1 | """Library of standard meshes and facilities for reading various |
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2 | mesh file formats |
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3 | """ |
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4 | |
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5 | |
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6 | def rectangular_old(m, n, len1=1.0, len2=1.0, origin = (0.0, 0.0)): |
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7 | |
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8 | """Setup a rectangular grid of triangles |
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9 | with m+1 by n+1 grid points |
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10 | and side lengths len1, len2. If side lengths are omitted |
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11 | the mesh defaults to the unit square. |
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12 | |
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13 | len1: x direction (left to right) |
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14 | len2: y direction (bottom to top) |
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15 | |
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16 | Return to lists: points and elements suitable for creating a Mesh or |
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17 | FVMesh object, e.g. Mesh(points, elements) |
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18 | """ |
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19 | |
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20 | from anuga.config import epsilon |
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21 | |
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22 | deltax = float(len1)/m |
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23 | deltay = float(len2)/n |
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24 | |
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25 | #Dictionary of vertex objects |
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26 | vertices = {} |
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27 | points = [] |
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28 | |
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29 | for i in range(m+1): |
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30 | for j in range(n+1): |
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31 | vertices[i,j] = len(points) |
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32 | points.append([i*delta1 + origin[0], j*delta2 + origin[1]]) |
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33 | |
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34 | |
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35 | #Construct 2 triangles per rectangular element and assign tags to boundary |
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36 | elements = [] |
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37 | boundary = {} |
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38 | for i in range(m): |
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39 | for j in range(n): |
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40 | v1 = vertices[i,j+1] |
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41 | v2 = vertices[i,j] |
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42 | v3 = vertices[i+1,j+1] |
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43 | v4 = vertices[i+1,j] |
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44 | |
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45 | #Update boundary dictionary and create elements |
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46 | if i == m-1: |
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47 | boundary[(len(elements), 2)] = 'right' |
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48 | if j == 0: |
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49 | boundary[(len(elements), 1)] = 'bottom' |
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50 | elements.append([v4,v3,v2]) #Lower element |
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51 | |
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52 | if i == 0: |
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53 | boundary[(len(elements), 2)] = 'left' |
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54 | if j == n-1: |
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55 | boundary[(len(elements), 1)] = 'top' |
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56 | elements.append([v1,v2,v3]) #Upper element |
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57 | |
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58 | return points, elements, boundary |
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59 | |
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60 | def rectangular(m, n, len1=1.0, len2=1.0, origin = (0.0, 0.0)): |
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61 | |
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62 | """Setup a rectangular grid of triangles |
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63 | with m+1 by n+1 grid points |
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64 | and side lengths len1, len2. If side lengths are omitted |
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65 | the mesh defaults to the unit square. |
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66 | |
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67 | len1: x direction (left to right) |
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68 | len2: y direction (bottom to top) |
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69 | |
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70 | Return to lists: points and elements suitable for creating a Mesh or |
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71 | FVMesh object, e.g. Mesh(points, elements) |
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72 | """ |
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73 | |
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74 | from anuga.config import epsilon |
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75 | from Numeric import zeros, Float, Int |
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76 | |
