1 | import numpy as num |
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2 | |
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3 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
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4 | |
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5 | class General_mesh: |
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6 | """Collection of 2D triangular elements |
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7 | |
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8 | A triangular element is defined in terms of three vertex ids, |
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9 | ordered counter clock-wise, each corresponding to a given node |
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10 | which is represented as a coordinate set (x,y). |
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11 | Vertices from different triangles can point to the same node. |
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12 | The nodes are implemented as an Nx2 numeric array containing the |
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13 | x and y coordinates. |
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14 | |
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15 | |
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16 | To instantiate: |
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17 | Mesh(nodes, triangles) |
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18 | |
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19 | where |
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20 | |
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21 | nodes is either a list of 2-tuples or an Nx2 numeric array of |
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22 | floats representing all x, y coordinates in the mesh. |
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23 | |
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24 | triangles is either a list of 3-tuples or an Mx3 numeric array of |
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25 | integers representing indices of all vertices in the mesh. |
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26 | Each vertex is identified by its index i in [0, N-1]. |
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27 | |
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28 | |
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29 | Example: |
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30 | |
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31 | a = [0.0, 0.0] |
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32 | b = [0.0, 2.0] |
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33 | c = [2.0,0.0] |
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34 | e = [2.0, 2.0] |
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35 | |
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36 | nodes = [a, b, c, e] |
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37 | triangles = [ [1,0,2], [1,2,3] ] # bac, bce |
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38 | |
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39 | # Create mesh with two triangles: bac and bce |
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40 | mesh = Mesh(nodes, triangles) |
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41 | |
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42 | |
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43 | |
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44 | Other: |
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45 | |
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46 | In addition mesh computes an Mx6 array called vertex_coordinates. |
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47 | This structure is derived from coordinates and contains for each |
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48 | triangle the three x,y coordinates at the vertices. |
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49 | |
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50 | See neighbourmesh.py for a specialisation of the general mesh class |
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51 | which includes information about neighbours and the mesh boundary. |
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52 | |
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53 | The mesh object is purely geometrical and contains no information |
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54 | about quantities defined on the mesh. |
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55 | |
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56 | """ |
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57 | |
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58 | #FIXME: It would be a good idea to use geospatial data as an alternative |
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59 | #input |
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60 | def __init__(self, nodes, triangles, |
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61 | geo_reference=None, |
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62 | number_of_full_nodes=None, |
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63 | number_of_full_triangles=None, |
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64 | verbose=False): |
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65 | """Build triangular 2d mesh from nodes and triangle information |
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66 | |
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67 | Input: |
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68 | |
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69 | nodes: x,y coordinates represented as a sequence of 2-tuples or |
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70 | a Nx2 numeric array of floats. |
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71 | |
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72 | triangles: sequence of 3-tuples or Mx3 numeric array of |
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73 | non-negative integers representing indices into |
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74 | the nodes array. |
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75 | |
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76 | georeference (optional): If specified coordinates are |
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77 | assumed to be relative to this origin. |
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78 | |
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79 | |
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80 | number_of_full_nodes and number_of_full_triangles relate to |
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81 | parallelism when each mesh has an extra layer of ghost points and |
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82 | ghost triangles attached to the end of the two arrays. |
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83 | In this case it is usefull to specify the number of real (called full) |
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84 | nodes and triangles. If omitted they will default to all. |
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85 | |
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86 | """ |
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87 | |
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88 | if verbose: print 'General_mesh: Building basic mesh structure in ANUGA domain' |
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89 | |
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90 | self.triangles = num.array(triangles, num.int) |
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91 | self.nodes = num.array(nodes, num.float) |
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92 | |
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93 | |
