1 | """Classes implementing general 2D geometrical mesh of triangles. |
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2 | |
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3 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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4 | Geoscience Australia, 2004 |
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5 | """ |
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6 | |
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7 | from general_mesh import General_mesh |
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8 | |
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9 | class Mesh(General_mesh): |
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10 | """Collection of triangular elements (purely geometric) |
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11 | |
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12 | A triangular element is defined in terms of three vertex ids, |
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13 | ordered counter clock-wise, |
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14 | each corresponding to a given coordinate set. |
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15 | Vertices from different elements can point to the same |
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16 | coordinate set. |
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17 | |
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18 | Coordinate sets are implemented as an N x 2 Numeric array containing |
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19 | x and y coordinates. |
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20 | |
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21 | |
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22 | To instantiate: |
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23 | Mesh(coordinates, triangles) |
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24 | |
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25 | where |
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26 | |
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27 | coordinates is either a list of 2-tuples or an Mx2 Numeric array of |
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28 | floats representing all x, y coordinates in the mesh. |
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29 | |
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30 | triangles is either a list of 3-tuples or an Nx3 Numeric array of |
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31 | integers representing indices of all vertices in the mesh. |
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32 | Each vertex is identified by its index i in [0, M-1]. |
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33 | |
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34 | |
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35 | Example: |
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36 | a = [0.0, 0.0] |
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37 | b = [0.0, 2.0] |
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38 | c = [2.0,0.0] |
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39 | e = [2.0, 2.0] |
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40 | |
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41 | points = [a, b, c, e] |
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42 | triangles = [ [1,0,2], [1,2,3] ] #bac, bce |
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43 | mesh = Mesh(points, triangles) |
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44 | |
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45 | #creates two triangles: bac and bce |
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46 | |
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47 | |
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48 | Mesh takes the optional third argument boundary which is a |
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49 | dictionary mapping from (element_id, edge_id) to boundary tag. |
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50 | The default value is None which will assign the default_boundary_tag |
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51 | as specified in config.py to all boundary edges. |
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52 | """ |
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53 | |
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54 | #FIXME: Maybe rename coordinates to points (as in a poly file) |
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55 | #But keep 'vertex_coordinates' |
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56 | |
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57 | #FIXME: Put in check for angles less than a set minimum |
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58 | |
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59 | |
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60 | def __init__(self, coordinates, triangles, boundary = None, |
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61 | tagged_elements = None, geo_reference = None, |
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62 | use_inscribed_circle = False): |
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63 | """ |
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64 | Build triangles from x,y coordinates (sequence of 2-tuples or |
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65 | Mx2 Numeric array of floats) and triangles (sequence of 3-tuples |
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66 | or Nx3 Numeric array of non-negative integers). |
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67 | """ |
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68 | |
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69 | |
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70 | |
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71 | from Numeric import array, zeros, Int, Float, maximum, sqrt, sum |
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72 | |
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73 | General_mesh.__init__(self, coordinates, triangles, geo_reference) |
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74 | |
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75 | N = self.number_of_elements |
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76 | |
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77 | self.use_inscribed_circle = use_inscribed_circle |
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78 | |
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79 | #Allocate space for geometric quantities |
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80 | self.centroid_coordinates = zeros((N, 2), Float) |
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81 | |
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82 | self.radii = zeros(N, Float) |
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83 | |
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84 | self.neighbours = zeros((N, 3), Int) |
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85 | self.neighbour_edges = zeros((N, 3), Int) |
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86 | self.number_of_boundaries = zeros(N, Int) |
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87 | self.surrogate_neighbours = zeros((N, 3), Int) |