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77 | delta1 = float(len1)/m |
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78 | delta2 = float(len2)/n |
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79 | |
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80 | #Calculate number of points |
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81 | Np = (m+1)*(n+1) |
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82 | |
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83 | class Index: |
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84 | |
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85 | def __init__(self, n,m): |
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86 | self.n = n |
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87 | self.m = m |
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88 | |
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89 | def __call__(self, i,j): |
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90 | return j+i*(self.n+1) |
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91 | |
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92 | |
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93 | index = Index(n,m) |
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94 | |
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95 | points = zeros( (Np,2), Float) |
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96 | |
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97 | for i in range(m+1): |
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98 | for j in range(n+1): |
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99 | |
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100 | points[index(i,j),:] = [i*delta1 + origin[0], j*delta2 + origin[1]] |
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101 | |
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102 | #Construct 2 triangles per rectangular element and assign tags to boundary |
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103 | #Calculate number of triangles |
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104 | Nt = 2*m*n |
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105 | |
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106 | |
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107 | elements = zeros( (Nt,3), Int) |
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108 | boundary = {} |
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109 | nt = -1 |
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110 | for i in range(m): |
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111 | for j in range(n): |
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112 | nt = nt + 1 |
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113 | i1 = index(i,j+1) |
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114 | i2 = index(i,j) |
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115 | i3 = index(i+1,j+1) |
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116 | i4 = index(i+1,j) |
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117 | |
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118 | |
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119 | #Update boundary dictionary and create elements |
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120 | if i == m-1: |
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121 | boundary[nt, 2] = 'right' |
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122 | if j == 0: |
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123 | boundary[nt, 1] = 'bottom' |
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124 | elements[nt,:] = [i4,i3,i2] #Lower element |
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125 | nt = nt + 1 |
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126 | |
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127 | if i == 0: |
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128 | boundary[nt, 2] = 'left' |
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129 | if j == n-1: |
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130 | boundary[nt, 1] = 'top' |
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131 | elements[nt,:] = [i1,i2,i3] #Upper element |
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132 | |
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133 | return points, elements, boundary |
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134 | |
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135 | |
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136 | def rectangular_cross(m, n, len1=1.0, len2=1.0, origin = (0.0, 0.0)): |
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137 | |
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138 | """Setup a rectangular grid of triangles |
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139 | with m+1 by n+1 grid points |
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140 | and side lengths len1, len2. If side lengths are omitted |
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141 | the mesh defaults to the unit square. |
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142 | |
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143 | len1: x direction (left to right) |
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144 | len2: y direction (bottom to top) |
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145 | |
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146 | Return to lists: points and elements suitable for creating a Mesh or |
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147 | FVMesh object, e.g. Mesh(points, elements) |
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148 | """ |
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149 | |
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150 | from anuga.config import epsilon |
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151 | from Numeric import zeros, Float, Int |
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152 | |
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153 | delta1 = float(len1)/m |
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154 | delta2 = float(len2)/n |
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155 | |
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156 | #Dictionary of vertex objects |
