1 | |
---|
2 | from Numeric import concatenate, reshape, take, allclose |
---|
3 | from Numeric import array, zeros, Int, Float, sqrt, sum |
---|
4 | |
---|
5 | from anuga.coordinate_transforms.geo_reference import Geo_reference |
---|
6 | |
---|
7 | class General_mesh: |
---|
8 | """Collection of triangular elements (purely geometric) |
---|
9 | |
---|
10 | A triangular element is defined in terms of three vertex ids, |
---|
11 | ordered counter clock-wise, |
---|
12 | each corresponding to a given coordinate set. |
---|
13 | Vertices from different elements can point to the same |
---|
14 | coordinate set. |
---|
15 | |
---|
16 | Coordinate sets are implemented as an N x 2 Numeric array containing |
---|
17 | x and y coordinates. |
---|
18 | |
---|
19 | |
---|
20 | To instantiate: |
---|
21 | Mesh(coordinates, triangles) |
---|
22 | |
---|
23 | where |
---|
24 | |
---|
25 | coordinates is either a list of 2-tuples or an Mx2 Numeric array of |
---|
26 | floats representing all x, y coordinates in the mesh. |
---|
27 | |
---|
28 | triangles is either a list of 3-tuples or an Nx3 Numeric array of |
---|
29 | integers representing indices of all vertices in the mesh. |
---|
30 | Each vertex is identified by its index i in [0, M-1]. |
---|
31 | |
---|
32 | |
---|
33 | Example: |
---|
34 | a = [0.0, 0.0] |
---|
35 | b = [0.0, 2.0] |
---|
36 | c = [2.0,0.0] |
---|
37 | e = [2.0, 2.0] |
---|
38 | |
---|
39 | points = [a, b, c, e] |
---|
40 | triangles = [ [1,0,2], [1,2,3] ] #bac, bce |
---|
41 | mesh = Mesh(points, triangles) |
---|
42 | |
---|
43 | #creates two triangles: bac and bce |
---|
44 | |
---|
45 | Other: |
---|
46 | |
---|
47 | In addition mesh computes an Nx6 array called vertex_coordinates. |
---|
48 | This structure is derived from coordinates and contains for each |
---|
49 | triangle the three x,y coordinates at the vertices. |
---|
50 | |
---|
51 | |
---|
52 | This is a cut down version of mesh from anuga.pyvolution mesh.py |
---|
53 | """ |
---|
54 | |
---|
55 | #FIXME: It would be a good idea to use geospatial data as an alternative |
---|
56 | #input |
---|
57 | def __init__(self, coordinates, triangles, |
---|
58 | geo_reference=None, |
---|
59 | verbose=False): |
---|
60 | """ |
---|
61 | Build triangles from x,y coordinates (sequence of 2-tuples or |
---|
62 | Mx2 Numeric array of floats) and triangles (sequence of 3-tuples |
---|
63 | or Nx3 Numeric array of non-negative integers). |
---|
64 | |
---|
65 | origin is a 3-tuple consisting of UTM zone, easting and northing. |
---|
66 | If specified coordinates are assumed to be relative to this origin. |
---|
67 | """ |
---|
68 | |
---|
69 | if verbose: print 'General_mesh: Building basic mesh structure' |
---|
70 | |
---|
71 | self.triangles = array(triangles,Int) |
---|
72 | self.coordinates = array(coordinates,Float) |
---|
73 | |
---|
74 | |
---|
75 | # FIXME: this stores a geo_reference, but when coords are returned |
---|
76 | # This geo_ref is not taken into account! |
---|
77 | if geo_reference is None: |
---|
78 | self.geo_reference = Geo_reference() #Use defaults |
---|
79 | else: |
---|
80 | self.geo_reference = geo_reference |
---|
81 | |
---|
82 | #Input checks |
---|
83 | msg = 'Triangles must an Nx3 Numeric array or a sequence of 3-tuples' |
---|
84 | assert len(self.triangles.shape) == 2, msg |
---|
85 | |
---|
86 | msg = 'Coordinates must an Mx2 Numeric array or a sequence of 2-tuples' |
---|
87 | assert len(self.coordinates.shape) == 2, msg |
---|
88 | |
---|
89 | msg = 'Vertex indices reference non-existing coordinate sets' |
---|
90 | assert max(max(self.triangles)) <= self.coordinates.shape[0], msg |
---|
91 | |
---|
92 | |
---|
93 | #Register number of elements (N) |
---|
94 | self.number_of_elements = N = self.triangles.shape[0] |
---|
95 | |
---|
96 | # FIXME: Maybe move to statistics? |
---|
97 | # Or use with get_extent |
---|
98 | xy_extent = [ min(self.coordinates[:,0]), min(self.coordinates[:,1]) , |
---|
99 | max(self.coordinates[:,0]), max(self.coordinates[:,1]) ] |
---|
100 | |
---|
101 | self.xy_extent = array(xy_extent, Float) |
---|
102 | |
---|
103 | |
---|
104 | #Allocate space for geometric quantities |
---|
105 | self.normals = zeros((N, 6), Float) |
---|
106 | self.areas = zeros(N, Float) |
---|