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88 | |
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89 | #Get x,y coordinates for all triangles and store |
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90 | V = self.vertex_coordinates |
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91 | |
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92 | #Initialise each triangle |
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93 | for i in range(N): |
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94 | #if i % (N/10) == 0: print '(%d/%d)' %(i, N) |
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95 | |
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96 | x0 = V[i, 0]; y0 = V[i, 1] |
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97 | x1 = V[i, 2]; y1 = V[i, 3] |
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98 | x2 = V[i, 4]; y2 = V[i, 5] |
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99 | |
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100 | #Compute centroid |
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101 | centroid = array([(x0 + x1 + x2)/3, (y0 + y1 + y2)/3]) |
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102 | self.centroid_coordinates[i] = centroid |
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103 | |
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104 | |
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105 | if self.use_inscribed_circle == False: |
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106 | #OLD code. Computed radii may exceed that of an |
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107 | #inscribed circle |
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108 | |
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109 | #Midpoints |
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110 | m0 = array([(x1 + x2)/2, (y1 + y2)/2]) |
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111 | m1 = array([(x0 + x2)/2, (y0 + y2)/2]) |
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112 | m2 = array([(x1 + x0)/2, (y1 + y0)/2]) |
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113 | |
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114 | #The radius is the distance from the centroid of |
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115 | #a triangle to the midpoint of the side of the triangle |
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116 | #closest to the centroid |
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117 | d0 = sqrt(sum( (centroid-m0)**2 )) |
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118 | d1 = sqrt(sum( (centroid-m1)**2 )) |
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119 | d2 = sqrt(sum( (centroid-m2)**2 )) |
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120 | |
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121 | self.radii[i] = min(d0, d1, d2) |
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122 | |
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123 | else: |
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124 | #NEW code added by Peter Row. True radius |
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125 | #of inscribed circle is computed |
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126 | |
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127 | from math import sqrt |
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128 | a = sqrt((x0-x1)**2+(y0-y1)**2) |
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129 | b = sqrt((x1-x2)**2+(y1-y2)**2) |
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130 | c = sqrt((x2-x0)**2+(y2-y0)**2) |
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131 | |
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132 | self.radii[i]=2.0*self.areas[i]/(a+b+c) |
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133 | |
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134 | |
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135 | #Initialise Neighbours (-1 means that it is a boundary neighbour) |
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136 | self.neighbours[i, :] = [-1, -1, -1] |
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137 | |
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138 | #Initialise edge ids of neighbours |
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139 | #In case of boundaries this slot is not used |
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140 | self.neighbour_edges[i, :] = [-1, -1, -1] |
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141 | |
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142 | |
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143 | #Build neighbour structure |
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144 | self.build_neighbour_structure() |
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145 | |
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146 | #Build surrogate neighbour structure |
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147 | self.build_surrogate_neighbour_structure() |
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148 | |
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149 | #Build boundary dictionary mapping (id, edge) to symbolic tags |
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150 | self.build_boundary_dictionary(boundary) |
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151 | |
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152 | #Build tagged element dictionary mapping (tag) to array of elements |
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153 | self.build_tagged_elements_dictionary(tagged_elements) |
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154 | |
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155 | #Update boundary indices FIXME: OBSOLETE |
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156 | #self.build_boundary_structure() |
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157 | |
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158 | #FIXME check integrity? |
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159 | |
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160 | def __repr__(self): |
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161 | return 'Mesh: %d triangles, %d elements, %d boundary segments'\ |
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162 | %(self.coordinates.shape[0], len(self), len(self.boundary)) |
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163 | |
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164 | |
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165 | def set_to_inscribed_circle(self,safety_factor = 1): |
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166 | #FIXME phase out eventually |
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167 | from math import sqrt |
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168 | N = self.number_of_elements |
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169 | V = self.vertex_coordinates |
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170 | |
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171 | #initialising min and max ratio |
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172 | i=0 |
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173 | old_rad = self.radii[i] |
