1 | |
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2 | from Numeric import concatenate, reshape, take, allclose |
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3 | from Numeric import array, zeros, Int, Float, sqrt, sum |
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4 | |
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5 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
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6 | |
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7 | class General_mesh: |
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8 | """Collection of 2D triangular elements |
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9 | |
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10 | A triangular element is defined in terms of three vertex ids, |
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11 | ordered counter clock-wise, each corresponding to a given node |
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12 | which is represented as a coordinate set (x,y). |
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13 | Vertices from different triangles can point to the same node. |
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14 | The nodes are implemented as an Nx2 Numeric array containing the |
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15 | x and y coordinates. |
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16 | |
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17 | |
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18 | To instantiate: |
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19 | Mesh(nodes, triangles) |
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20 | |
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21 | where |
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22 | |
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23 | nodes is either a list of 2-tuples or an Nx2 Numeric array of |
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24 | floats representing all x, y coordinates in the mesh. |
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25 | |
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26 | triangles is either a list of 3-tuples or an Mx3 Numeric array of |
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27 | integers representing indices of all vertices in the mesh. |
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28 | Each vertex is identified by its index i in [0, N-1]. |
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29 | |
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30 | |
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31 | Example: |
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32 | |
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33 | a = [0.0, 0.0] |
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34 | b = [0.0, 2.0] |
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35 | c = [2.0,0.0] |
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36 | e = [2.0, 2.0] |
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37 | |
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38 | nodes = [a, b, c, e] |
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39 | triangles = [ [1,0,2], [1,2,3] ] # bac, bce |
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40 | |
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41 | # Create mesh with two triangles: bac and bce |
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42 | mesh = Mesh(nodes, triangles) |
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43 | |
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44 | |
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45 | |
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46 | Other: |
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47 | |
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48 | In addition mesh computes an Mx6 array called vertex_coordinates. |
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49 | This structure is derived from coordinates and contains for each |
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50 | triangle the three x,y coordinates at the vertices. |
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51 | |
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52 | See neighbourmesh.py for a specialisation of the general mesh class |
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53 | which includes information about neighbours and the mesh boundary. |
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54 | |
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55 | The mesh object is purely geometrical and contains no information |
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56 | about quantities defined on the mesh. |
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57 | |
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58 | """ |
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59 | |
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60 | #FIXME: It would be a good idea to use geospatial data as an alternative |
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61 | #input |
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62 | def __init__(self, nodes, triangles, |
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63 | geo_reference=None, |
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64 | number_of_full_nodes=None, |
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65 | number_of_full_triangles=None, |
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66 | verbose=False): |
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67 | """Build triangular 2d mesh from nodes and triangle information |
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68 | |
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69 | Input: |
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70 | |
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71 | nodes: x,y coordinates represented as a sequence of 2-tuples or |
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72 | a Nx2 Numeric array of floats. |
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73 | |
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74 | triangles: sequence of 3-tuples or Mx3 Numeric array of |
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75 | non-negative integers representing indices into |
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76 | the nodes array. |
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77 | |
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78 | georeference (optional): If specified coordinates are |
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79 | assumed to be relative to this origin. |
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80 | |
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81 | |
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82 | number_of_full_nodes and number_of_full_triangles relate to |
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83 | parallelism when each mesh has an extra layer of ghost points and |
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84 | ghost triangles attached to the end of the two arrays. |
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85 | In this case it is usefull to specify the number of real (called full) |
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86 | nodes and triangles. If omitted they will default to all. |
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87 | |
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88 | """ |
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89 | |
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90 | if verbose: print 'General_mesh: Building basic mesh structure' |
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91 | |
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92 | self.triangles = array(triangles, Int) |
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93 | self.nodes = array(nodes, Float) |
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94 | |
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95 | |
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96 | # Register number of elements and nodes |
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97 | self.number_of_triangles = N = self.triangles.shape[0] |
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98 | self.number_of_nodes = self.nodes.shape[0] |
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99 | |
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100 | |
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101 | |
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102 | if number_of_full_nodes is None: |
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103 | self.number_of_full_nodes = self.number_of_nodes |
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104 | else: |
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105 | assert int(number_of_full_nodes) |
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106 | self.number_of_full_nodes = number_of_full_nodes |
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107 | |
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108 | |
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109 | if number_of_full_triangles is None: |
