[6152] | 1 | """ |
---|
| 2 | General functions used in fit and interpolate. |
---|
| 3 | |
---|
| 4 | Ole Nielsen, Stephen Roberts, Duncan Gray |
---|
| 5 | Geoscience Australia, 2006. |
---|
| 6 | |
---|
| 7 | """ |
---|
| 8 | import time |
---|
| 9 | |
---|
[6553] | 10 | from anuga.utilities.polygon import is_inside_triangle |
---|
[6152] | 11 | from anuga.utilities.numerical_tools import get_machine_precision |
---|
| 12 | from anuga.config import max_float |
---|
| 13 | |
---|
[6304] | 14 | import numpy as num |
---|
[6152] | 15 | |
---|
| 16 | |
---|
| 17 | initial_search_value = 'uncomment search_functions code first'#0 |
---|
| 18 | search_one_cell_time = initial_search_value |
---|
| 19 | search_more_cells_time = initial_search_value |
---|
| 20 | |
---|
[6553] | 21 | # FIXME(Ole): Could we come up with a less confusing structure? |
---|
| 22 | LAST_TRIANGLE = [[-10, |
---|
| 23 | (num.array([[max_float, max_float], |
---|
| 24 | [max_float, max_float], |
---|
| 25 | [max_float, max_float]]), |
---|
| 26 | (num.array([1.,1.]), |
---|
| 27 | num.array([0.,0.]), |
---|
| 28 | num.array([-1.1,-1.1])))]] |
---|
[6152] | 29 | |
---|
[6553] | 30 | def search_tree_of_vertices(root, x): |
---|
[6152] | 31 | """ |
---|
| 32 | Find the triangle (element) that the point x is in. |
---|
| 33 | |
---|
| 34 | Inputs: |
---|
| 35 | root: A quad tree of the vertices |
---|
| 36 | x: The point being placed |
---|
| 37 | |
---|
| 38 | Return: |
---|
| 39 | element_found, sigma0, sigma1, sigma2, k |
---|
| 40 | |
---|
| 41 | where |
---|
| 42 | element_found: True if a triangle containing x was found |
---|
| 43 | sigma0, sigma1, sigma2: The interpolated values |
---|
| 44 | k: Index of triangle (if found) |
---|
| 45 | |
---|
| 46 | """ |
---|
| 47 | global search_one_cell_time |
---|
| 48 | global search_more_cells_time |
---|
| 49 | |
---|
| 50 | # Search the last triangle first |
---|
[6553] | 51 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 52 | _search_triangles_of_vertices(last_triangle, x) |
---|
[6152] | 53 | |
---|
| 54 | if element_found is True: |
---|
| 55 | return element_found, sigma0, sigma1, sigma2, k |
---|
| 56 | |
---|
[6553] | 57 | |
---|
[6152] | 58 | # Get triangles in the cell that the point is in. |
---|
| 59 | # Triangle is a list, first element triangle_id, |
---|
| 60 | # second element the triangle |
---|
| 61 | triangles = root.search(x[0], x[1]) |
---|
[6553] | 62 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
| 63 | _search_triangles_of_vertices(triangles, x) |
---|
| 64 | |
---|
[6152] | 65 | is_more_elements = True |
---|
| 66 | |
---|
| 67 | while not element_found and is_more_elements: |
---|
| 68 | triangles, branch = root.expand_search() |
---|
| 69 | if branch == []: |
---|
| 70 | # Searching all the verts from the root cell that haven't |
---|
| 71 | # been searched. This is the last try |
---|
| 72 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
[6553] | 73 | _search_triangles_of_vertices(triangles, x) |
---|
[6152] | 74 | is_more_elements = False |
---|
| 75 | else: |
---|
| 76 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
[6553] | 77 | _search_triangles_of_vertices(triangles, x) |
---|
| 78 | |
---|
