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 | import time |
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9 | |
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10 | from anuga.utilities.polygon import is_inside_triangle |
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11 | from anuga.utilities.numerical_tools import get_machine_precision |
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12 | from anuga.config import max_float |
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13 | |
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14 | import numpy as num |
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15 | |
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16 | |
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17 | initial_search_value = 'uncomment search_functions code first'#0 |
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18 | search_one_cell_time = initial_search_value |
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19 | search_more_cells_time = initial_search_value |
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20 | |
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21 | # FIXME(Ole): Could we come up with a less confusing structure? |
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22 | LAST_TRIANGLE = [[-10, |
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23 | (num.array([[max_float, max_float], |
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24 | [max_float, max_float], |
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25 | [max_float, max_float]]), |
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26 | (num.array([1.,1.]), |
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27 | num.array([0.,0.]), |
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28 | num.array([-1.1,-1.1])))]] |
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29 | |
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30 | def search_tree_of_vertices(root, x): |
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31 | """ |
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32 | Find the triangle (element) that the point x is in. |
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33 | |
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34 | Inputs: |
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35 | root: A quad tree of the vertices |
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36 | x: The point being placed |
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37 | |
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38 | Return: |
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39 | element_found, sigma0, sigma1, sigma2, k |
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40 | |
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41 | where |
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42 | element_found: True if a triangle containing x was found |
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43 | sigma0, sigma1, sigma2: The interpolated values |
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44 | k: Index of triangle (if found) |
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45 | |
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46 | """ |
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47 | global search_one_cell_time |
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48 | global search_more_cells_time |
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49 | |
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50 | # Search the last triangle first |
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51 | element_found, sigma0, sigma1, sigma2, k = \ |
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52 | _search_triangles_of_vertices(last_triangle, x) |
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53 | |
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54 | if element_found is True: |
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55 | return element_found, sigma0, sigma1, sigma2, k |
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56 | |
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57 | |
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58 | # Get triangles in the cell that the point is in. |
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59 | # Triangle is a list, first element triangle_id, |
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60 | # second element the triangle |
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61 | triangles = root.search(x[0], x[1]) |
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62 | element_found, sigma0, sigma1, sigma2, k = \ |
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63 | _search_triangles_of_vertices(triangles, x) |
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64 | |
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65 | is_more_elements = True |
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66 | |
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67 | while not element_found and is_more_elements: |
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68 | triangles, branch = root.expand_search() |
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69 | if branch == []: |
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70 | # Searching all the verts from the root cell that haven't |
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71 | # been searched. This is the last try |
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72 | element_found, sigma0, sigma1, sigma2, k = \ |
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73 | _search_triangles_of_vertices(triangles, x) |
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74 | is_more_elements = False |
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75 | else: |
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76 | element_found, sigma0, sigma1, sigma2, k = \ |
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77 | _search_triangles_of_vertices(triangles, x) |
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78 | |
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79 | |
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80 | return element_found, sigma0, sigma1, sigma2, k |
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81 | |
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82 | |
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83 | def _search_triangles_of_vertices(triangles, x): |
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84 | """Search for triangle containing x amongs candidate_vertices in triangles |
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85 | |
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86 | This is called by search_tree_of_vertices once the appropriate node |
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87 | has been found from the quad tree. |
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88 | |
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89 | |
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90 | This function is responsible for most of the compute time in |
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91 | fit and interpolate. |
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92 | """ |
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93 | global last_triangle |
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94 | |
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95 | # These statments are needed if triangles is empty |
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96 | sigma2 = -10.0 |
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97 | sigma0 = -10.0 |
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98 | sigma1 = -10.0 |
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99 | k = -10 |
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100 | # For all vertices in same cell as point x |
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101 | element_found = False |
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102 | for k, tri_verts_norms in triangles: |
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103 | tri = tri_verts_norms[0] |
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104 | # k is the triangle index |
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105 | # tri is a list of verts (x, y), representing a tringle |
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106 | # Find triangle that contains x (if any) and interpolate |
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107 | |
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108 | # Input check disabled to speed things up. |
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109 | if is_inside_triangle(x, tri, |
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110 | closed=True, |
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111 | check_inputs=False): |
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112 | |
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113 | n0, n1, n2 = tri_verts_norms[1] |
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114 | sigma0, sigma1, sigma2 =\ |
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115 | compute_interpolation_values(tri, n0, n1, n2, x) |
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116 | |
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117 | element_found = True |
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118 | |
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119 | # Don't look for any other triangles in the triangle list |
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120 | last_triangle = [[k, tri_verts_norms]] |
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121 | break |
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122 | |
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123 | return element_found, sigma0, sigma1, sigma2, k |
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124 | |
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125 | |
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126 | |
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127 | def compute_interpolation_values(triangle, n0, n1, n2, x): |
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128 | """Compute linear interpolation of point x and triangle. |
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129 | |
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130 | n0, n1, n2 are normal to the tree edges. |
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131 | """ |
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132 | |
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133 | # Get the three vertex_points of candidate triangle k |
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134 | xi0, xi1, xi2 = triangle |
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135 | |
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136 | sigma0 = num.dot((x-xi1), n0)/num.dot((xi0-xi1), n0) |
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137 | sigma1 = num.dot((x-xi2), n1)/num.dot((xi1-xi2), n1) |
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138 | sigma2 = num.dot((x-xi0), n2)/num.dot((xi2-xi0), n2) |
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139 | |
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140 | return sigma0, sigma1, sigma2 |
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141 | |
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142 | def set_last_triangle(): |
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143 | global last_triangle |
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144 | last_triangle = LAST_TRIANGLE |
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145 | |
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146 | def search_times(): |
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147 | |
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148 | global search_one_cell_time |
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149 | global search_more_cells_time |
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150 | |
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151 | return search_one_cell_time, search_more_cells_time |
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152 | |
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153 | def reset_search_times(): |
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154 | |
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155 | global search_one_cell_time |
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156 | global search_more_cells_time |
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157 | search_one_cell_time = initial_search_value |
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158 | search_more_cells_time = initial_search_value |
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