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110 | self.number_of_full_triangles = self.number_of_triangles |
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111 | else: |
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112 | assert int(number_of_full_triangles) |
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113 | self.number_of_full_triangles = number_of_full_triangles |
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114 | |
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115 | |
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116 | #print self.number_of_full_nodes, self.number_of_nodes |
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117 | #print self.number_of_full_triangles, self.number_of_triangles |
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118 | |
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119 | |
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120 | |
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121 | # FIXME: this stores a geo_reference, but when coords are returned |
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122 | # This geo_ref is not taken into account! |
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123 | if geo_reference is None: |
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124 | self.geo_reference = Geo_reference() #Use defaults |
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125 | else: |
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126 | self.geo_reference = geo_reference |
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127 | |
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128 | # Input checks |
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129 | msg = 'Triangles must an Mx3 Numeric array or a sequence of 3-tuples. ' |
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130 | msg += 'The supplied array has the shape: %s'\ |
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131 | %str(self.triangles.shape) |
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132 | assert len(self.triangles.shape) == 2, msg |
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133 | |
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134 | msg = 'Nodes must an Nx2 Numeric array or a sequence of 2-tuples' |
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135 | msg += 'The supplied array has the shape: %s'\ |
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136 | %str(self.nodes.shape) |
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137 | assert len(self.nodes.shape) == 2, msg |
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138 | |
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139 | msg = 'Vertex indices reference non-existing coordinate sets' |
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140 | assert max(max(self.triangles)) <= self.nodes.shape[0], msg |
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141 | |
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142 | |
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143 | # FIXME: Maybe move to statistics? |
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144 | # Or use with get_extent |
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145 | xy_extent = [ min(self.nodes[:,0]), min(self.nodes[:,1]) , |
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146 | max(self.nodes[:,0]), max(self.nodes[:,1]) ] |
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147 | |
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148 | self.xy_extent = array(xy_extent, Float) |
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149 | |
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150 | |
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151 | # Allocate space for geometric quantities |
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152 | self.normals = zeros((N, 6), Float) |
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153 | self.areas = zeros(N, Float) |
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154 | self.edgelengths = zeros((N, 3), Float) |
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155 | |
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156 | # Get x,y coordinates for all triangles and store |
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157 | self.vertex_coordinates = V = self.compute_vertex_coordinates() |
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158 | |
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159 | |
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160 | # Initialise each triangle |
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161 | if verbose: |
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162 | print 'General_mesh: Computing areas, normals and edgelenghts' |
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163 | |
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164 | for i in range(N): |
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165 | if verbose and i % ((N+10)/10) == 0: print '(%d/%d)' %(i, N) |
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166 | |
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167 | x0, y0 = V[3*i, :] |
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168 | x1, y1 = V[3*i+1, :] |
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169 | x2, y2 = V[3*i+2, :] |
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170 | |
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171 | # Area |
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172 | self.areas[i] = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
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173 | |
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174 | msg = 'Triangle (%f,%f), (%f,%f), (%f, %f)' %(x0,y0,x1,y1,x2,y2) |
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175 | msg += ' is degenerate: area == %f' %self.areas[i] |
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176 | assert self.areas[i] > 0.0, msg |
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177 | |
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178 | |
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179 | # Normals |
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180 | # The normal vectors |
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181 | # - point outward from each edge |
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182 | # - are orthogonal to the edge |
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183 | # - have unit length |
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184 | # - Are enumerated according to the opposite corner: |
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185 | # (First normal is associated with the edge opposite |
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186 | # the first vertex, etc) |
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187 | # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle |
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188 | |
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189 | n0 = array([x2 - x1, y2 - y1]) |
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190 | l0 = sqrt(sum(n0**2)) |
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191 | |
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192 | n1 = array([x0 - x2, y0 - y2]) |
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193 | l1 = sqrt(sum(n1**2)) |
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194 | |
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195 | n2 = array([x1 - x0, y1 - y0]) |
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196 | l2 = sqrt(sum(n2**2)) |
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197 | |
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198 | # Normalise |
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199 | n0 /= l0 |
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200 | n1 /= l1 |
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201 | n2 /= l2 |
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202 | |
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203 | # Compute and store |
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204 | self.normals[i, :] = [n0[1], -n0[0], |
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205 | n1[1], -n1[0], |
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206 | n2[1], -n2[0]] |
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207 | |
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208 | # Edgelengths |
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209 | self.edgelengths[i, :] = [l0, l1, l2] |
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210 | |
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211 | |
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212 | # Build vertex list |
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213 | if verbose: print 'Building vertex list' |
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214 | self.build_vertexlist() |
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215 | |
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216 | |
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217 | |
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218 | def __len__(self): |
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219 | return self.number_of_triangles |
