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 | |
---|
10 | from anuga.utilities.numerical_tools import get_machine_precision |
---|
11 | from anuga.utilities.numerical_tools import ensure_numeric |
---|
12 | from anuga.config import max_float |
---|
13 | |
---|
14 | from anuga.utilities import compile |
---|
15 | if compile.can_use_C_extension('polygon_ext.c'): |
---|
16 | # Underlying C implementations can be accessed |
---|
17 | from polygon_ext import _is_inside_triangle |
---|
18 | else: |
---|
19 | msg = 'C implementations could not be accessed by %s.\n ' %__file__ |
---|
20 | msg += 'Make sure compile_all.py has been run as described in ' |
---|
21 | msg += 'the ANUGA installation guide.' |
---|
22 | raise Exception, msg |
---|
23 | |
---|
24 | import numpy as num |
---|
25 | |
---|
26 | |
---|
27 | initial_search_value = 'uncomment search_functions code first'#0 |
---|
28 | search_one_cell_time = initial_search_value |
---|
29 | search_more_cells_time = initial_search_value |
---|
30 | |
---|
31 | # FIXME(Ole): Could we come up with a less confusing structure? |
---|
32 | # FIXME(James): remove this global var |
---|
33 | LAST_TRIANGLE = [[-10, |
---|
34 | (num.array([[max_float, max_float], |
---|
35 | [max_float, max_float], |
---|
36 | [max_float, max_float]]), |
---|
37 | (num.array([1.,1.]), |
---|
38 | num.array([0.,0.]), |
---|
39 | num.array([-1.1,-1.1])))]] |
---|
40 | |
---|
41 | last_triangle = LAST_TRIANGLE |
---|
42 | |
---|
43 | def search_tree_of_vertices(root, mesh, x): |
---|
44 | """ |
---|
45 | Find the triangle (element) that the point x is in. |
---|
46 | |
---|
47 | Inputs: |
---|
48 | root: A quad tree of the vertices |
---|
49 | mesh: The mesh which the quad tree indexes into |
---|
50 | x: The point being placed |
---|
51 | |
---|
52 | Return: |
---|
53 | element_found, sigma0, sigma1, sigma2, k |
---|
54 | |
---|
55 | where |
---|
56 | element_found: True if a triangle containing x was found |
---|
57 | sigma0, sigma1, sigma2: The interpolated values |
---|
58 | k: Index of triangle (if found) |
---|
59 | |
---|
60 | """ |
---|
61 | global search_one_cell_time |
---|
62 | global search_more_cells_time |
---|
63 | |
---|
64 | # Search the last triangle first |
---|
65 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
66 | _search_triangles_of_vertices(last_triangle, x) |
---|
67 | |
---|
68 | if element_found is True: |
---|
69 | return element_found, sigma0, sigma1, sigma2, k |
---|
70 | |
---|
71 | |
---|
72 | # Get triangles in the cell that the point is in. |
---|
73 | tri_indices = root.search(x[0], x[1]) |
---|
74 | triangles = _trilist_from_indices(mesh, tri_indices) |
---|
75 | |
---|
76 | element_found, sigma0, sigma1, sigma2, k = \ |
---|
77 | _search_triangles_of_vertices(triangles, x) |
---|
78 | |
---|
79 | is_more_elements = True |
---|
80 | |
---|
81 | # while not element_found and is_more_elements: |
---|
82 | # triangles, branch = root.expand_search() |
---|
83 | # if branch == []: |
---|
84 | # # Searching all the verts from the root cell that haven't |
---|
85 | # # been searched. This is the last try |
---|
86 | # element_found, sigma0, sigma1, sigma2, k = \ |
---|
87 | # _search_triangles_of_vertices(triangles, x) |
---|
88 | # is_more_elements = False |
---|
89 | # else: |
---|
90 | # element_found, sigma0, sigma1, sigma2, k = \ |
---|
91 | # _search_triangles_of_vertices(triangles, x) |
---|
92 | |
---|
93 | |
---|
94 | return element_found, sigma0, sigma1, sigma2, k |
---|
95 | |
---|
96 | |
---|
97 | def _search_triangles_of_vertices(triangles, x): |
---|