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94 | # Register number of elements and nodes |
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95 | self.number_of_triangles = N = self.triangles.shape[0] |
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96 | self.number_of_nodes = self.nodes.shape[0] |
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97 | |
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98 | |
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99 | |
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100 | if number_of_full_nodes is None: |
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101 | self.number_of_full_nodes = self.number_of_nodes |
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102 | else: |
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103 | assert int(number_of_full_nodes) |
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104 | self.number_of_full_nodes = number_of_full_nodes |
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105 | |
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106 | |
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107 | if number_of_full_triangles is None: |
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108 | self.number_of_full_triangles = self.number_of_triangles |
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109 | else: |
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110 | assert int(number_of_full_triangles) |
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111 | self.number_of_full_triangles = number_of_full_triangles |
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112 | |
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113 | |
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114 | #print self.number_of_full_nodes, self.number_of_nodes |
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115 | #print self.number_of_full_triangles, self.number_of_triangles |
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116 | |
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117 | |
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118 | |
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119 | # FIXME: this stores a geo_reference, but when coords are returned |
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120 | # This geo_ref is not taken into account! |
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121 | if geo_reference is None: |
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122 | self.geo_reference = Geo_reference() #Use defaults |
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123 | else: |
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124 | self.geo_reference = geo_reference |
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125 | |
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126 | # Input checks |
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127 | msg = 'Triangles must an Mx3 numeric array or a sequence of 3-tuples. ' |
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128 | msg += 'The supplied array has the shape: %s'\ |
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129 | %str(self.triangles.shape) |
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130 | assert len(self.triangles.shape) == 2, msg |
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131 | |
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132 | msg = 'Nodes must an Nx2 numeric array or a sequence of 2-tuples' |
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133 | msg += 'The supplied array has the shape: %s'\ |
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134 | %str(self.nodes.shape) |
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135 | assert len(self.nodes.shape) == 2, msg |
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136 | |
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137 | msg = 'Vertex indices reference non-existing coordinate sets' |
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138 | assert max(self.triangles.flat) < self.nodes.shape[0], msg |
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139 | |
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140 | |
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141 | # FIXME: Maybe move to statistics? |
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142 | # Or use with get_extent |
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143 | xy_extent = [ min(self.nodes[:,0]), min(self.nodes[:,1]) , |
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144 | max(self.nodes[:,0]), max(self.nodes[:,1]) ] |
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145 | |
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146 | self.xy_extent = num.array(xy_extent, num.float) |
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147 | |
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148 | |
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149 | # Allocate space for geometric quantities |
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150 | self.normals = num.zeros((N, 6), num.float) |
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151 | self.areas = num.zeros(N, num.float) |
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152 | self.edgelengths = num.zeros((N, 3), num.float) |
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153 | |
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154 | # Get x,y coordinates for all triangles and store |
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155 | self.vertex_coordinates = V = self.compute_vertex_coordinates() |
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156 | |
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157 | |
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158 | # Initialise each triangle |
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159 | if verbose: |
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160 | print 'General_mesh: Computing areas, normals and edgelenghts' |
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161 | |
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162 | for i in range(N): |
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163 | if verbose and i % ((N+10)/10) == 0: print '(%d/%d)' %(i, N) |
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164 | |
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165 | x0, y0 = V[3*i, :] |
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166 | x1, y1 = V[3*i+1, :] |
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167 | x2, y2 = V[3*i+2, :] |
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168 | |
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169 | # Area |
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170 | self.areas[i] = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
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171 | |
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172 | msg = 'Triangle (%f,%f), (%f,%f), (%f, %f)' %(x0,y0,x1,y1,x2,y2) |
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173 | msg += ' is degenerate: area == %f' %self.areas[i] |
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174 | assert self.areas[i] > 0.0, msg |
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175 | |
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176 | |
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177 | # Normals |
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178 | # The normal vectors |
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179 | # - point outward from each edge |
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180 | # - are orthogonal to the edge |
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181 | # - have unit length |
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182 | # - Are enumerated according to the opposite corner: |
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183 | # (First normal is associated with the edge opposite |
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184 | # the first vertex, etc) |