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174 | x0 = V[i, 0]; y0 = V[i, 1] |
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175 | x1 = V[i, 2]; y1 = V[i, 3] |
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176 | x2 = V[i, 4]; y2 = V[i, 5] |
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177 | a = sqrt((x0-x1)**2+(y0-y1)**2) |
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178 | b = sqrt((x1-x2)**2+(y1-y2)**2) |
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179 | c = sqrt((x2-x0)**2+(y2-y0)**2) |
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180 | ratio = old_rad/self.radii[i] |
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181 | max_ratio = ratio |
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182 | min_ratio = ratio |
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183 | |
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184 | for i in range(N): |
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185 | old_rad = self.radii[i] |
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186 | x0 = V[i, 0]; y0 = V[i, 1] |
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187 | x1 = V[i, 2]; y1 = V[i, 3] |
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188 | x2 = V[i, 4]; y2 = V[i, 5] |
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189 | a = sqrt((x0-x1)**2+(y0-y1)**2) |
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190 | b = sqrt((x1-x2)**2+(y1-y2)**2) |
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191 | c = sqrt((x2-x0)**2+(y2-y0)**2) |
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192 | self.radii[i]=self.areas[i]/(2*(a+b+c))*safety_factor |
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193 | ratio = old_rad/self.radii[i] |
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194 | if ratio >= max_ratio: max_ratio = ratio |
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195 | if ratio <= min_ratio: min_ratio = ratio |
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196 | return max_ratio,min_ratio |
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197 | |
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198 | def build_neighbour_structure(self): |
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199 | """Update all registered triangles to point to their neighbours. |
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200 | |
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201 | Also, keep a tally of the number of boundaries for each triangle |
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202 | |
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203 | Postconditions: |
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204 | neighbours and neighbour_edges is populated |
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205 | number_of_boundaries integer array is defined. |
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206 | """ |
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207 | |
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208 | #Step 1: |
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209 | #Build dictionary mapping from segments (2-tuple of points) |
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210 | #to left hand side edge (facing neighbouring triangle) |
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211 | |
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212 | N = self.number_of_elements |
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213 | neighbourdict = {} |
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214 | for i in range(N): |
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215 | |
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216 | #Register all segments as keys mapping to current triangle |
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217 | #and segment id |
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218 | a = self.triangles[i, 0] |
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219 | b = self.triangles[i, 1] |
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220 | c = self.triangles[i, 2] |
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221 | if neighbourdict.has_key((a,b)): |
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222 | msg = "Edge 2 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[a,b][1],neighbourdict[a,b][0]) |
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223 | raise msg |
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224 | if neighbourdict.has_key((b,c)): |
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225 | msg = "Edge 0 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[b,c][1],neighbourdict[b,c][0]) |
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226 | raise msg |
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227 | if neighbourdict.has_key((c,a)): |
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228 | msg = "Edge 1 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[c,a][1],neighbourdict[c,a][0]) |
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229 | raise msg |
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230 | |
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231 | neighbourdict[a,b] = (i, 2) #(id, edge) |
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232 | neighbourdict[b,c] = (i, 0) #(id, edge) |
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233 | neighbourdict[c,a] = (i, 1) #(id, edge) |
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234 | |
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235 | |
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236 | #Step 2: |
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237 | #Go through triangles again, but this time |
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238 | #reverse direction of segments and lookup neighbours. |
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239 | for i in range(N): |
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240 | a = self.triangles[i, 0] |
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241 | b = self.triangles[i, 1] |
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242 | c = self.triangles[i, 2] |
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243 | |
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244 | self.number_of_boundaries[i] = 3 |
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245 | if neighbourdict.has_key((b,a)): |
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246 | self.neighbours[i, 2] = neighbourdict[b,a][0] |
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247 | self.neighbour_edges[i, 2] = neighbourdict[b,a][1] |
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248 | self.number_of_boundaries[i] -= 1 |
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249 | |
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250 | if neighbourdict.has_key((c,b)): |
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251 | self.neighbours[i, 0] = neighbourdict[c,b][0] |
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252 | self.neighbour_edges[i, 0] = neighbourdict[c,b][1] |
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253 | self.number_of_boundaries[i] -= 1 |
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254 | |
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255 | if neighbourdict.has_key((a,c)): |
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256 | self.neighbours[i, 1] = neighbourdict[a,c][0] |