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157 | vertices = {} |
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158 | points = [] |
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159 | |
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160 | for i in range(m+1): |
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161 | for j in range(n+1): |
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162 | vertices[i,j] = len(points) |
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163 | points.append([delta1*i + origin[0], delta2*j + origin[1]]) |
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164 | |
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165 | # Construct 4 triangles per element |
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166 | elements = [] |
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167 | boundary = {} |
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168 | for i in range(m): |
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169 | for j in range(n): |
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170 | v1 = vertices[i,j+1] |
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171 | v2 = vertices[i,j] |
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172 | v3 = vertices[i+1,j+1] |
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173 | v4 = vertices[i+1,j] |
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174 | x = (points[v1][0]+points[v2][0]+points[v3][0]+points[v4][0])*0.25 |
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175 | y = (points[v1][1]+points[v2][1]+points[v3][1]+points[v4][1])*0.25 |
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176 | |
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177 | # Create centre point |
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178 | v5 = len(points) |
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179 | points.append([x, y]) |
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180 | |
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181 | #Create left triangle |
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182 | if i == 0: |
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183 | boundary[(len(elements), 1)] = 'left' |
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184 | elements.append([v2,v5,v1]) |
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185 | |
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186 | #Create bottom triangle |
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187 | if j == 0: |
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188 | boundary[(len(elements), 1)] = 'bottom' |
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189 | elements.append([v4,v5,v2]) |
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190 | |
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191 | #Create right triangle |
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192 | if i == m-1: |
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193 | boundary[(len(elements), 1)] = 'right' |
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194 | elements.append([v3,v5,v4]) |
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195 | |
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196 | #Create top triangle |
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197 | if j == n-1: |
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198 | boundary[(len(elements), 1)] = 'top' |
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199 | elements.append([v1,v5,v3]) |
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200 | |
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201 | |
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202 | return points, elements, boundary |
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203 | |
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204 | def oblique(m, n, lenx = 1.0, leny = 1.0, theta = 8.95, origin = (0.0, 0.0)): |
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205 | """Setup a oblique grid of triangles |
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206 | with m segments in the x-direction and n segments in the y-direction |
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207 | |
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208 | """ |
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209 | |
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210 | from Numeric import array |
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211 | import math |
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212 | |
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213 | from anuga.config import epsilon |
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214 | |
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215 | |
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216 | deltax = lenx/float(m) |
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217 | deltay = leny/float(n) |
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218 | a = 0.75*lenx*math.tan(theta/180.*math.pi) |
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219 | x1 = lenx |
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220 | y1 = 0 |
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221 | x2 = lenx |
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222 | y2 = leny |
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223 | x3 = 0.25*lenx |
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224 | y3 = leny |
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225 | x4 = x3 |
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226 | y4 = 0 |
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227 | a2 = a/(x1-x4) |
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228 | a1 = -a2*x4 |
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229 | a4 = ((a1 + a2*x3)/y3-(a1 + a2*x2)/y2)/(x2-x3) |
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230 | a3 = 1. - (a1 + a2*x3)/y3 - a4*x3 |
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231 | |
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232 | # Dictionary of vertex objects |
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233 | vertices = {} |
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234 | points = [] |
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235 | |