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220 | |
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221 | |
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222 | def __repr__(self): |
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223 | return 'Mesh: %d vertices, %d triangles'\ |
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224 | %(self.nodes.shape[0], len(self)) |
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225 | |
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226 | def get_normals(self): |
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227 | """Return all normal vectors. |
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228 | Return normal vectors for all triangles as an Nx6 array |
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229 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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230 | """ |
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231 | return self.normals |
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232 | |
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233 | |
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234 | def get_normal(self, i, j): |
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235 | """Return normal vector j of the i'th triangle. |
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236 | Return value is the numeric array slice [x, y] |
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237 | """ |
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238 | return self.normals[i, 2*j:2*j+2] |
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239 | |
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240 | |
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241 | def get_nodes(self, absolute=False): |
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242 | """Return all nodes in mesh. |
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243 | |
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244 | The nodes are ordered in an Nx2 array where N is the number of nodes. |
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245 | This is the same format they were provided in the constructor |
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246 | i.e. without any duplication. |
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247 | |
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248 | Boolean keyword argument absolute determines whether coordinates |
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249 | are to be made absolute by taking georeference into account |
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250 | Default is False as many parts of ANUGA expects relative coordinates. |
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251 | (To see which, switch to default absolute=True and run tests). |
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252 | """ |
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253 | |
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254 | N = self.number_of_full_nodes |
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255 | V = self.nodes[:N,:] |
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256 | if absolute is True: |
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257 | if not self.geo_reference.is_absolute(): |
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258 | V = self.geo_reference.get_absolute(V) |
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259 | |
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260 | return V |
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261 | |
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262 | |
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263 | |
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264 | def get_vertex_coordinates(self, absolute=False): |
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265 | """Return vertex coordinates for all triangles. |
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266 | |
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267 | Return all vertex coordinates for all triangles as a 3*M x 2 array |
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268 | where the jth vertex of the ith triangle is located in row 3*i+j and |
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269 | M the number of triangles in the mesh. |
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270 | |
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271 | Boolean keyword argument absolute determines whether coordinates |
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272 | are to be made absolute by taking georeference into account |
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273 | Default is False as many parts of ANUGA expects relative coordinates. |
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274 | """ |
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275 | |
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276 | V = self.vertex_coordinates |
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277 | if absolute is True: |
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278 | if not self.geo_reference.is_absolute(): |
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279 | V = self.geo_reference.get_absolute(V) |
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280 | |
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281 | return V |
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282 | |
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283 | |
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284 | |
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285 | def get_vertex_coordinate(self, i, j, absolute=False): |
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286 | """Return coordinates for vertex j of the i'th triangle. |
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287 | Return value is the numeric array slice [x, y] |
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288 | """ |
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289 | |
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290 | V = self.get_vertex_coordinates(absolute=absolute) |
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291 | return V[3*i+j, :] |
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292 | |
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293 | |
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294 | def compute_vertex_coordinates(self): |
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295 | """Return all vertex coordinates for all triangles as a 3*M x 2 array |
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296 | where the jth vertex of the ith triangle is located in row 3*i+j. |
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297 | |
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298 | This function is used to precompute this important structure. Use |
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299 | get_vertex coordinates to retrieve the points. |
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300 | """ |
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301 | |
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302 | M = self.number_of_triangles |
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303 | vertex_coordinates = zeros((3*M, 2), Float) |
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304 | |
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305 | for i in range(M): |
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306 | for j in range(3): |
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307 | k = self.triangles[i,j] # Index of vertex j in triangle i |
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308 | vertex_coordinates[3*i+j,:] = self.nodes[k] |
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309 | |
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310 | return vertex_coordinates |
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311 | |
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312 | |
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313 | |
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314 | def get_triangles(self, indices=None): |
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315 | """Get mesh triangles. |
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316 | |
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317 | Return Mx3 integer array where M is the number of triangles. |
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318 | Each row corresponds to one triangle and the three entries are |
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319 | indices into the mesh nodes which can be obtained using the method |
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320 | get_nodes() |
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321 | |
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322 | Optional argument, indices is the set of triangle ids of interest. |
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323 | """ |
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324 | |
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325 | M = self.number_of_full_triangles |
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326 | |
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327 | if indices is None: |
