1 | |
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2 | from Numeric import concatenate, reshape, take |
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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 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 triangular elements (purely geometric) |
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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, |
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12 | each corresponding to a given coordinate set. |
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13 | Vertices from different elements can point to the same |
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14 | coordinate set. |
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15 | |
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16 | Coordinate sets are implemented as an N x 2 Numeric array containing |
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17 | x and y coordinates. |
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18 | |
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19 | |
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20 | To instantiate: |
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21 | Mesh(coordinates, triangles) |
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22 | |
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23 | where |
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24 | |
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25 | coordinates is either a list of 2-tuples or an Mx2 Numeric array of |
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26 | floats representing all x, y coordinates in the mesh. |
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27 | |
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28 | triangles is either a list of 3-tuples or an Nx3 Numeric array of |
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29 | integers representing indices of all vertices in the mesh. |
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30 | Each vertex is identified by its index i in [0, M-1]. |
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31 | |
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32 | |
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33 | Example: |
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34 | a = [0.0, 0.0] |
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35 | b = [0.0, 2.0] |
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36 | c = [2.0,0.0] |
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37 | e = [2.0, 2.0] |
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38 | |
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39 | points = [a, b, c, e] |
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40 | triangles = [ [1,0,2], [1,2,3] ] #bac, bce |
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41 | mesh = Mesh(points, triangles) |
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42 | |
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43 | #creates two triangles: bac and bce |
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44 | |
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45 | Other: |
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46 | |
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47 | In addition mesh computes an Nx6 array called vertex_coordinates. |
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48 | This structure is derived from coordinates and contains for each |
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49 | triangle the three x,y coordinates at the vertices. |
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50 | |
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51 | |
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52 | This is a cut down version of mesh from pyvolution mesh.py |
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53 | """ |
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54 | |
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55 | #FIXME: It would be a good idea to use geospatial data as an alternative |
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56 | #input |
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57 | def __init__(self, coordinates, triangles, |
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58 | geo_reference=None, |
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59 | verbose=False): |
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60 | """ |
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61 | Build triangles from x,y coordinates (sequence of 2-tuples or |
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62 | Mx2 Numeric array of floats) and triangles (sequence of 3-tuples |
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63 | or Nx3 Numeric array of non-negative integers). |
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64 | |
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65 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
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66 | If specified coordinates are assumed to be relative to this origin. |
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67 | """ |
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68 | |
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69 | if verbose: print 'General_mesh: Building basic mesh structure' |
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70 | |
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71 | self.triangles = array(triangles,Int) |
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72 | self.coordinates = array(coordinates,Float) |
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73 | |
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74 | |
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75 | # FIXME: this stores a geo_reference, but when coords are returned |
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76 | # This geo_ref is not taken into account! |
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77 | if geo_reference is None: |
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78 | self.geo_reference = Geo_reference() #Use defaults |
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79 | else: |
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80 | self.geo_reference = geo_reference |
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81 | |
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82 | #Input checks |
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83 | msg = 'Triangles must an Nx3 Numeric array or a sequence of 3-tuples' |
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84 | assert len(self.triangles.shape) == 2, msg |
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85 | |
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86 | msg = 'Coordinates must an Mx2 Numeric array or a sequence of 2-tuples' |
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87 | assert len(self.coordinates.shape) == 2, msg |
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88 | |
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89 | msg = 'Vertex indices reference non-existing coordinate sets' |
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90 | assert max(max(self.triangles)) <= self.coordinates.shape[0], msg |
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91 | |
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92 | |
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93 | #Register number of elements (N) |
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94 | self.number_of_elements = N = self.triangles.shape[0] |
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95 | |
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96 | #FIXME: Maybe move to statistics? |
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97 | |
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98 | xy_extent = [ min(self.coordinates[:,0]), min(self.coordinates[:,1]) , |
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99 | max(self.coordinates[:,0]), max(self.coordinates[:,1]) ] |
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100 | |
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101 | self.xy_extent = array(xy_extent, Float) |
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102 | |
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103 | |
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104 | #Allocate space for geometric quantities |
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105 | self.normals = zeros((N, 6), Float) |
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106 | self.areas = zeros(N, Float) |
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107 | self.edgelengths = zeros((N, 3), Float) |
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108 | |
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109 | #Get x,y coordinates for all triangles and store |
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110 | self.vertex_coordinates = V = self.compute_vertex_coordinates() |
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111 | |
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112 | |
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113 | #Initialise each triangle |
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114 | if verbose: |
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115 | print 'General_mesh: Computing areas, normals and edgelenghts' |
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116 | |
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117 | for i in range(N): |
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118 | if verbose and i % ((N+10)/10) == 0: print '(%d/%d)' %(i, N) |
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119 | |
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120 | |