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236 | for i in range(m+1): |
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237 | x = deltax*i |
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238 | for j in range(n+1): |
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239 | y = deltay*j |
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240 | if x > 0.25*lenx: |
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241 | y = a1 + a2*x + a3*y + a4*x*y |
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242 | |
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243 | vertices[i,j] = len(points) |
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244 | points.append([x + origin[0], y + origin[1]]) |
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245 | |
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246 | # Construct 2 triangles per element |
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247 | elements = [] |
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248 | boundary = {} |
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249 | for i in range(m): |
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250 | for j in range(n): |
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251 | v1 = vertices[i,j+1] |
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252 | v2 = vertices[i,j] |
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253 | v3 = vertices[i+1,j+1] |
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254 | v4 = vertices[i+1,j] |
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255 | |
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256 | #Update boundary dictionary and create elements |
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257 | if i == m-1: |
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258 | boundary[(len(elements), 2)] = 'right' |
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259 | if j == 0: |
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260 | boundary[(len(elements), 1)] = 'bottom' |
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261 | elements.append([v4,v3,v2]) #Lower |
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262 | |
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263 | if i == 0: |
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264 | boundary[(len(elements), 2)] = 'left' |
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265 | if j == n-1: |
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266 | boundary[(len(elements), 1)] = 'top' |
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267 | |
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268 | elements.append([v1,v2,v3]) #Upper |
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269 | |
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270 | return points, elements, boundary |
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271 | |
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272 | |
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273 | def circular(m, n, radius=1.0, center = (0.0, 0.0)): |
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274 | """Setup a circular grid of triangles with m concentric circles and |
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275 | with n radial segments. If radius is are omitted the mesh defaults to |
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276 | the unit circle radius. |
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277 | |
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278 | radius: radius of circle |
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279 | |
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280 | #FIXME: The triangles become degenerate for large values of m or n. |
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281 | """ |
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282 | |
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283 | |
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284 | |
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285 | from math import pi, cos, sin |
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286 | |
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287 | radius = float(radius) #Ensure floating point format |
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288 | |
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289 | #Dictionary of vertex objects and list of points |
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290 | vertices = {} |
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291 | points = [[0.0, 0.0]] #Center point |
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292 | vertices[0, 0] = 0 |
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293 | |
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294 | for i in range(n): |
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295 | theta = 2*i*pi/n |
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296 | x = cos(theta) |
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297 | y = sin(theta) |
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298 | for j in range(1,m+1): |
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299 | delta = j*radius/m |
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300 | vertices[i,j] = len(points) |
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301 | points.append([delta*x, delta*y]) |
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302 | |
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303 | #Construct 2 triangles per element |
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304 | elements = [] |
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305 | for i in range(n): |
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306 | for j in range(1,m): |
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307 | |
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308 | i1 = (i + 1) % n #Wrap around |
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309 | |
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310 | v1 = vertices[i,j+1] |
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311 | v2 = vertices[i,j] |
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312 | v3 = vertices[i1,j+1] |
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313 | v4 = vertices[i1,j] |