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257 | self.neighbour_edges[i, 1] = neighbourdict[a,c][1] |
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258 | self.number_of_boundaries[i] -= 1 |
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259 | |
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260 | |
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261 | def build_surrogate_neighbour_structure(self): |
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262 | """Build structure where each triangle edge points to its neighbours |
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263 | if they exist. Otherwise point to the triangle itself. |
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264 | |
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265 | The surrogate neighbour structure is useful for computing gradients |
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266 | based on centroid values of neighbours. |
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267 | |
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268 | Precondition: Neighbour structure is defined |
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269 | Postcondition: |
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270 | Surrogate neighbour structure is defined: |
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271 | surrogate_neighbours: i0, i1, i2 where all i_k >= 0 point to |
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272 | triangles. |
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273 | |
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274 | """ |
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275 | |
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276 | N = self.number_of_elements |
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277 | for i in range(N): |
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278 | #Find all neighbouring volumes that are not boundaries |
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279 | for k in range(3): |
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280 | if self.neighbours[i, k] < 0: |
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281 | self.surrogate_neighbours[i, k] = i #Point this triangle |
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282 | else: |
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283 | self.surrogate_neighbours[i, k] = self.neighbours[i, k] |
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284 | |
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285 | |
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286 | |
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287 | def build_boundary_dictionary(self, boundary = None): |
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288 | """Build or check the dictionary of boundary tags. |
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289 | self.boundary is a dictionary of tags, |
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290 | keyed by volume id and edge: |
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291 | { (id, edge): tag, ... } |
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292 | |
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293 | Postconditions: |
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294 | self.boundary is defined. |
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295 | """ |
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296 | |
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297 | from config import default_boundary_tag |
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298 | |
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299 | if boundary is None: |
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300 | boundary = {} |
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301 | for vol_id in range(self.number_of_elements): |
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302 | for edge_id in range(0, 3): |
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303 | if self.neighbours[vol_id, edge_id] < 0: |
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304 | boundary[(vol_id, edge_id)] = default_boundary_tag |
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305 | else: |
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306 | #Check that all keys in given boundary exist |
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307 | for vol_id, edge_id in boundary.keys(): |
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308 | msg = 'Segment (%d, %d) does not exist' %(vol_id, edge_id) |
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309 | a, b = self.neighbours.shape |
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310 | assert vol_id < a and edge_id < b, msg |
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311 | |
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312 | #FIXME: This assert violates internal boundaries (delete it) |
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313 | #msg = 'Segment (%d, %d) is not a boundary' %(vol_id, edge_id) |
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314 | #assert self.neighbours[vol_id, edge_id] < 0, msg |
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315 | |
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316 | #Check that all boundary segments are assigned a tag |
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317 | for vol_id in range(self.number_of_elements): |
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318 | for edge_id in range(0, 3): |
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319 | if self.neighbours[vol_id, edge_id] < 0: |
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320 | if not boundary.has_key( (vol_id, edge_id) ): |
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321 | msg = 'WARNING: Given boundary does not contain ' |
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322 | msg += 'tags for edge (%d, %d). '\ |
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323 | %(vol_id, edge_id) |
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324 | msg += 'Assigning default tag (%s).'\ |
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325 | %default_boundary_tag |
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326 | |
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327 | #FIXME: Print only as per verbosity |
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328 | #print msg |
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329 | |
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330 | #FIXME: Make this situation an error in the future |
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331 | #and make another function which will |
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332 | #enable default boundary-tags where |
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333 | #tags a not specified |
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334 | boundary[ (vol_id, edge_id) ] =\ |
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335 | default_boundary_tag |
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336 | |
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337 | |
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338 | |
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339 | self.boundary = boundary |