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121 | x0 = V[i, 0]; y0 = V[i, 1] |
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122 | x1 = V[i, 2]; y1 = V[i, 3] |
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123 | x2 = V[i, 4]; y2 = V[i, 5] |
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124 | |
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125 | #Area |
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126 | self.areas[i] = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
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127 | |
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128 | msg = 'Triangle (%f,%f), (%f,%f), (%f, %f)' %(x0,y0,x1,y1,x2,y2) |
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129 | msg += ' is degenerate: area == %f' %self.areas[i] |
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130 | assert self.areas[i] > 0.0, msg |
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131 | |
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132 | |
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133 | #Normals |
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134 | #The normal vectors |
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135 | # - point outward from each edge |
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136 | # - are orthogonal to the edge |
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137 | # - have unit length |
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138 | # - Are enumerated according to the opposite corner: |
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139 | # (First normal is associated with the edge opposite |
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140 | # the first vertex, etc) |
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141 | # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle |
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142 | |
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143 | n0 = array([x2 - x1, y2 - y1]) |
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144 | l0 = sqrt(sum(n0**2)) |
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145 | |
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146 | n1 = array([x0 - x2, y0 - y2]) |
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147 | l1 = sqrt(sum(n1**2)) |
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148 | |
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149 | n2 = array([x1 - x0, y1 - y0]) |
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150 | l2 = sqrt(sum(n2**2)) |
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151 | |
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152 | #Normalise |
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153 | n0 /= l0 |
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154 | n1 /= l1 |
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155 | n2 /= l2 |
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156 | |
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157 | #Compute and store |
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158 | self.normals[i, :] = [n0[1], -n0[0], |
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159 | n1[1], -n1[0], |
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160 | n2[1], -n2[0]] |
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161 | |
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162 | #Edgelengths |
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163 | self.edgelengths[i, :] = [l0, l1, l2] |
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164 | |
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165 | |
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166 | #Build vertex list |
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167 | if verbose: print 'Building vertex list' |
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168 | self.build_vertexlist() |
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169 | |
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170 | |
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171 | |
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172 | def __len__(self): |
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173 | return self.number_of_elements |
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174 | |
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175 | def __repr__(self): |
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176 | return 'Mesh: %d triangles, %d elements'\ |
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177 | %(self.coordinates.shape[0], len(self)) |
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178 | |
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179 | def get_normals(self): |
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180 | """Return all normal vectors. |
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181 | Return normal vectors for all triangles as an Nx6 array |
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182 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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183 | """ |
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184 | return self.normals |
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185 | |
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186 | |
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187 | def get_normal(self, i, j): |
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188 | """Return normal vector j of the i'th triangle. |
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189 | Return value is the numeric array slice [x, y] |
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190 | """ |
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191 | return self.normals[i, 2*j:2*j+2] |
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192 | |
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193 | |
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194 | |
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195 | def get_vertex_coordinates(self, obj=False, absolute=False): |
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196 | """Return all vertex coordinates. |
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197 | Return all vertex coordinates for all triangles as an Nx6 array |
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198 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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199 | |
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200 | if obj is True, the x/y pairs are returned in a 3*N x 2 array. |
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201 | FIXME, we might make that the default. |
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202 | FIXME Maybe use keyword: continuous = False for this condition? |
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203 | FIXME - Maybe use something referring to unique vertices? |
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204 | |
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205 | Boolean keyword argument absolute determines whether coordinates |
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206 | are to be made absolute by taking georeference into account |
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207 | """ |
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208 | |
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209 | V = self.vertex_coordinates |
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210 | if absolute is True: |
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211 | V0 = self.geo_reference.get_absolute(V[:,0:2]) |
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212 | V1 = self.geo_reference.get_absolute(V[:,2:4]) |
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213 | V2 = self.geo_reference.get_absolute(V[:,4:6]) |
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214 | |
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215 | V = concatenate( (V0, V1, V2), axis=1 ) |
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216 | |
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217 | |
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218 | if obj is True: |
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219 | #return concatenate( (V[:,0:2], V[:,2:4], V[:,4:6]), axis=0) |
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220 | |
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221 | N = V.shape[0] |
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222 | return reshape(V, (3*N, 2)) |
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223 | else: |
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224 | return V |
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225 | |
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226 | |
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227 | def get_vertex_coordinate(self, i, j, absolute=False): |
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228 | """Return coordinates for vertex j of the i'th triangle. |
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229 | Return value is the numeric array slice [x, y] |
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230 | """ |
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231 | |
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232 | V = self.get_vertex_coordinates(absolute=absolute) |
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233 | return V[i, 2*j:2*j+2] |
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234 | |
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235 | ##return self.vertex_coordinates[i, 2*j:2*j+2] |
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236 | |
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237 | |
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238 | def compute_vertex_coordinates(self): |
