1 | """ |
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2 | General functions used in fit and interpolate. |
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3 | |
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4 | Ole Nielsen, Stephen Roberts, Duncan Gray |
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5 | Geoscience Australia, 2006. |
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6 | |
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7 | """ |
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8 | from Numeric import dot |
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9 | |
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10 | from anuga.utilities.numerical_tools import get_machine_precision |
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11 | |
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12 | def search_tree_of_vertices(root, mesh, x): |
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13 | """ |
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14 | Find the triangle (element) that the point x is in. |
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15 | |
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16 | Inputs: |
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17 | root: A quad tree of the vertices |
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18 | mesh: The underlying mesh |
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19 | x: The point being placed |
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20 | |
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21 | Return: |
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22 | element_found, sigma0, sigma1, sigma2, k |
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23 | |
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24 | where |
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25 | element_found: True if a triangle containing x was found |
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26 | sigma0, sigma1, sigma2: The interpolated values |
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27 | k: Index of triangle (if found) |
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28 | |
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29 | """ |
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30 | #Find triangle containing x: |
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31 | element_found = False |
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32 | |
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33 | # This will be returned if element_found = False |
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34 | sigma2 = -10.0 |
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35 | sigma0 = -10.0 |
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36 | sigma1 = -10.0 |
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37 | k = -10.0 |
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38 | |
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39 | #Get triangles in the cell that the point is in. |
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40 | # Triangle is a list, first element triangle_id, |
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41 | # second element the triangle |
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42 | triangles = root.search(x[0], x[1]) |
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43 | is_more_elements = True |
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44 | |
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45 | element_found, sigma0, sigma1, sigma2, k = \ |
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46 | _search_triangles_of_vertices(mesh, |
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47 | triangles, x) |
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48 | while not element_found and is_more_elements: |
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49 | triangles, branch = root.expand_search() |
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50 | if branch == []: |
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51 | # Searching all the verts from the root cell that haven't |
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52 | # been searched. This is the last try |
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53 | element_found, sigma0, sigma1, sigma2, k = \ |
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54 | _search_triangles_of_vertices(mesh,triangles, x) |
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55 | is_more_elements = False |
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56 | else: |
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57 | element_found, sigma0, sigma1, sigma2, k = \ |
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58 | _search_triangles_of_vertices(mesh,triangles, x) |
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59 | |
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60 | return element_found, sigma0, sigma1, sigma2, k |
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61 | |
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62 | |
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63 | def _search_triangles_of_vertices(mesh, triangles, x): |
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64 | """Search for triangle containing x amongs candidate_vertices in mesh |
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65 | |
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66 | This is called by search_tree_of_vertices once the appropriate node |
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67 | has been found from the quad tree. |
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68 | |
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69 | |
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70 | This function is responsible for most of the compute time in |
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71 | fit and interpolate. |
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72 | """ |
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73 | |
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74 | #Find triangle containing x: |
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75 | element_found = False |
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76 | |
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77 | # This will be returned if element_found = False |
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78 | sigma2 = -10.0 |
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79 | sigma0 = -10.0 |
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80 | sigma1 = -10.0 |
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81 | k = -10 |
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82 | |
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83 | #For all vertices in same cell as point x |
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84 | for k, tri_verts_norms in triangles: |
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85 | tri = tri_verts_norms[0] |
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86 | n0, n1, n2 = tri_verts_norms[1] |
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87 | # k is the triangle index |
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88 | # tri is a list of verts (x, y), representing a tringle |
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89 | # Find triangle that contains x (if any) and interpolate |
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90 | element_found, sigma0, sigma1, sigma2 =\ |
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91 | find_triangle_compute_interpolation(tri, n0, n1, n2, x) |
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92 | if element_found is True: |
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93 | # Don't look for any other triangles in the triangle list |
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94 | break |
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95 | return element_found, sigma0, sigma1, sigma2, k |
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96 | |
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97 | |
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98 | |
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99 | def find_triangle_compute_interpolation(triangle, n0, n1, n2, x): |
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100 | """Compute linear interpolation of point x and triangle k in mesh. |
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101 | It is assumed that x belongs to triangle k. |
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102 | """ |
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103 | |
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104 | # Get the three vertex_points of candidate triangle k |
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105 | xi0, xi1, xi2 = triangle |
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106 | |
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107 | # this is where we can call some fast c code. |
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108 | |
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109 | # Integrity check - machine precision is too hard |
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110 | # so we use hardwired single precision |
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111 | epsilon = 1.0e-6 |
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112 | |
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113 | xmax = max(xi0[0], xi1[0], xi2[0]) |
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114 | xmin = min(xi0[0], xi1[0], xi2[0]) |
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115 | ymax = max(xi0[1], xi1[1], xi2[1]) |
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116 | ymin = min(xi0[1], xi1[1], xi2[1]) |
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117 | |
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118 | |
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119 | if x[0] > xmax + epsilon: |
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120 | return False,0,0,0 |
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121 | if x[0] < xmin - epsilon: |
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122 | return False,0,0,0 |
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123 | if x[1] > ymax + epsilon: |
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124 | return False,0,0,0 |
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125 | if x[1] < ymin - epsilon: |
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126 | return False,0,0,0 |
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127 | |
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128 | # Get the three normals |
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129 | #n0 = norms[0] |
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130 | #n1 = norms[1] |
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131 | #n2 = norms[2] |
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132 | |
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133 | # Compute interpolation |
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134 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
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135 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
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136 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
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137 | |
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138 | delta = abs(sigma0+sigma1+sigma2-1.0) # Should be close to zero |
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139 | msg = 'abs(sigma0+sigma1+sigma2-1) = %.15e, eps = %.15e'\ |
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140 | %(delta, epsilon) |
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141 | assert delta < epsilon, msg |
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142 | |
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143 | |
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144 | # Check that this triangle contains the data point |
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145 | # Sigmas are allowed to get negative within |
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146 | # machine precision on some machines (e.g. nautilus) |
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147 | epsilon = get_machine_precision() * 2 |
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148 | if sigma0 >= -epsilon and sigma1 >= -epsilon and sigma2 >= -epsilon: |
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149 | element_found = True |
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150 | else: |
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151 | element_found = False |
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152 | return element_found, sigma0, sigma1, sigma2 |
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