G.vertex_properties["RGBA"] = G.new_vertex_property("vector<double>", val=color)
      bbl, bbu = net.aabb()
  
      return G, bbl, bbu
  
  def gen_cluster_graph(G, num_clusters, cluster_pos):
      #create a graph that stores the edges of between the clusters
      G_cluster = nwt.gt.Graph(directed=False)
      G_cluster.vertex_properties["pos"] = G_cluster.new_vertex_property("vector<double>", val=np.zeros((3,1), dtype=np.float32))
      G_cluster.vertex_properties["RGBA"] = G_cluster.new_vertex_property("vector<double>", val=np.zeros((4,1), dtype=np.float32))
      for v in range(num_clusters):
          G_cluster.add_vertex()
          G_cluster.vertex_properties["pos"][G_cluster.vertex(v)] = np.asarray(cluster_pos[v], dtype=np.float32)
      G_cluster.edge_properties["weight"] = G_cluster.new_edge_property("int", val = 0)
      G_cluster.edge_properties["volume"] = G_cluster.new_edge_property("float", val = 0.0)
      #for each edge in the original graph, generate appropriate subgraph edges without repretiions
      #i.e. controls the thichness of the edges in the subgraph view.
      for e in G.edges():
          #if the source and target cluster is not equal to each other
          #add an inter subgraph edge.
          if(G.vertex_properties["clusters"][e.source()] != G.vertex_properties["clusters"][e.target()]):
              t0 = e.source()
              t1 = e.target()
              ct0 = G_cluster.vertex(G.vertex_properties["clusters"][t0])
              ct1 = G_cluster.vertex(G.vertex_properties["clusters"][t1])
              if(G_cluster.edge(ct0, ct1) == None):
                  if(G_cluster.edge(ct1, ct0) == None):
              #temp_e.append([G.vertex_properties["clusters"][e.source()], G.vertex_properties["clusters"][e.target()]])
                      G_cluster.add_edge(G_cluster.vertex(G.vertex_properties["clusters"][t0]), \
                                               G_cluster.vertex(G.vertex_properties["clusters"][t1]))
                      G_cluster.edge_properties["weight"][G_cluster.edge(G_cluster.vertex(G.vertex_properties["clusters"][t0]), \
                                                     G_cluster.vertex(G.vertex_properties["clusters"][t1]))] += 1
                      G_cluster.edge_properties["volume"][G_cluster.edge(G_cluster.vertex(G.vertex_properties["clusters"][t0]), \
                                                 G_cluster.vertex(G.vertex_properties["clusters"][t1]))] += G.edge_properties["volume"][e]
                      G_cluster.vertex_properties["RGBA"][G_cluster.vertex(G.vertex_properties["clusters"][t0])]    \
                                              = G.vertex_properties["RGBA"][t0]
                      G_cluster.vertex_properties["RGBA"][G_cluster.vertex(G.vertex_properties["clusters"][t1])]    \
                                              = G.vertex_properties["RGBA"][t1]
                  else:
                      G_cluster.edge_properties["weight"][G_cluster.edge(G_cluster.vertex(G.vertex_properties["clusters"][t1]), \
                                                     G_cluster.vertex(G.vertex_properties["clusters"][t0]))] += 1
                      G_cluster.edge_properties["volume"][G_cluster.edge(G_cluster.vertex(G.vertex_properties["clusters"][t1]), \
                                                 G_cluster.vertex(G.vertex_properties["clusters"][t0]))] += G.edge_properties["volume"][e]
                      G_cluster.vertex_properties["RGBA"][G_cluster.vertex(G.vertex_properties["clusters"][t1])]    \
                                              = G.vertex_properties["RGBA"][t1]
                      G_cluster.vertex_properties["RGBA"][G_cluster.vertex(G.vertex_properties["clusters"][t0])]    \
                                              = G.vertex_properties["RGBA"][t0]
              else:
                  G_cluster.edge_properties["weight"][G_cluster.edge(G_cluster.vertex(G.vertex_properties["clusters"][t0]), \
                                           G_cluster.vertex(G.vertex_properties["clusters"][t1]))] += 1
                  G_cluster.edge_properties["volume"][G_cluster.edge(G_cluster.vertex(G.vertex_properties["clusters"][t0]), \
                                             G_cluster.vertex(G.vertex_properties["clusters"][t1]))] += G.edge_properties["volume"][e]
                  G_cluster.vertex_properties["RGBA"][G_cluster.vertex(G.vertex_properties["clusters"][t0])]    \
                                          = G.vertex_properties["RGBA"][t0]
                  G_cluster.vertex_properties["RGBA"][G_cluster.vertex(G.vertex_properties["clusters"][t1])]    \
                                          = G.vertex_properties["RGBA"][t1]
      G_cluster.vertex_properties["degree"] = G_cluster.degree_property_map("total")
      vbetweeness_centrality = G_cluster.new_vertex_property("double")
      ebetweeness_centrality = G_cluster.new_edge_property("double")
      nwt.gt.graph_tool.centrality.betweenness(G_cluster, vprop=vbetweeness_centrality, eprop=ebetweeness_centrality)
      ebc = ebetweeness_centrality.get_array()/0.01
      G_cluster.vertex_properties["bc"] = vbetweeness_centrality
      G_cluster.edge_properties["bc"] = ebetweeness_centrality
      G_cluster.edge_properties["bc_scaled"] = G_cluster.new_edge_property("double", vals=ebc)