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328 | indices = range(M) |
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329 | |
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330 | return take(self.triangles, indices) |
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331 | |
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332 | |
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333 | |
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334 | def get_disconnected_triangles(self): |
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335 | """Get mesh based on nodes obtained from get_vertex_coordinates. |
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336 | |
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337 | Return array Mx3 array of integers where each row corresponds to |
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338 | a triangle. A triangle is a triplet of indices into |
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339 | point coordinates obtained from get_vertex_coordinates and each |
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340 | index appears only once |
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341 | |
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342 | This provides a mesh where no triangles share nodes |
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343 | (hence the name disconnected triangles) and different |
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344 | nodes may have the same coordinates. |
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345 | |
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346 | This version of the mesh is useful for storing meshes with |
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347 | discontinuities at each node and is e.g. used for storing |
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348 | data in sww files. |
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349 | |
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350 | The triangles created will have the format |
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351 | |
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352 | [[0,1,2], |
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353 | [3,4,5], |
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354 | [6,7,8], |
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355 | ... |
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356 | [3*M-3 3*M-2 3*M-1]] |
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357 | """ |
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358 | |
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359 | M = len(self) # Number of triangles |
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360 | K = 3*M # Total number of unique vertices |
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361 | T = reshape(array(range(K)).astype(Int), (M,3)) |
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362 | |
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363 | return T |
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364 | |
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365 | |
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366 | |
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367 | def get_unique_vertices(self, indices=None): |
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368 | """FIXME(Ole): This function needs a docstring |
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369 | """ |
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370 | triangles = self.get_triangles(indices=indices) |
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371 | unique_verts = {} |
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372 | for triangle in triangles: |
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373 | unique_verts[triangle[0]] = 0 |
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374 | unique_verts[triangle[1]] = 0 |
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375 | unique_verts[triangle[2]] = 0 |
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376 | return unique_verts.keys() |
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377 | |
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378 | |
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379 | def build_vertexlist(self): |
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380 | """Build vertexlist indexed by vertex ids and for each entry (point id) |
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381 | build a list of (triangles, vertex_id) pairs that use the point |
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382 | as vertex. |
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383 | |
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384 | The vertex list will have length N, where N is the number of nodes |
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385 | in the mesh. |
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386 | |
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387 | Preconditions: |
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388 | self.nodes and self.triangles are defined |
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389 | |
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390 | Postcondition: |
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391 | self.vertexlist is built |
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392 | """ |
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393 | |
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394 | vertexlist = [None]*self.number_of_nodes |
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395 | for i in range(self.number_of_triangles): |
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396 | |
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397 | a = self.triangles[i, 0] |
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398 | b = self.triangles[i, 1] |
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399 | c = self.triangles[i, 2] |
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400 | |
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401 | #Register the vertices v as lists of |
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402 | #(triangle_id, vertex_id) tuples associated with them |
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403 | #This is used for averaging multiple vertex values. |
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404 | for vertex_id, v in enumerate([a,b,c]): |
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405 | if vertexlist[v] is None: |
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406 | vertexlist[v] = [] |
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407 | |
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408 | vertexlist[v].append( (i, vertex_id) ) |
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409 | |
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410 | self.vertexlist = vertexlist |
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411 | |
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412 | |
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413 | def get_extent(self, absolute=False): |
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414 | """Return min and max of all x and y coordinates |
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415 | |
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416 | Boolean keyword argument absolute determines whether coordinates |
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417 | are to be made absolute by taking georeference into account |
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418 | """ |
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419 | |
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420 | |
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421 | |
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422 | C = self.get_vertex_coordinates(absolute=absolute) |
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423 | X = C[:,0:6:2].copy() |
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424 | Y = C[:,1:6:2].copy() |
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425 | |
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426 | xmin = min(X.flat) |
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427 | xmax = max(X.flat) |
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428 | ymin = min(Y.flat) |
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429 | ymax = max(Y.flat) |
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430 | |
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431 | return xmin, xmax, ymin, ymax |
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432 | |
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433 | |
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434 | def get_area(self): |
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435 | """Return total area of mesh |
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436 | """ |
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437 | |
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438 | return sum(self.areas) |
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439 | |
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440 | |
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