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340 | |
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341 | |
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342 | def build_tagged_elements_dictionary(self, tagged_elements = None): |
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343 | """Build the dictionary of element tags. |
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344 | self.tagged_elements is a dictionary of element arrays, |
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345 | keyed by tag: |
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346 | { (tag): [e1, e2, e3..] } |
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347 | |
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348 | Postconditions: |
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349 | self.element_tag is defined |
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350 | """ |
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351 | from Numeric import array, Int |
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352 | |
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353 | if tagged_elements is None: |
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354 | tagged_elements = {} |
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355 | else: |
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356 | #Check that all keys in given boundary exist |
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357 | for tag in tagged_elements.keys(): |
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358 | tagged_elements[tag] = array(tagged_elements[tag]).astype(Int) |
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359 | |
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360 | msg = 'Not all elements exist. ' |
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361 | assert max(tagged_elements[tag]) < self.number_of_elements, msg |
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362 | #print "tagged_elements", tagged_elements |
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363 | self.tagged_elements = tagged_elements |
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364 | |
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365 | def build_boundary_structure(self): |
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366 | """Traverse boundary and |
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367 | enumerate neighbour indices from -1 and |
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368 | counting down. |
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369 | |
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370 | Precondition: |
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371 | self.boundary is defined. |
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372 | Post condition: |
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373 | neighbour array has unique negative indices for boundary |
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374 | boundary_segments array imposes an ordering on segments |
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375 | (not otherwise available from the dictionary) |
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376 | |
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377 | Note: If a segment is listed in the boundary dictionary |
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378 | it *will* become a boundary - even if there is a neighbouring triangle. |
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379 | This would be the case for internal boundaries |
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380 | """ |
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381 | |
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382 | #FIXME: Now Obsolete - maybe use some comments from here in |
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383 | #domain.set_boundary |
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384 | |
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385 | if self.boundary is None: |
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386 | msg = 'Boundary dictionary must be defined before ' |
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387 | msg += 'building boundary structure' |
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388 | raise msg |
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389 | |
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390 | |
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391 | self.boundary_segments = self.boundary.keys() |
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392 | self.boundary_segments.sort() |
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393 | |
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394 | index = -1 |
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395 | for id, edge in self.boundary_segments: |
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396 | |
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397 | #FIXME: One would detect internal boundaries as follows |
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398 | #if self.neighbours[id, edge] > -1: |
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399 | # print 'Internal boundary' |
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400 | |
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401 | self.neighbours[id, edge] = index |
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402 | index -= 1 |
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403 | |
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404 | |
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405 | def get_boundary_tags(self): |
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406 | """Return list of available boundary tags |
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407 | """ |
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408 | |
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409 | tags = {} |
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410 | for v in self.boundary.values(): |
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411 | tags[v] = 1 |
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412 | |
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413 | return tags.keys() |
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414 | |
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415 | |
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416 | def get_boundary_polygon(self): |
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417 | """Return bounding polygon as a list of points |
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418 | |
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419 | FIXME: If triangles are listed as discontinuous |
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420 | (e.g vertex coordinates listed multiple times), |
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421 | this may not work as expected. |
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422 | """ |
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423 | from Numeric import allclose, sqrt, array, minimum, maximum |
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424 | |
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425 | |
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426 | |
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427 | #V = self.get_vertex_coordinates() |