      G_cluster.edge_properties["log"] = G_cluster.new_edge_property("double", vals=abs(np.log(G_cluster.edge_properties["volume"].get_array())))    

      dg = G_cluster.vertex_properties["degree"].get_array()
      dg = 2*max(dg) - dg
      d = G_cluster.new_vertex_property("int", vals=dg)
      G_cluster.vertex_properties["10-degree"] = d
      
      return G_cluster
                                      
                                      
  
  
  def gen_clusters(G, bbl, bbu, n_c = 20, edge_metric = 'volume', vertex_metric = 'degree'):
  
      #Generate the clusters
      labels = nwt.Network.spectral_clustering(G,'length', n_clusters = n_c)
      #self.labels = nwt.Network.spectral_clustering(G,'length')
  
      #Add clusters as a vertex property
      G.vertex_properties["clusters"] = G.new_vertex_property("int", vals=labels)
      G.vertex_properties["idx"] = G.vertex_index
      
      #gen bc metric
      vbetweeness_centrality = G.new_vertex_property("double")
      ebetweeness_centrality = G.new_edge_property("double")
      nwt.gt.graph_tool.centrality.betweenness(G, vprop=vbetweeness_centrality, eprop=ebetweeness_centrality, norm=True)
      G.vertex_properties["bc"] = vbetweeness_centrality
      G.edge_properties["bc"] = ebetweeness_centrality
      
      num_clusters = len(np.unique(labels))
  
      #add colormap
      G.vertex_properties["RGBA"] = nwt.Network.map_property_to_color(G, G.vertex_properties["clusters"])
      temp_pos = []
      for i in range(num_clusters):
          num_v_in_cluster = len(np.argwhere(labels == i))
          vfilt = np.zeros([G.num_vertices(), 1], dtype="bool")
          vfilt[np.argwhere(labels == i)] = 1
          vfilt_prop = G.new_vertex_property("bool", vals = vfilt)
          G.set_vertex_filter(vfilt_prop)
      
          #get the filtered properties
          g = nwt.gt.Graph(G, prune=True, directed=False)
          positions = g.vertex_properties["pos"].get_2d_array(range(3)).T
          position = np.sum(positions, 0)/num_v_in_cluster
          temp_pos.append(position)
          G.clear_filters()
      
      return gen_cluster_graph(G, num_clusters, temp_pos), G
  
  
  def gen_subclusters(G, G_cluster, i, reposition = False):
      vfilt = np.zeros([G.num_vertices(), 1], dtype='bool')
      labels = G.vertex_properties["clusters"].get_array()
      num_v_in_cluster = len(np.argwhere(labels == i))
      vfilt[np.argwhere(labels == i)] = 1
      vfilt_prop = G.new_vertex_property("bool", vals = vfilt)
      G.set_vertex_filter(vfilt_prop)
      
      g = nwt.gt.Graph(G, prune=True, directed=False)
  
      
      if reposition == True:
          vbetweeness_centrality = g.new_vertex_property("double")
          ebetweeness_centrality = g.new_edge_property("double")
          nwt.gt.graph_tool.centrality.betweenness(g, vprop=vbetweeness_centrality, eprop=ebetweeness_centrality, norm=True)
          g.vertex_properties["bc"] = vbetweeness_centrality
          g.edge_properties["bc"] = ebetweeness_centrality
          g.vertex_properties["pos"] = nwt.gt.sfdp_layout(g, eweight = ebetweeness_centrality)
      
      positions = g.vertex_properties["pos"].get_2d_array(range(2)).T
      center = np.sum(positions, 0)/num_v_in_cluster
      G.clear_filters()
      return g, center
  