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314 | |
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315 | elements.append([v4,v2,v3]) #Lower |
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316 | elements.append([v1,v3,v2]) #Upper |
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317 | |
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318 | |
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319 | #Do the center |
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320 | v1 = vertices[0,0] |
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321 | for i in range(n): |
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322 | i1 = (i + 1) % n #Wrap around |
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323 | v2 = vertices[i,1] |
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324 | v3 = vertices[i1,1] |
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325 | |
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326 | elements.append([v1,v2,v3]) #center |
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327 | |
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328 | return points, elements |
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329 | |
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330 | |
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331 | def from_polyfile(name): |
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332 | """Read mesh from .poly file, an obj like file format |
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333 | listing first vertex coordinates and then connectivity |
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334 | """ |
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335 | |
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336 | from anuga.utilities.numerical_tools import anglediff |
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337 | from math import pi |
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338 | import os.path |
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339 | root, ext = os.path.splitext(name) |
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340 | |
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341 | if ext == 'poly': |
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342 | filename = name |
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343 | else: |
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344 | filename = name + '.poly' |
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345 | |
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346 | |
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347 | fid = open(filename) |
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348 | |
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349 | points = [] #x, y |
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350 | values = [] #z |
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351 | ##vertex_values = [] #Repeated z |
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352 | triangles = [] #v0, v1, v2 |
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353 | |
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354 | lines = fid.readlines() |
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355 | |
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356 | keyword = lines[0].strip() |
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357 | msg = 'First line in .poly file must contain the keyword: POINTS' |
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358 | assert keyword == 'POINTS', msg |
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359 | |
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360 | offending = 0 |
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361 | i = 1 |
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362 | while keyword == 'POINTS': |
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363 | line = lines[i].strip() |
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364 | i += 1 |
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365 | |
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366 | if line == 'POLYS': |
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367 | keyword = line |
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368 | break |
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369 | |
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370 | fields = line.split(':') |
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371 | assert int(fields[0]) == i-1, 'Point indices not consecutive' |
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372 | |
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373 | #Split the three floats |
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374 | xyz = fields[1].split() |
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375 | |
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376 | x = float(xyz[0]) |
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377 | y = float(xyz[1]) |
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378 | z = float(xyz[2]) |
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379 | |
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380 | points.append([x, y]) |
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381 | values.append(z) |
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382 | |
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383 | |
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384 | k = i |
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385 | while keyword == 'POLYS': |
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386 | line = lines[i].strip() |
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387 | i += 1 |
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388 | |
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389 | if line == 'END': |
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390 | keyword = line |
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391 | break |
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392 | |
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393 | |
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394 | fields = line.split(':') |
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395 | assert int(fields[0]) == i-k, 'Poly indices not consecutive' |