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185 | # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle |
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186 | |
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187 | n0 = num.array([x2 - x1, y2 - y1], num.float) |
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188 | l0 = num.sqrt(num.sum(n0**2)) |
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189 | |
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190 | n1 = num.array([x0 - x2, y0 - y2], num.float) |
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191 | l1 = num.sqrt(num.sum(n1**2)) |
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192 | |
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193 | n2 = num.array([x1 - x0, y1 - y0], num.float) |
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194 | l2 = num.sqrt(num.sum(n2**2)) |
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195 | |
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196 | # Normalise |
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197 | n0 /= l0 |
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198 | n1 /= l1 |
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199 | n2 /= l2 |
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200 | |
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201 | # Compute and store |
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202 | self.normals[i, :] = [n0[1], -n0[0], |
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203 | n1[1], -n1[0], |
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204 | n2[1], -n2[0]] |
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205 | |
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206 | # Edgelengths |
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207 | self.edgelengths[i, :] = [l0, l1, l2] |
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208 | |
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209 | |
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210 | # Build structure listing which trianglse belong to which node. |
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211 | if verbose: print 'Building inverted triangle structure' |
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212 | self.build_inverted_triangle_structure() |
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213 | |
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214 | |
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215 | |
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216 | def __len__(self): |
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217 | return self.number_of_triangles |
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218 | |
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219 | |
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220 | def __repr__(self): |
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221 | return 'Mesh: %d vertices, %d triangles'\ |
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222 | %(self.nodes.shape[0], len(self)) |
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223 | |
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224 | def get_normals(self): |
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225 | """Return all normal vectors. |
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226 | Return normal vectors for all triangles as an Nx6 array |
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227 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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228 | """ |
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229 | return self.normals |
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230 | |
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231 | |
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232 | def get_normal(self, i, j): |
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233 | """Return normal vector j of the i'th triangle. |
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234 | Return value is the numeric array slice [x, y] |
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235 | """ |
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236 | return self.normals[i, 2*j:2*j+2] |
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237 | |
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238 | def get_number_of_nodes(self): |
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239 | return self.number_of_nodes |
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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 | def get_node(self, i, |
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263 | absolute=False): |
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264 | """Return node coordinates for triangle i. |
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265 | |
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266 | Boolean keyword argument absolute determines whether coordinates |
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267 | are to be made absolute by taking georeference into account |
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268 | Default is False as many parts of ANUGA expects relative coordinates. |
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269 | (To see which, switch to default absolute=True and run tests). |
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270 | """ |
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271 | |
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272 | |
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273 | V = self.nodes[i,:] |
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274 | if absolute is True: |
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275 | if not self.geo_reference.is_absolute(): |
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276 | return V + num.array([self.geo_reference.get_xllcorner(), |
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277 | self.geo_reference.get_yllcorner()], num.float) |
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278 | else: |
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279 | return V |
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280 | else: |
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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_coordinates(self, |
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286 | triangle_id=None, |
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287 | absolute=False): |
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288 | """Return vertex coordinates for all triangles. |
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289 | |
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290 | Return all vertex coordinates for all triangles as a 3*M x 2 array |
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291 | where the jth vertex of the ith triangle is located in row 3*i+j and |
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292 | M the number of triangles in the mesh. |
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293 | |
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294 | if triangle_id is specified (an integer) the 3 vertex coordinates |
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295 | for triangle_id are returned. |
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296 | |
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297 | Boolean keyword argument absolute determines whether coordinates |
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298 | are to be made absolute by taking georeference into account |
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299 | Default is False as many parts of ANUGA expects relative coordinates. |
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300 | """ |
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301 | |
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302 | V = self.vertex_coordinates |