[6152] | 79 | |
---|
| 80 | return element_found, sigma0, sigma1, sigma2, k |
---|
| 81 | |
---|
| 82 | |
---|
[6553] | 83 | def _search_triangles_of_vertices(triangles, x): |
---|
| 84 | """Search for triangle containing x amongs candidate_vertices in triangles |
---|
[6152] | 85 | |
---|
| 86 | This is called by search_tree_of_vertices once the appropriate node |
---|
| 87 | has been found from the quad tree. |
---|
| 88 | |
---|
| 89 | |
---|
| 90 | This function is responsible for most of the compute time in |
---|
| 91 | fit and interpolate. |
---|
| 92 | """ |
---|
| 93 | global last_triangle |
---|
| 94 | |
---|
[6553] | 95 | # These statments are needed if triangles is empty |
---|
[6152] | 96 | sigma2 = -10.0 |
---|
| 97 | sigma0 = -10.0 |
---|
| 98 | sigma1 = -10.0 |
---|
| 99 | k = -10 |
---|
[6553] | 100 | # For all vertices in same cell as point x |
---|
| 101 | element_found = False |
---|
[6152] | 102 | for k, tri_verts_norms in triangles: |
---|
| 103 | tri = tri_verts_norms[0] |
---|
| 104 | # k is the triangle index |
---|
| 105 | # tri is a list of verts (x, y), representing a tringle |
---|
| 106 | # Find triangle that contains x (if any) and interpolate |
---|
[6553] | 107 | |
---|
| 108 | # Input check disabled to speed things up. |
---|
| 109 | if is_inside_triangle(x, tri, |
---|
| 110 | closed=True, |
---|
| 111 | check_inputs=False): |
---|
| 112 | |
---|
| 113 | n0, n1, n2 = tri_verts_norms[1] |
---|
| 114 | sigma0, sigma1, sigma2 =\ |
---|
| 115 | compute_interpolation_values(tri, n0, n1, n2, x) |
---|
| 116 | |
---|
| 117 | element_found = True |
---|
| 118 | |
---|
[6152] | 119 | # Don't look for any other triangles in the triangle list |
---|
[6553] | 120 | last_triangle = [[k, tri_verts_norms]] |
---|
| 121 | break |
---|
| 122 | |
---|
[6152] | 123 | return element_found, sigma0, sigma1, sigma2, k |
---|
| 124 | |
---|
| 125 | |
---|
| 126 | |
---|
[6553] | 127 | def compute_interpolation_values(triangle, n0, n1, n2, x): |
---|
| 128 | """Compute linear interpolation of point x and triangle. |
---|
| 129 | |
---|
| 130 | n0, n1, n2 are normal to the tree edges. |
---|
[6152] | 131 | """ |
---|
| 132 | |
---|
| 133 | # Get the three vertex_points of candidate triangle k |
---|
| 134 | xi0, xi1, xi2 = triangle |
---|
| 135 | |
---|
| 136 | sigma0 = num.dot((x-xi1), n0)/num.dot((xi0-xi1), n0) |
---|
| 137 | sigma1 = num.dot((x-xi2), n1)/num.dot((xi1-xi2), n1) |
---|
| 138 | sigma2 = num.dot((x-xi0), n2)/num.dot((xi2-xi0), n2) |
---|
| 139 | |
---|
[6553] | 140 | return sigma0, sigma1, sigma2 |
---|
[6152] | 141 | |
---|
| 142 | def set_last_triangle(): |
---|
| 143 | global last_triangle |
---|
| 144 | last_triangle = LAST_TRIANGLE |
---|
| 145 | |
---|
| 146 | def search_times(): |
---|
| 147 | |
---|
| 148 | global search_one_cell_time |
---|
| 149 | global search_more_cells_time |
---|
| 150 | |
---|
| 151 | return search_one_cell_time, search_more_cells_time |
---|
| 152 | |
---|
| 153 | def reset_search_times(): |
---|
| 154 | |
---|
| 155 | global search_one_cell_time |
---|
| 156 | global search_more_cells_time |
---|
| 157 | search_one_cell_time = initial_search_value |
---|
| 158 | search_more_cells_time = initial_search_value |
---|