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396 | |
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397 | #Split the three indices |
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398 | vvv = fields[1].split() |
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399 | |
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400 | i0 = int(vvv[0])-1 |
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401 | i1 = int(vvv[1])-1 |
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402 | i2 = int(vvv[2])-1 |
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403 | |
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404 | #Check for and exclude degenerate areas |
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405 | x0 = points[i0][0] |
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406 | y0 = points[i0][1] |
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407 | x1 = points[i1][0] |
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408 | y1 = points[i1][1] |
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409 | x2 = points[i2][0] |
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410 | y2 = points[i2][1] |
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411 | |
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412 | area = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
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413 | if area > 0: |
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414 | |
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415 | #Ensure that points are arranged in counter clock-wise order |
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416 | v0 = [x1-x0, y1-y0] |
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417 | v1 = [x2-x1, y2-y1] |
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418 | v2 = [x0-x2, y0-y2] |
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419 | |
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420 | a0 = anglediff(v1, v0) |
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421 | a1 = anglediff(v2, v1) |
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422 | a2 = anglediff(v0, v2) |
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423 | |
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424 | |
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425 | if a0 < pi and a1 < pi and a2 < pi: |
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426 | #all is well |
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427 | j0 = i0 |
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428 | j1 = i1 |
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429 | j2 = i2 |
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430 | else: |
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431 | #Swap two vertices |
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432 | j0 = i1 |
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433 | j1 = i0 |
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434 | j2 = i2 |
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435 | |
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436 | triangles.append([j0, j1, j2]) |
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437 | ##vertex_values.append([values[j0], values[j1], values[j2]]) |
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438 | else: |
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439 | offending +=1 |
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440 | |
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441 | print 'Removed %d offending triangles out of %d' %(offending, len(lines)) |
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442 | return points, triangles, values |
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443 | |
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444 | |
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445 | |
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446 | def strang_mesh(filename): |
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447 | """Read Strang generated mesh. |
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448 | """ |
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449 | |
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450 | from math import pi |
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451 | from anuga.utilities.numerical_tools import anglediff |
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452 | |
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453 | |
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454 | fid = open(filename) |
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455 | points = [] # List of x, y coordinates |
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456 | triangles = [] # List of vertex ids as listed in the file |
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457 | |
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458 | for line in fid.readlines(): |
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459 | fields = line.split() |
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460 | if len(fields) == 2: |
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461 | # we are reading vertex coordinates |
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462 | points.append([float(fields[0]), float(fields[1])]) |
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463 | elif len(fields) == 3: |
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464 | # we are reading triangle point id's (format ae+b) |
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465 | triangles.append([int(float(fields[0]))-1, |
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466 | int(float(fields[1]))-1, |
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467 | int(float(fields[2]))-1]) |
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468 | else: |
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469 | raise 'wrong format in ' + filename |
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470 | |
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471 | elements = [] #Final list of elements |
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472 | |
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473 | for t in triangles: |
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474 | #Get vertex coordinates |
