| 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 | |
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| 11 | def search_tree_of_vertices(root, mesh, x): |
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| 12 | """ |
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| 13 | Find the triangle (element) that the point x is in. |
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| 14 | |
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| 15 | root: A quad tree of the vertices |
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| 16 | Return the associated sigma and k values |
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| 17 | (and if the element was found) . |
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| 18 | """ |
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| 19 | #Find triangle containing x: |
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| 20 | element_found = False |
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| 21 | |
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| 22 | # This will be returned if element_found = False |
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| 23 | sigma2 = -10.0 |
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| 24 | sigma0 = -10.0 |
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| 25 | sigma1 = -10.0 |
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| 26 | k = -10.0 |
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| 27 | |
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| 28 | #Find vertices near x |
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| 29 | candidate_vertices = root.search(x[0], x[1]) |
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| 30 | is_more_elements = True |
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| 31 | |
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| 32 | element_found, sigma0, sigma1, sigma2, k = \ |
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| 33 | _search_triangles_of_vertices(mesh, |
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| 34 | candidate_vertices, x) |
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| 35 | while not element_found and is_more_elements: |
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| 36 | candidate_vertices, branch = root.expand_search() |
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| 37 | if branch == []: |
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| 38 | # Searching all the verts from the root cell that haven't |
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| 39 | # been searched. This is the last try |
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| 40 | element_found, sigma0, sigma1, sigma2, k = \ |
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| 41 | _search_triangles_of_vertices(mesh, |
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| 42 | candidate_vertices, x) |
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| 43 | is_more_elements = False |
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| 44 | else: |
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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 | candidate_vertices, x) |
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| 48 | |
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| 49 | return element_found, sigma0, sigma1, sigma2, k |
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| 50 | |
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| 51 | def _search_triangles_of_vertices(mesh, candidate_vertices, x): |
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| 52 | #Find triangle containing x: |
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| 53 | element_found = False |
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| 54 | |
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| 55 | # This will be returned if element_found = False |
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| 56 | sigma2 = -10.0 |
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| 57 | sigma0 = -10.0 |
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| 58 | sigma1 = -10.0 |
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| 59 | k = -10.0 |
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| 60 | #print "*$* candidate_vertices", candidate_vertices |
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| 61 | #For all vertices in same cell as point x |
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| 62 | for v in candidate_vertices: |
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| 63 | #FIXME (DSG-DSG): this catches verts with no triangle. |
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| 64 | #Currently pmesh is producing these. |
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| 65 | #this should be stopped, |
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| 66 | if mesh.vertexlist[v] is None: |
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| 67 | continue |
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| 68 | #for each triangle id (k) which has v as a vertex |
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| 69 | for k, _ in mesh.vertexlist[v]: |
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| 70 | #Get the three vertex_points of candidate triangle |
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| 71 | xi0 = mesh.get_vertex_coordinate(k, 0) |
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| 72 | xi1 = mesh.get_vertex_coordinate(k, 1) |
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| 73 | xi2 = mesh.get_vertex_coordinate(k, 2) |
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| 74 | |
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| 75 | #Get the three normals |
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| 76 | n0 = mesh.get_normal(k, 0) |
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| 77 | n1 = mesh.get_normal(k, 1) |
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| 78 | n2 = mesh.get_normal(k, 2) |
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| 79 | |
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| 80 | #Compute interpolation |
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| 81 | sigma2 = dot((x-xi0), n2)/dot((xi2-xi0), n2) |
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| 82 | sigma0 = dot((x-xi1), n0)/dot((xi0-xi1), n0) |
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| 83 | sigma1 = dot((x-xi2), n1)/dot((xi1-xi2), n1) |
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| 84 | |
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| 85 | #FIXME: Maybe move out to test or something |
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| 86 | epsilon = 1.0e-6 |
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| 87 | assert abs(sigma0 + sigma1 + sigma2 - 1.0) < epsilon |
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| 88 | |
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| 89 | #Check that this triangle contains the data point |
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| 90 | |
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| 91 | #Sigmas can get negative within |
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| 92 | #machine precision on some machines (e.g nautilus) |
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| 93 | #Hence the small eps |
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| 94 | eps = 1.0e-15 |
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| 95 | if sigma0 >= -eps and sigma1 >= -eps and sigma2 >= -eps: |
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| 96 | element_found = True |
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| 97 | break |
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| 98 | |
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| 99 | if element_found is True: |
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| 100 | #Don't look for any other triangle |
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| 101 | break |
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| 102 | return element_found, sigma0, sigma1, sigma2, k |
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| 103 | |
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| 104 | |
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