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303 | |
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304 | if triangle_id is None: |
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305 | if absolute is True: |
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306 | if not self.geo_reference.is_absolute(): |
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307 | V = self.geo_reference.get_absolute(V) |
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308 | |
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309 | return V |
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310 | else: |
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311 | i = triangle_id |
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312 | msg = 'triangle_id must be an integer' |
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313 | assert int(i) == i, msg |
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314 | assert 0 <= i < self.number_of_triangles |
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315 | |
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316 | i3 = 3*i |
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317 | if absolute is True and not self.geo_reference.is_absolute(): |
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318 | offset=num.array([self.geo_reference.get_xllcorner(), |
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319 | self.geo_reference.get_yllcorner()], num.float) |
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320 | return num.array([V[i3,:]+offset, |
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321 | V[i3+1,:]+offset, |
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322 | V[i3+2,:]+offset], num.float) |
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323 | else: |
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324 | return num.array([V[i3,:], V[i3+1,:], V[i3+2,:]], num.float) |
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325 | |
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326 | |
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327 | |
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328 | def get_vertex_coordinate(self, i, j, absolute=False): |
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329 | """Return coordinates for vertex j of the i'th triangle. |
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330 | Return value is the numeric array slice [x, y] |
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331 | """ |
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332 | |
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333 | msg = 'vertex id j must be an integer in [0,1,2]' |
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334 | assert j in [0,1,2], msg |
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335 | |
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336 | V = self.get_vertex_coordinates(triangle_id=i, |
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337 | absolute=absolute) |
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338 | return V[j,:] |
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339 | |
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340 | |
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341 | |
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342 | def compute_vertex_coordinates(self): |
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343 | """Return all vertex coordinates for all triangles as a 3*M x 2 array |
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344 | where the jth vertex of the ith triangle is located in row 3*i+j. |
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345 | |
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346 | This function is used to precompute this important structure. Use |
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347 | get_vertex coordinates to retrieve the points. |
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348 | """ |
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349 | |
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350 | M = self.number_of_triangles |
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351 | vertex_coordinates = num.zeros((3*M, 2), num.float) |
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352 | |
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353 | for i in range(M): |
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354 | for j in range(3): |
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355 | k = self.triangles[i,j] # Index of vertex j in triangle i |
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356 | vertex_coordinates[3*i+j,:] = self.nodes[k] |
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357 | |
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358 | return vertex_coordinates |
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359 | |
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360 | |
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361 | |
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362 | def get_triangles(self, indices=None): |
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363 | """Get mesh triangles. |
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364 | |
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365 | Return Mx3 integer array where M is the number of triangles. |
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366 | Each row corresponds to one triangle and the three entries are |
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367 | indices into the mesh nodes which can be obtained using the method |
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368 | get_nodes() |
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369 | |
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370 | Optional argument, indices is the set of triangle ids of interest. |
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371 | """ |
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372 | |
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373 | M = self.number_of_full_triangles |
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374 | |
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375 | if indices is None: |
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376 | return self.triangles |
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377 | #indices = range(M) |
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378 | |
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379 | return num.take(self.triangles, indices, axis=0) |
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380 | |
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381 | |
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382 | |
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383 | def get_disconnected_triangles(self): |
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384 | """Get mesh based on nodes obtained from get_vertex_coordinates. |
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385 | |
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386 | Return array Mx3 array of integers where each row corresponds to |
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387 | a triangle. A triangle is a triplet of indices into |
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388 | point coordinates obtained from get_vertex_coordinates and each |
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389 | index appears only once |
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390 | |
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391 | This provides a mesh where no triangles share nodes |
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392 | (hence the name disconnected triangles) and different |
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393 | nodes may have the same coordinates. |
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394 | |