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475 | v0 = t[0] |
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476 | v1 = t[1] |
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477 | v2 = t[2] |
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478 | |
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479 | x0 = points[v0][0] |
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480 | y0 = points[v0][1] |
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481 | x1 = points[v1][0] |
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482 | y1 = points[v1][1] |
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483 | x2 = points[v2][0] |
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484 | y2 = points[v2][1] |
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485 | |
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486 | #Check that points are arranged in counter clock-wise order |
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487 | vec0 = [x1-x0, y1-y0] |
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488 | vec1 = [x2-x1, y2-y1] |
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489 | vec2 = [x0-x2, y0-y2] |
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490 | |
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491 | a0 = anglediff(vec1, vec0) |
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492 | a1 = anglediff(vec2, vec1) |
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493 | a2 = anglediff(vec0, vec2) |
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494 | |
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495 | if a0 < pi and a1 < pi and a2 < pi: |
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496 | elements.append([v0, v1, v2]) |
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497 | else: |
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498 | elements.append([v0, v2, v1]) |
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499 | |
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500 | return points, elements |
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501 | |
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502 | # #Map from edge number to indices of associated vertices |
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503 | # edge_map = ((1,2), (0,2), (0,1)) |
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504 | |
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505 | def contracting_channel(m, n, W_upstream = 1., W_downstream = 0.75, |
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506 | L_1 = 5.0, L_2 = 2.0, L_3 = 10, origin = (0.0, 0.0)): |
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507 | """Setup a contracting channel grid of triangles |
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508 | with m segments in the x-direction and n segments in the y-direction |
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509 | |
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510 | """ |
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511 | |
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512 | from Numeric import array |
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513 | import math |
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514 | |
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515 | from anuga.config import epsilon |
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516 | |
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517 | |
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518 | lenx = L_1 + L_2 + L_3 |
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519 | leny = W_upstream |
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520 | deltax = lenx/float(m) |
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521 | deltay = leny/float(n) |
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522 | |
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523 | x1 = 0 |
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524 | y1 = 0 |
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525 | x2 = L_1 |
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526 | y2 = 0 |
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527 | x3 = L_1 + L_2 |
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528 | y3 = (W_upstream - W_downstream)/2 |
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529 | x4 = L_1 + L_2 + L_3 |
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530 | y4 = y3 |
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531 | x5 = x4 |
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532 | y5 = y4 + W_downstream |
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533 | x6 = L_1 + L_2 |
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534 | y6 = y5 |
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535 | x7 = L_1 |
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536 | y7 = W_upstream |
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537 | x8 = 0 |
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538 | y8 = W_upstream |
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539 | a1 = 0 |
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540 | a2 = (W_upstream - W_downstream)/(2*L_2) |
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541 | a3 = 1 |
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542 | a4 = (W_downstream - W_upstream)/(L_2*W_upstream) |
---|
543 | |
---|
544 | # Dictionary of vertex objects |
---|
545 | vertices = {} |
---|
546 | points = [] |
---|
547 | |
---|
548 | for i in range(m+1): |
---|
549 | x = deltax*i |
---|
550 | for j in range(n+1): |
---|
551 | y = deltay*j |
---|
552 | if x > L_1 and x <= (L_1 + L_2): |
---|
553 | y = a1 + a2*(x - L_1) + a3*y + a4*(x - L_1)*y |
---|
554 | elif x > L_1 + L_2: |
---|
555 | y = (W_upstream - W_downstream)/2 + deltay*j*W_downstream/W_upstream |
---|
556 | |
---|
557 | vertices[i,j] = len(points) |
---|
558 | points.append([x + origin[0], y + origin[1]]) |
---|
559 | |
---|
560 | # Construct 2 triangles per element |
---|
561 | elements = [] |
---|
562 | boundary = {} |
---|
563 | for i in range(m): |
---|
564 | for j in range(n): |
---|
565 | v1 = vertices[i,j+1] |
---|
566 | v2 = vertices[i,j] |
---|
567 | v3 = vertices[i+1,j+1] |
---|
568 | v4 = vertices[i+1,j] |
