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 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 | root: A quad tree of the vertices |
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17 | Return the associated sigma and k values |
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18 | (and if the element was found) . |
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19 | """ |
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20 | #Find triangle containing x: |
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21 | element_found = False |
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22 | |
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23 | # This will be returned if element_found = False |
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24 | sigma2 = -10.0 |
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25 | sigma0 = -10.0 |
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26 | sigma1 = -10.0 |
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27 | k = -10.0 |
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28 | |
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29 | #Find vertices near x |
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30 | candidate_vertices = root.search(x[0], x[1]) |
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31 | is_more_elements = True |
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32 | |
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33 | element_found, sigma0, sigma1, sigma2, k = \ |
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34 | _search_triangles_of_vertices(mesh, |
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35 | candidate_vertices, x) |
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36 | while not element_found and is_more_elements: |
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37 | candidate_vertices, branch = root.expand_search() |
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38 | if branch == []: |
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39 | # Searching all the verts from the root cell that haven't |
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40 | # been searched. This is the last try |
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41 | element_found, sigma0, sigma1, sigma2, k = \ |
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42 | _search_triangles_of_vertices(mesh, |
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43 | candidate_vertices, x) |
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44 | is_more_elements = False |
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45 | else: |
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46 | element_found, sigma0, sigma1, sigma2, k = \ |
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47 | _search_triangles_of_vertices(mesh, |
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48 | candidate_vertices, x) |
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49 | |
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50 | return element_found, sigma0, sigma1, sigma2, k |
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51 | |
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52 | def _search_triangles_of_vertices(mesh, candidate_vertices, x): |
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53 | #Find triangle containing x: |
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54 | element_found = False |
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55 | |
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56 | # This will be returned if element_found = False |
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57 | sigma2 = -10.0 |
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58 | sigma0 = -10.0 |
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59 | sigma1 = -10.0 |
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60 | k = -10.0 |
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61 | #print "*$* candidate_vertices", candidate_vertices |
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62 | #For all vertices in same cell as point x |
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63 | for v in candidate_vertices: |
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64 | #FIXME (DSG-DSG): this catches verts with no triangle. |
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65 | #Currently pmesh is producing these. |
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66 | #this should be stopped, |
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67 | if mesh.vertexlist[v] is None: |
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68 | continue |
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69 | #for each triangle id (k) which has v as a vertex |
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70 | for k, _ in mesh.vertexlist[v]: |
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71 | #Get the three vertex_points of candidate triangle |
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72 | xi0 = mesh.get_vertex_coordinate(k, 0) |
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73 | xi1 = mesh.get_vertex_coordinate(k, 1) |
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74 | xi2 = mesh.get_vertex_coordinate(k, 2) |
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75 | |
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76 | #Get the three normals |
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77 | n0 = mesh.get_normal(k, 0) |
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78 | n1 = mesh.get_normal(k, 1) |
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79 | n2 = mesh.get_normal(k, 2) |
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80 | |
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81 | #Compute interpolation |
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82 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
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83 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
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84 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
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85 | |
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86 | # Integrity check - machine precision is too hard. |
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87 | #epsilon = get_machine_precision() |
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88 | # Use single precision as we used to here |
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89 | epsilon = 1.0e-6 |
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90 | msg = 'abs(sigma0+sigma1+sigma2-1) = %.15e, eps = %.15e'\ |
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91 | %(abs(sigma0+sigma1+sigma2-1), epsilon) |
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92 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon, msg |
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93 | |
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94 | #Check that this triangle contains the data point |
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95 | |
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96 | # Sigmas are allowed to get negative within |
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97 | # machine precision on some machines (e.g nautilus) |
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98 | epsilon = get_machine_precision() |
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99 | if sigma0 >= -epsilon and sigma1 >= -epsilon and sigma2 >= -epsilon: |
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100 | element_found = True |
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101 | break |
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102 | |
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103 | if element_found is True: |
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104 | #Don't look for any other triangle |
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105 | break |
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106 | return element_found, sigma0, sigma1, sigma2, k |
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107 | |
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108 | |
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