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395 | This version of the mesh is useful for storing meshes with |
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396 | discontinuities at each node and is e.g. used for storing |
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397 | data in sww files. |
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398 | |
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399 | The triangles created will have the format |
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400 | |
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401 | [[0,1,2], |
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402 | [3,4,5], |
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403 | [6,7,8], |
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404 | ... |
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405 | [3*M-3 3*M-2 3*M-1]] |
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406 | """ |
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407 | |
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408 | M = len(self) # Number of triangles |
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409 | K = 3*M # Total number of unique vertices |
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410 | |
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411 | T = num.reshape(num.arange(K, dtype=num.int), (M,3)) |
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412 | |
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413 | return T |
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414 | |
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415 | |
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416 | |
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417 | def get_unique_vertices(self, indices=None): |
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418 | """FIXME(Ole): This function needs a docstring""" |
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419 | |
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420 | triangles = self.get_triangles(indices=indices) |
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421 | unique_verts = {} |
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422 | for triangle in triangles: |
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423 | #print 'triangle(%s)=%s' % (type(triangle), str(triangle)) |
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424 | unique_verts[triangle[0]] = 0 |
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425 | unique_verts[triangle[1]] = 0 |
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426 | unique_verts[triangle[2]] = 0 |
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427 | return unique_verts.keys() |
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428 | |
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429 | |
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430 | def get_triangles_and_vertices_per_node(self, node=None): |
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431 | """Get triangles associated with given node. |
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432 | |
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433 | Return list of triangle_ids, vertex_ids for specified node. |
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434 | If node in None or absent, this information will be returned |
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435 | for all (full) nodes in a list L where L[v] is the triangle |
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436 | list for node v. |
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437 | """ |
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438 | |
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439 | triangle_list = [] |
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440 | if node is not None: |
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441 | # Get index for this node |
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442 | first = num.sum(self.number_of_triangles_per_node[:node]) |
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443 | |
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444 | # Get number of triangles for this node |
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445 | count = self.number_of_triangles_per_node[node] |
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446 | |
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447 | for i in range(count): |
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448 | index = self.vertex_value_indices[first+i] |
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449 | |
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450 | volume_id = index / 3 |
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451 | vertex_id = index % 3 |
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452 | |
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453 | triangle_list.append( (volume_id, vertex_id) ) |
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454 | |
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455 | triangle_list = num.array(triangle_list, num.int) #array default# |
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456 | else: |
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457 | # Get info for all nodes recursively. |
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458 | # If need be, we can speed this up by |
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459 | # working directly with the inverted triangle structure |
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460 | for i in range(self.number_of_full_nodes): |
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461 | |
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462 | L = self.get_triangles_and_vertices_per_node(node=i) |
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463 | |
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464 | triangle_list.append(L) |
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465 | |
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466 | return triangle_list |
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467 | |
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468 | |
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469 | def build_inverted_triangle_structure(self): |
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470 | """Build structure listing triangles belonging to each node |
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471 | |
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472 | Two arrays are created and store as mesh attributes |
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473 | |
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474 | number_of_triangles_per_node: An integer array of length N |
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475 | listing for each node how many triangles use it. N is the number of |
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476 | nodes in mesh. |
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477 | |
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478 | vertex_value_indices: An array of length M listing indices into |
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479 | triangles ordered by node number. The (triangle_id, vertex_id) |
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480 | pairs are obtained from each index as (index/3, index%3) or each |
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481 | index can be used directly into a flattened triangles array. This |
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482 | is for example the case in the quantity.c where this structure is |
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483 | used to average vertex values efficiently. |
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484 | |
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485 | |
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486 | Example: |
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487 | |