---|
569 | |
---|
570 | #Update boundary dictionary and create elements |
---|
571 | if i == m-1: |
---|
572 | boundary[(len(elements), 2)] = 'right' |
---|
573 | if j == 0: |
---|
574 | boundary[(len(elements), 1)] = 'bottom' |
---|
575 | elements.append([v4,v3,v2]) #Lower |
---|
576 | |
---|
577 | if i == 0: |
---|
578 | boundary[(len(elements), 2)] = 'left' |
---|
579 | if j == n-1: |
---|
580 | boundary[(len(elements), 1)] = 'top' |
---|
581 | |
---|
582 | elements.append([v1,v2,v3]) #Upper |
---|
583 | |
---|
584 | return points, elements, boundary |
---|
585 | |
---|
586 | |
---|
587 | def contracting_channel_cross(m, n, W_upstream = 1., W_downstream = 0.75, |
---|
588 | L_1 = 5.0, L_2 = 2.0, L_3 = 10, origin = (0.0, 0.0)): |
---|
589 | """Setup a contracting channel grid of triangles |
---|
590 | with m segments in the x-direction and n segments in the y-direction |
---|
591 | |
---|
592 | """ |
---|
593 | |
---|
594 | from Numeric import array |
---|
595 | import math |
---|
596 | |
---|
597 | from anuga.config import epsilon |
---|
598 | |
---|
599 | |
---|
600 | lenx = L_1 + L_2 + L_3 |
---|
601 | leny = W_upstream |
---|
602 | deltax = lenx/float(m) |
---|
603 | deltay = leny/float(n) |
---|
604 | |
---|
605 | x1 = 0 |
---|
606 | y1 = 0 |
---|
607 | x2 = L_1 |
---|
608 | y2 = 0 |
---|
609 | x3 = L_1 + L_2 |
---|
610 | y3 = (W_upstream - W_downstream)/2 |
---|
611 | x4 = L_1 + L_2 + L_3 |
---|
612 | y4 = y3 |
---|
613 | x5 = x4 |
---|
614 | y5 = y4 + W_downstream |
---|
615 | x6 = L_1 + L_2 |
---|
616 | y6 = y5 |
---|
617 | x7 = L_1 |
---|
618 | y7 = W_upstream |
---|
619 | x8 = 0 |
---|
620 | y8 = W_upstream |
---|
621 | a1 = 0 |
---|
622 | a2 = (W_upstream - W_downstream)/(2*L_2) |
---|
623 | a3 = 1 |
---|
624 | a4 = (W_downstream - W_upstream)/(L_2*W_upstream) |
---|
625 | |
---|
626 | # Dictionary of vertex objects |
---|
627 | vertices = {} |
---|
628 | points = [] |
---|
629 | |
---|
630 | for i in range(m+1): |
---|
631 | x = deltax*i |
---|
632 | for j in range(n+1): |
---|
633 | y = deltay*j |
---|
634 | if x > L_1 and x <= (L_1 + L_2): |
---|
635 | y = a1 + a2*(x - L_1) + a3*y + a4*(x - L_1)*y |
---|
636 | elif x > L_1 + L_2: |
---|
637 | y = (W_upstream - W_downstream)/2 + deltay*j*W_downstream/W_upstream |
---|
638 | |
---|
639 | vertices[i,j] = len(points) |
---|
640 | points.append([x + origin[0], y + origin[1]]) |
---|
641 | |
---|
642 | # Construct 4 triangles per element |
---|
643 | elements = [] |
---|
644 | boundary = {} |
---|
645 | for i in range(m): |
---|
646 | for j in range(n): |
---|
647 | v1 = vertices[i,j+1] |
---|
648 | v2 = vertices[i,j] |
---|
649 | v3 = vertices[i+1,j+1] |
---|
650 | v4 = vertices[i+1,j] |
---|
651 | x = (points[v1][0]+points[v2][0]+points[v3][0]+points[v4][0])*0.25 |
---|
652 | y = (points[v1][1]+points[v2][1]+points[v3][1]+points[v4][1])*0.25 |
---|
653 | v5 = len(points) |
---|
654 | points.append([x, y]) |
---|
655 | |
---|
656 | #Create left triangle |
---|
657 | if i == 0: |
---|
658 | boundary[(len(elements), 1)] = 'left' |
---|
659 | elements.append([v2,v5,v1]) |
---|
660 | |
---|
661 | #Create bottom triangle |
---|
662 | if j == 0: |
---|
663 | boundary[(len(elements), 1)] = 'bottom' |
---|
664 | elements.append([v4,v5,v2]) |
---|
665 | |
---|
666 | #Create right triangle |
---|
667 | if i == m-1: |
---|
668 | boundary[(len(elements), 1)] = 'right' |
---|
669 | elements.append([v3,v5,v4]) |
---|
670 | |
---|
671 | #Create top triangle |
---|
672 | if j == n-1: |
---|
673 | boundary[(len(elements), 1)] = 'top' |
---|
674 | elements.append([v1,v5,v3]) |
---|
675 | |
---|
676 | |
---|
677 | return points, elements, boundary |
---|
678 | |
---|
679 | |
---|
680 | |
---|
681 | |
---|
682 | def oblique_cross(m, n, lenx = 1.0, leny = 1.0, theta = 8.95, origin = (0.0, 0.0)): |
---|
683 | """Setup a oblique grid of triangles |
---|
684 | with m segments in the x-direction and n segments in the y-direction |
---|
685 | |
---|
686 | """ |
---|
687 | |
---|
688 | from Numeric import array |
---|
689 | import math |
---|
690 | |
---|
691 | from anuga.config import epsilon |
---|
692 | |
---|
693 | |
---|
694 | deltax = lenx/float(m) |
---|
695 | deltay = leny/float(n) |
---|
696 | a = 0.75*lenx*math.tan(theta/180.*math.pi) |
---|
697 | x1 = lenx |
---|
698 | y1 = 0 |
---|
699 | x2 = lenx |
---|
700 | y2 = leny |
---|
701 | x3 = 0.25*lenx |
---|
702 | y3 = leny |
---|
703 | x4 = x3 |
---|
704 | y4 = 0 |
---|
705 | a2 = a/(x1-x4) |
---|
706 | a1 = -a2*x4 |
---|
707 | a4 = ((a1 + a2*x3)/y3-(a1 + a2*x2)/y2)/(x2-x3) |
---|
708 | a3 = 1. - (a1 + a2*x3)/y3 - a4*x3 |
---|
709 | |
---|
710 | # Dictionary of vertex objects |
---|
711 | vertices = {} |
---|
712 | points = [] |
---|
713 | |
---|
714 | for i in range(m+1): |
---|
715 | x = deltax*i |
---|
716 | for j in range(n+1): |
---|
717 | y = deltay*j |
---|
718 | if x > 0.25*lenx: |
---|
719 | y = a1 + a2*x + a3*y + a4*x*y |
---|
720 | |
---|
721 | vertices[i,j] = len(points) |
---|
722 | points.append([x + origin[0], y + origin[1]]) |
---|
723 | |
---|
724 | # Construct 4 triangles per element |
---|
725 | elements = [] |
---|
726 | boundary = {} |
---|
727 | for i in range(m): |
---|
728 | for j in range(n): |
---|
729 | v1 = vertices[i,j+1] |
---|
730 | v2 = vertices[i,j] |
---|
731 | v3 = vertices[i+1,j+1] |
---|
732 | v4 = vertices[i+1,j] |
---|
733 | x = (points[v1][0]+points[v2][0]+points[v3][0]+points[v4][0])*0.25 |
---|
734 | y = (points[v1][1]+points[v2][1]+points[v3][1]+points[v4][1])*0.25 |
---|
735 | v5 = len(points) |
---|
736 | points.append([x, y]) |
---|
737 | |
---|
738 | #Update boundary dictionary and create elements |
---|
739 | #Create left triangle |
---|
740 | if i == 0: |
---|
741 | boundary[(len(elements), 1)] = 'left' |
---|
742 | elements.append([v2,v5,v1]) |
---|
743 | |
---|
744 | #Create bottom triangle |
---|
745 | if j == 0: |
---|
746 | boundary[(len(elements), 1)] = 'bottom' |
---|
747 | elements.append([v4,v5,v2]) |
---|
748 | |
---|
749 | #Create right triangle |
---|
750 | if i == m-1: |
---|
751 | boundary[(len(elements), 1)] = 'right' |
---|
752 | elements.append([v3,v5,v4]) |
---|
753 | |
---|
754 | #Create top triangle |
---|
755 | if j == n-1: |
---|
756 | boundary[(len(elements), 1)] = 'top' |
---|
757 | elements.append([v1,v5,v3]) |
---|
758 | |
---|
759 | |
---|
760 | return points, elements, boundary |
---|