  #def gen_hierarchical_layout(G, G_cluster):
  
  def gen_polygons(G_c, bb):
      G_c.vertex_properties["region_idx"] = G_c.new_vertex_property("int")
      pts = G_c.vertex_properties["pos"].get_2d_array(range(2)).T
      bl = np.asarray([bb[0], bb[2]])
      lx = bb[1]-bb[0]
      ly = bb[3]-bb[2]
      r = copy.deepcopy(bl)
      t = copy.deepcopy(bl)
      tr = copy.deepcopy(bl)
      r[0] = r[0] + lx
      t[1] = t[1] + ly
      tr[0] = tr[0] + lx
      tr[1] = tr[1] + ly
      
      boundary = np.asarray([bl, t, tr, r, bl])
      diameter = np.linalg.norm(boundary.ptp(axis=0))
      boundary_polygon = Polygon(boundary)
      vor = Voronoi(pts)
      polygons = []
      idx = 0
      for poly in voronoi_polygons(vor, diameter):
          coords = np.array(poly.intersection(boundary_polygon).exterior.coords)
          polygons.append([coords])
          for v in G_c.vertices():
              point = Point(G_c.vertex_properties["pos"][v])
              if poly.contains(point):
                  G_c.vertex_properties["region_idx"][v] = idx
                  idx+=1
                  break
      return G_c, polygons, vor
                                  
  def centroid_region(vertices):
      # Polygon's signed area
      A = 0
      # Centroid's x
      C_x = 0
      # Centroid's y
      C_y = 0
      for i in range(0, len(vertices) - 1):
          s = (vertices[i, 0] * vertices[i + 1, 1] - vertices[i + 1, 0] * vertices[i, 1])
          A = A + s
          C_x = C_x + (vertices[i, 0] + vertices[i + 1, 0]) * s
          C_y = C_y + (vertices[i, 1] + vertices[i + 1, 1]) * s
      A = 0.5 * A
      C_x = (1.0 / (6.0 * A)) * C_x
      C_y = (1.0 / (6.0 * A)) * C_y
      
      return np.array([C_x, C_y])    

   
  def find_equlibrium(masses, t = 0.01):
      for m in masses:
          sum_torque = 0
          for torque in m.torque:
              if torque[3] == "clockwise":
                  sum_torque -= torque[0]
              else:
                  sum_torque += torque[0]
          m.vel = m.aa * t + m.vel
          m.aa = sum_torque/m.MoI
          #print(m.G.vertex_properties["clusters"][0], m.vel)
          if m.vel != 0.0:
              if m.vel < 0.0:
                  m.rotate(abs(m.vel * t),"counterclock")
              else:
                  m.rotate(abs(m.vel * t), "clockwise")
  
  
  def gen_Eades(G, masses, M = 10):
      for i in range(M):
          get_forces(G, masses)
          for j in masses:
              j.translate(0.001)
          
  def onion_springs(G, masses, min_length):
      for v in G.vertices():
          
  

      
  def gen_image(G, G_c, itr, bb_flag = False, bb = None, reposition = False):
  #def gen_image(G, G_c, vor, vor_filtered):
      #Draw the layout using graph-tool (for comparison)
      title = "clusters.pdf"
      nwt.gt.graph_draw(G_c, pos=G_c.vertex_properties["pos"], vertex_fill_color=G_c.vertex_index, output=title, bg_color=[0.0, 0.0, 0.0, 1.0], output_size=(1000,1000))
      
      #get points of the centers of every cluster
      #generate voronoi region and plot it.

      fig, ax = plt.subplots(4, 1, sharex='col', sharey='row')

      fig.tight_layout()

      grid = plt.GridSpec(4,1)

      grid.update(wspace=0.025, hspace=0.2)
      ax[0].axis('off')
      ax[1].axis('off')
      ax[2].axis('off')

      ax[3].axis('off')
      

      #Add plots to the axes and get their handles

      all_plots = fig.add_subplot(grid[0])
      ax[0].set_title(itr)
      no_links = fig.add_subplot(grid[1], sharey=all_plots, sharex=all_plots)
      voronoi = fig.add_subplot(grid[2], sharey=all_plots, sharex=all_plots)

      rotated = fig.add_subplot(grid[3], sharey=all_plots, sharex=all_plots)
      
      #Get the points and generate the voronoi region

      pts = G_c.vertex_properties["pos"].get_2d_array(range(2)).T
      if bb_flag == False:
          vor = Voronoi(pts)
          voronoi_plot_2d(vor, all_plots)
          voronoi_plot_2d(vor, no_links)
          voronoi_plot_2d(vor, voronoi)
          a = voronoi.get_ylim()
          b = voronoi.get_xlim()
          bb = np.array([b[0], b[1], a[0], a[1]])