98 | """Search for triangle containing x amongs candidate_vertices in triangles |
---|
99 | |
---|
100 | This is called by search_tree_of_vertices once the appropriate node |
---|
101 | has been found from the quad tree. |
---|
102 | |
---|
103 | |
---|
104 | This function is responsible for most of the compute time in |
---|
105 | fit and interpolate. |
---|
106 | """ |
---|
107 | global last_triangle |
---|
108 | |
---|
109 | x = ensure_numeric(x, num.float) |
---|
110 | |
---|
111 | # These statments are needed if triangles is empty |
---|
112 | sigma2 = -10.0 |
---|
113 | sigma0 = -10.0 |
---|
114 | sigma1 = -10.0 |
---|
115 | k = -10 |
---|
116 | # For all vertices in same cell as point x |
---|
117 | element_found = False |
---|
118 | for k, tri_verts_norms in triangles: |
---|
119 | tri = tri_verts_norms[0] |
---|
120 | tri = ensure_numeric(tri) |
---|
121 | # k is the triangle index |
---|
122 | # tri is a list of verts (x, y), representing a triangle |
---|
123 | # Find triangle that contains x (if any) and interpolate |
---|
124 | |
---|
125 | # Input check disabled to speed things up. |
---|
126 | if bool(_is_inside_triangle(x, tri, int(True), 1.0e-12, 1.0e-12)): |
---|
127 | |
---|
128 | n0, n1, n2 = tri_verts_norms[1] |
---|
129 | sigma0, sigma1, sigma2 =\ |
---|
130 | compute_interpolation_values(tri, n0, n1, n2, x) |
---|
131 | |
---|
132 | element_found = True |
---|
133 | |
---|
134 | # Don't look for any other triangles in the triangle list |
---|
135 | last_triangle = [[k, tri_verts_norms]] |
---|
136 | break |
---|
137 | |
---|
138 | return element_found, sigma0, sigma1, sigma2, k |
---|
139 | |
---|
140 | |
---|
141 | def _trilist_from_indices(mesh, indices): |
---|
142 | """return a list of lists. For the inner lists, |
---|
143 | The first element is the triangle index, |
---|
144 | the second element is a list.for this list |
---|
145 | the first element is a list of three (x, y) vertices, |
---|
146 | the following elements are the three triangle normals. |
---|
147 | |
---|
148 | """ |
---|
149 | |
---|
150 | ret_list = [] |
---|
151 | for i in indices: |
---|
152 | vertices = mesh.get_vertex_coordinates(triangle_id=i, absolute=True) |
---|
153 | n0 = mesh.get_normal(i, 0) |
---|
154 | n1 = mesh.get_normal(i, 1) |
---|
155 | n2 = mesh.get_normal(i, 2) |
---|
156 | ret_list.append([i, [vertices, (n0, n1, n2)]]) |
---|
157 | return ret_list |
---|
158 | |
---|
159 | |
---|
160 | def compute_interpolation_values(triangle, n0, n1, n2, x): |
---|
161 | """Compute linear interpolation of point x and triangle. |
---|
162 | |
---|
163 | n0, n1, n2 are normal to the tree edges. |
---|
164 | """ |
---|
165 | |
---|
166 | # Get the three vertex_points of candidate triangle k |
---|
167 | xi0, xi1, xi2 = triangle |
---|
168 | |
---|
169 | sigma0 = num.dot((x-xi1), n0)/num.dot((xi0-xi1), n0) |
---|
170 | sigma1 = num.dot((x-xi2), n1)/num.dot((xi1-xi2), n1) |
---|
171 | sigma2 = num.dot((x-xi0), n2)/num.dot((xi2-xi0), n2) |
---|
172 | |
---|
173 | return sigma0, sigma1, sigma2 |
---|
174 | |
---|
175 | def set_last_triangle(): |
---|
176 | global last_triangle |
---|
177 | last_triangle = LAST_TRIANGLE |
---|
178 | |
---|
179 | def search_times(): |
---|
180 | |
---|
181 | global search_one_cell_time |
---|
182 | global search_more_cells_time |
---|
183 | |
---|
184 | return search_one_cell_time, search_more_cells_time |
---|
185 | |
---|
186 | def reset_search_times(): |
---|
187 | |
---|
188 | global search_one_cell_time |
---|
189 | global search_more_cells_time |
---|
190 | search_one_cell_time = initial_search_value |
---|
191 | search_more_cells_time = initial_search_value |
---|