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428 | segments = {} |
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429 | |
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430 | #pmin = (min(self.coordinates[:,0]), min(self.coordinates[:,1])) |
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431 | #pmax = (max(self.coordinates[:,0]), max(self.coordinates[:,1])) |
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432 | |
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433 | #FIXME:Can this be written more compactly, e.g. |
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434 | #using minimum and maximium? |
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435 | pmin = array( [min(self.coordinates[:,0]), |
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436 | min(self.coordinates[:,1]) ] ) |
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437 | |
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438 | pmax = array( [max(self.coordinates[:,0]), |
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439 | max(self.coordinates[:,1]) ] ) |
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440 | |
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441 | mindist = sqrt(sum( (pmax-pmin)**2 )) |
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442 | for i, edge_id in self.boundary.keys(): |
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443 | #Find vertex ids for boundary segment |
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444 | if edge_id == 0: a = 1; b = 2 |
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445 | if edge_id == 1: a = 2; b = 0 |
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446 | if edge_id == 2: a = 0; b = 1 |
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447 | |
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448 | A = tuple(self.get_vertex_coordinate(i, a)) |
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449 | B = tuple(self.get_vertex_coordinate(i, b)) |
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450 | |
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451 | #Take the point closest to pmin as starting point |
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452 | #Note: Could be arbitrary, but nice to have |
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453 | #a unique way of selecting |
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454 | dist_A = sqrt(sum( (A-pmin)**2 )) |
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455 | dist_B = sqrt(sum( (B-pmin)**2 )) |
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456 | |
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457 | #Find minimal point |
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458 | if dist_A < mindist: |
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459 | mindist = dist_A |
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460 | p0 = A |
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461 | if dist_B < mindist: |
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462 | mindist = dist_B |
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463 | p0 = B |
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464 | |
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465 | |
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466 | if p0 is None: |
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467 | raise 'Weird' |
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468 | p0 = A #We need a starting point (FIXME) |
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469 | |
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470 | print 'A', A |
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471 | print 'B', B |
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472 | print 'pmin', pmin |
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473 | print |
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474 | |
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475 | segments[A] = B |
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476 | |
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477 | |
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478 | #Start with smallest point and follow boundary (counter clock wise) |
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479 | polygon = [p0] |
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480 | while len(polygon) < len(self.boundary): |
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481 | p1 = segments[p0] |
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482 | polygon.append(p1) |
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483 | p0 = p1 |
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484 | |
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485 | return polygon |
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486 | |
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487 | |
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488 | def check_integrity(self): |
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489 | """Check that triangles are internally consistent e.g. |
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490 | that area corresponds to edgelengths, that vertices |
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491 | are arranged in a counter-clockwise order, etc etc |
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492 | Neighbour structure will be checked by class Mesh |
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493 | """ |
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494 | |
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495 | from config import epsilon |
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496 | from math import pi |
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497 | from util import anglediff |
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498 | |
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499 | N = self.number_of_elements |
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500 | |
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501 | #Get x,y coordinates for all vertices for all triangles |
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502 | V = self.get_vertex_coordinates() |
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503 | |
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504 | #Check each triangle |
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505 | for i in range(N): |
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506 | x0 = V[i, 0]; y0 = V[i, 1] |
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507 | x1 = V[i, 2]; y1 = V[i, 3] |
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508 | x2 = V[i, 4]; y2 = V[i, 5] |
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509 | |
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510 | #Check that area hasn't been compromised |
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511 | area = self.areas[i] |
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512 | ref = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
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513 | msg = 'Wrong area for vertex coordinates: %f %f %f %f %f %f'\ |
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514 | %(x0,y0,x1,y1,x2,y2) |
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515 | assert abs((area - ref)/area) < epsilon, msg |