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488 | a = [0.0, 0.0] # node 0 |
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489 | b = [0.0, 2.0] # node 1 |
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490 | c = [2.0, 0.0] # node 2 |
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491 | d = [0.0, 4.0] # node 3 |
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492 | e = [2.0, 2.0] # node 4 |
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493 | f = [4.0, 0.0] # node 5 |
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494 | |
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495 | nodes = array([a, b, c, d, e, f]) |
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496 | |
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497 | #bac, bce, ecf, dbe, daf, dae |
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498 | triangles = array([[1,0,2], [1,2,4], [4,2,5], [3,1,4]]) |
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499 | |
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500 | |
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501 | For this structure |
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502 | |
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503 | number_of_triangles_per_node = [1 3 3 1 3 1] |
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504 | which means that node a has 1 triangle associated with it, node b |
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505 | has 3, node has 3 and so on. |
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506 | |
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507 | vertex_value_indices = [ 1 0 3 10 2 4 7 9 5 6 11 8] |
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508 | which reflects the fact that |
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509 | node 0 is used by triangle 0, vertex 1 (index = 1) |
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510 | node 1 is used by triangle 0, vertex 0 (index = 0) |
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511 | and by triangle 1, vertex 0 (index = 3) |
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512 | and by triangle 3, vertex 1 (index = 10) |
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513 | node 2 is used by triangle 0, vertex 2 (index = 2) |
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514 | and by triangle 1, vertex 1 (index = 4) |
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515 | and by triangle 2, vertex 1 (index = 7) |
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516 | node 3 is used by triangle 3, vertex 0 (index = 9) |
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517 | node 4 is used by triangle 1, vertex 2 (index = 5) |
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518 | and by triangle 2, vertex 0 (index = 6) |
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519 | and by triangle 3, vertex 2 (index = 11) |
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520 | node 5 is used by triangle 2, vertex 2 (index = 8) |
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521 | |
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522 | |
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523 | Preconditions: |
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524 | self.nodes and self.triangles are defined |
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525 | |
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526 | Postcondition: |
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527 | self.number_of_triangles_per_node is built |
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528 | self.vertex_value_indices is built |
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529 | """ |
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530 | |
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531 | # Count number of triangles per node |
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532 | number_of_triangles_per_node = num.zeros(self.number_of_full_nodes, |
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533 | num.int) #array default# |
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534 | for volume_id, triangle in enumerate(self.get_triangles()): |
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535 | for vertex_id in triangle: |
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536 | number_of_triangles_per_node[vertex_id] += 1 |
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537 | |
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538 | # Allocate space for inverted structure |
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539 | number_of_entries = num.sum(number_of_triangles_per_node) |
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540 | vertex_value_indices = num.zeros(number_of_entries, num.int) #array default# |
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541 | |
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542 | # Register (triangle, vertex) indices for each node |
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543 | vertexlist = [None]*self.number_of_full_nodes |
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544 | for volume_id in range(self.number_of_full_triangles): |
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545 | |
---|
546 | a = self.triangles[volume_id, 0] |
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547 | b = self.triangles[volume_id, 1] |
---|
548 | c = self.triangles[volume_id, 2] |
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549 | |
---|
550 | for vertex_id, node_id in enumerate([a,b,c]): |
---|
551 | if vertexlist[node_id] is None: |
---|
552 | vertexlist[node_id] = [] |
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553 | |
---|
554 | vertexlist[node_id].append( (volume_id, vertex_id) ) |
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555 | |
---|
556 | |
---|
557 | # Build inverted triangle index array |
---|
558 | k = 0 |
---|
559 | for vertices in vertexlist: |
---|
560 | if vertices is not None: |
---|
561 | for volume_id, vertex_id in vertices: |
---|
562 | vertex_value_indices[k] = 3*volume_id + vertex_id |
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563 | |
---|
564 | k += 1 |
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565 | |
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566 | # Save structure |
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567 | self.number_of_triangles_per_node = number_of_triangles_per_node |
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568 | self.vertex_value_indices = vertex_value_indices |
---|
569 | |
---|
570 | |
---|
571 | |
---|
572 | |
---|
573 | def get_extent(self, absolute=False): |
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574 | """Return min and max of all x and y coordinates |
---|
575 | |
---|
576 | Boolean keyword argument absolute determines whether coordinates |
---|
577 | are to be made absolute by taking georeference into account |
---|
578 | """ |
---|
579 | |
---|
580 | |
---|
581 | |
---|
582 | C = self.get_vertex_coordinates(absolute=absolute) |
---|
583 | X = C[:,0:6:2].copy() |
---|
584 | Y = C[:,1:6:2].copy() |
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585 | |
---|
586 | xmin = min(X.flat) |
---|
587 | xmax = max(X.flat) |
---|
588 | ymin = min(Y.flat) |
---|
589 | ymax = max(Y.flat) |
---|
590 | #print "C",C |
---|
591 | return xmin, xmax, ymin, ymax |
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592 | |
---|
593 | def get_areas(self): |
---|
594 | """Get areas of all individual triangles. |
---|
595 | """ |
---|
596 | return self.areas |
---|
597 | |
---|
598 | def get_area(self): |
---|
599 | """Return total area of mesh |
---|
600 | """ |
---|
601 | |
---|
602 | return num.sum(self.areas) |
---|
603 | |
---|
604 | def set_georeference(self, g): |
---|
605 | self.geo_reference = g |
---|
606 | |
---|
607 | def get_georeference(self): |
---|
608 | return self.geo_reference |
---|
609 | |
---|
610 | |
---|
611 | |
---|