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239 | """Return vertex coordinates for all triangles as an Nx6 array |
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240 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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241 | """ |
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242 | |
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243 | #FIXME (Ole): Perhaps they should be ordered as in obj files?? |
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244 | #See quantity.get_vertex_values |
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245 | #FIXME (Ole) - oh yes they should |
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246 | |
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247 | N = self.number_of_elements |
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248 | vertex_coordinates = zeros((N, 6), Float) |
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249 | |
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250 | for i in range(N): |
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251 | for j in range(3): |
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252 | k = self.triangles[i,j] #Index of vertex 0 |
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253 | v_k = self.coordinates[k] |
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254 | vertex_coordinates[i, 2*j+0] = v_k[0] |
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255 | vertex_coordinates[i, 2*j+1] = v_k[1] |
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256 | |
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257 | return vertex_coordinates |
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258 | |
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259 | def get_vertices(self, indices=None): |
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260 | """Get connectivity |
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261 | indices is the set of element ids of interest |
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262 | """ |
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263 | |
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264 | if (indices == None): |
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265 | indices = range(len(self)) #len(self)=number of elements |
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266 | |
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267 | return take(self.triangles, indices) |
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268 | |
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269 | #FIXME - merge these two (get_vertices and get_triangles) |
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270 | def get_triangles(self, obj=False): |
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271 | """Get connetivity |
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272 | Return triangles (triplets of indices into point coordinates) |
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273 | |
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274 | If obj is True return structure commensurate with replicated |
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275 | points, allowing for discontinuities |
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276 | (FIXME: Need good name for this concept) |
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277 | """ |
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278 | |
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279 | if obj is True: |
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280 | m = len(self) #Number of triangles |
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281 | M = 3*m #Total number of unique vertices |
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282 | T = reshape(array(range(M)).astype(Int), (m,3)) |
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283 | else: |
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284 | T = self.triangles |
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285 | |
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286 | return T |
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287 | |
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288 | |
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289 | |
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290 | def get_unique_vertices(self, indices=None): |
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291 | triangles = self.get_vertices(indices=indices) |
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292 | unique_verts = {} |
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293 | for triangle in triangles: |
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294 | unique_verts[triangle[0]] = 0 |
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295 | unique_verts[triangle[1]] = 0 |
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296 | unique_verts[triangle[2]] = 0 |
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297 | return unique_verts.keys() |
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298 | |
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299 | def build_vertexlist(self): |
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300 | """Build vertexlist index by vertex ids and for each entry (point id) |
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301 | build a list of (triangles, vertex_id) pairs that use the point |
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302 | as vertex. |
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303 | |
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304 | Preconditions: |
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305 | self.coordinates and self.triangles are defined |
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306 | |
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307 | Postcondition: |
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308 | self.vertexlist is built |
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309 | """ |
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310 | |
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311 | vertexlist = [None]*len(self.coordinates) |
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312 | for i in range(self.number_of_elements): |
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313 | |
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314 | a = self.triangles[i, 0] |
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315 | b = self.triangles[i, 1] |
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316 | c = self.triangles[i, 2] |
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317 | |
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318 | #Register the vertices v as lists of |
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319 | #(triangle_id, vertex_id) tuples associated with them |
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320 | #This is used for averaging multiple vertex values. |
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321 | for vertex_id, v in enumerate([a,b,c]): |
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322 | if vertexlist[v] is None: |
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323 | vertexlist[v] = [] |
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324 | |
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325 | vertexlist[v].append( (i, vertex_id) ) |
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326 | |
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327 | self.vertexlist = vertexlist |
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328 | |
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329 | |
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330 | def get_extent(self, absolute=False): |
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331 | """Return min and max of all x and y coordinates |
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332 | |
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333 | Boolean keyword argument absolute determines whether coordinates |
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334 | are to be made absolute by taking georeference into account |
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335 | """ |
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336 | |
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337 | |
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338 | |
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339 | C = self.get_vertex_coordinates(absolute=absolute) |
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340 | X = C[:,0:6:2].copy() |
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341 | Y = C[:,1:6:2].copy() |
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342 | |
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343 | xmin = min(X.flat) |
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344 | xmax = max(X.flat) |
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345 | ymin = min(Y.flat) |
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346 | ymax = max(Y.flat) |
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347 | |
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348 | return xmin, xmax, ymin, ymax |
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349 | |
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350 | |
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351 | def get_area(self): |
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352 | """Return total area of mesh |
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353 | """ |
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354 | |
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355 | return sum(self.areas) |
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356 | |
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357 | |
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