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516 | |
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517 | #Check that points are arranged in counter clock-wise order |
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518 | v0 = [x1-x0, y1-y0] |
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519 | v1 = [x2-x1, y2-y1] |
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520 | v2 = [x0-x2, y0-y2] |
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521 | |
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522 | a0 = anglediff(v1, v0) |
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523 | a1 = anglediff(v2, v1) |
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524 | a2 = anglediff(v0, v2) |
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525 | |
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526 | msg = '''Vertices (%s,%s), (%s,%s), (%s,%s) are not arranged |
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527 | in counter clockwise order''' %(x0, y0, x1, y1, x2, y2) |
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528 | assert a0 < pi and a1 < pi and a2 < pi, msg |
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529 | |
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530 | #Check that normals are orthogonal to edge vectors |
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531 | #Note that normal[k] lies opposite vertex k |
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532 | |
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533 | normal0 = self.normals[i, 0:2] |
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534 | normal1 = self.normals[i, 2:4] |
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535 | normal2 = self.normals[i, 4:6] |
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536 | |
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537 | for u, v in [ (v0, normal2), (v1, normal0), (v2, normal1) ]: |
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538 | |
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539 | #Normalise |
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540 | from math import sqrt |
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541 | l_u = sqrt(u[0]*u[0] + u[1]*u[1]) |
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542 | l_v = sqrt(v[0]*v[0] + v[1]*v[1]) |
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543 | |
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544 | x = (u[0]*v[0] + u[1]*v[1])/l_u/l_v #Inner product |
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545 | |
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546 | msg = 'Normal vector (%f,%f) is not perpendicular to' %tuple(v) |
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547 | msg += ' edge (%f,%f) in triangle %d.' %(tuple(u) + (i,)) |
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548 | msg += ' Inner product is %e.' %x |
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549 | assert x < epsilon, msg |
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550 | |
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551 | |
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552 | #Check that all vertices have been registered |
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553 | for v_id, v in enumerate(self.vertexlist): |
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554 | |
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555 | msg = 'Vertex %s does not belong to an element.' |
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556 | #assert v is not None, msg |
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557 | if v is None: |
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558 | print msg%v_id |
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559 | |
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560 | #Check integrity of neighbour structure |
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561 | for i in range(N): |
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562 | for v in self.triangles[i, :]: |
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563 | #Check that all vertices have been registered |
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564 | assert self.vertexlist[v] is not None |
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565 | |
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566 | #Check that this triangle is listed with at least one vertex |
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567 | assert (i, 0) in self.vertexlist[v] or\ |
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568 | (i, 1) in self.vertexlist[v] or\ |
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569 | (i, 2) in self.vertexlist[v] |
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570 | |
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571 | |
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572 | |
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573 | #Check neighbour structure |
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574 | for k, neighbour_id in enumerate(self.neighbours[i,:]): |
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575 | |
---|
576 | #Assert that my neighbour's neighbour is me |
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577 | #Boundaries need not fulfill this |
---|
578 | if neighbour_id >= 0: |
---|
579 | edge = self.neighbour_edges[i, k] |
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580 | msg = 'Triangle %d has neighbour %d but it does not point back. \n' %(i,neighbour_id) |
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581 | msg += 'Only points to (%s)' %(self.neighbours[neighbour_id,:]) |
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582 | assert self.neighbours[neighbour_id, edge] == i ,msg |
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583 | |
---|
584 | |
---|
585 | |
---|
586 | #Check that all boundaries have |
---|
587 | # unique, consecutive, negative indices |
---|
588 | |
---|
589 | #L = len(self.boundary) |
---|
590 | #for i in range(L): |
---|
591 | # id, edge = self.boundary_segments[i] |
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592 | # assert self.neighbours[id, edge] == -i-1 |
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593 | |
---|
594 | |
---|
595 | #NOTE: This assert doesn't hold true if there are internal boundaries |
---|
596 | #FIXME: Look into this further. |
---|
597 | #FIXME (Ole): In pyvolution mark 3 this is OK again |
---|
598 | #NOTE: No longer works because neighbour structure is modified by |
---|
599 | # domain set_boundary. |
---|
600 | #for id, edge in self.boundary: |
---|
601 | # assert self.neighbours[id,edge] < 0 |
---|
602 | # |
---|
603 | #NOTE (Ole): I reckon this was resolved late 2004? |
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604 | # |
---|
605 | #See domain.set_boundary |
---|
606 | |
---|
607 | |
---|
608 | def get_centroid_coordinates(self): |
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609 | """Return all centroid coordinates. |
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610 | Return all centroid coordinates for all triangles as an Nx2 array |
---|
611 | (ordered as x0, y0 for each triangle) |
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612 | """ |
---|
613 | return self.centroid_coordinates |
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