107 | self.edgelengths = zeros((N, 3), Float) |
---|
108 | |
---|
109 | #Get x,y coordinates for all triangles and store |
---|
110 | self.vertex_coordinates = V = self.compute_vertex_coordinates() |
---|
111 | |
---|
112 | |
---|
113 | #Initialise each triangle |
---|
114 | if verbose: |
---|
115 | print 'General_mesh: Computing areas, normals and edgelenghts' |
---|
116 | |
---|
117 | for i in range(N): |
---|
118 | if verbose and i % ((N+10)/10) == 0: print '(%d/%d)' %(i, N) |
---|
119 | |
---|
120 | |
---|
121 | x0 = V[i, 0]; y0 = V[i, 1] |
---|
122 | x1 = V[i, 2]; y1 = V[i, 3] |
---|
123 | x2 = V[i, 4]; y2 = V[i, 5] |
---|
124 | |
---|
125 | #Area |
---|
126 | self.areas[i] = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
---|
127 | |
---|
128 | msg = 'Triangle (%f,%f), (%f,%f), (%f, %f)' %(x0,y0,x1,y1,x2,y2) |
---|
129 | msg += ' is degenerate: area == %f' %self.areas[i] |
---|
130 | assert self.areas[i] > 0.0, msg |
---|
131 | |
---|
132 | |
---|
133 | #Normals |
---|
134 | #The normal vectors |
---|
135 | # - point outward from each edge |
---|
136 | # - are orthogonal to the edge |
---|
137 | # - have unit length |
---|
138 | # - Are enumerated according to the opposite corner: |
---|
139 | # (First normal is associated with the edge opposite |
---|
140 | # the first vertex, etc) |
---|
141 | # - Stored as six floats n0x,n0y,n1x,n1y,n2x,n2y per triangle |
---|
142 | |
---|
143 | n0 = array([x2 - x1, y2 - y1]) |
---|
144 | l0 = sqrt(sum(n0**2)) |
---|
145 | |
---|
146 | n1 = array([x0 - x2, y0 - y2]) |
---|
147 | l1 = sqrt(sum(n1**2)) |
---|
148 | |
---|
149 | n2 = array([x1 - x0, y1 - y0]) |
---|
150 | l2 = sqrt(sum(n2**2)) |
---|
151 | |
---|
152 | #Normalise |
---|
153 | n0 /= l0 |
---|
154 | n1 /= l1 |
---|
155 | n2 /= l2 |
---|
156 | |
---|
157 | #Compute and store |
---|
158 | self.normals[i, :] = [n0[1], -n0[0], |
---|
159 | n1[1], -n1[0], |
---|
160 | n2[1], -n2[0]] |
---|
161 | |
---|
162 | #Edgelengths |
---|
163 | self.edgelengths[i, :] = [l0, l1, l2] |
---|
164 | |
---|
165 | |
---|
166 | #Build vertex list |
---|
167 | if verbose: print 'Building vertex list' |
---|
168 | self.build_vertexlist() |
---|
169 | |
---|
170 | |
---|
171 | |
---|
172 | def __len__(self): |
---|
173 | return self.number_of_elements |
---|
174 | |
---|
175 | def __repr__(self): |
---|
176 | return 'Mesh: %d triangles, %d elements'\ |
---|
177 | %(self.coordinates.shape[0], len(self)) |
---|
178 | |
---|
179 | def get_normals(self): |
---|
180 | """Return all normal vectors. |
---|
181 | Return normal vectors for all triangles as an Nx6 array |
---|
182 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
---|
183 | """ |
---|
184 | return self.normals |
---|
185 | |
---|
186 | |
---|
187 | def get_normal(self, i, j): |
---|
188 | """Return normal vector j of the i'th triangle. |
---|
189 | Return value is the numeric array slice [x, y] |
---|
190 | """ |
---|
191 | return self.normals[i, 2*j:2*j+2] |
---|
192 | |
---|
193 | |
---|
194 | |
---|
195 | def get_vertex_coordinates(self, obj=False, absolute=False): |
---|
196 | """Return all vertex coordinates. |
---|
197 | Return all vertex coordinates for all triangles as an Nx6 array |
---|
198 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
---|
199 | |
---|
200 | if obj is True, the x/y pairs are returned in a 3*N x 2 array. |
---|
201 | FIXME, we might make that the default. |
---|
202 | FIXME Maybe use keyword: continuous = False for this condition? |
---|
203 | FIXME - Maybe use something referring to unique vertices? |
---|
204 | |
---|
205 | Boolean keyword argument absolute determines whether coordinates |
---|
206 | are to be made absolute by taking georeference into account |
---|
207 | Default is False as many parts of ANUGA expects relative coordinates. |
---|
208 | (To see which, switch to default absolute=True and run tests). |
---|
209 | """ |
---|
210 | |
---|
211 | V = self.vertex_coordinates |
---|
212 | if absolute is True: |
---|
213 | if not self.geo_reference.is_absolute(): |
---|
214 | |
---|
215 | V0 = self.geo_reference.get_absolute(V[:,0:2]) |
---|
216 | V1 = self.geo_reference.get_absolute(V[:,2:4]) |
---|
217 | V2 = self.geo_reference.get_absolute(V[:,4:6]) |
---|
218 | |
---|
219 | # This does double the memory need |
---|
220 | V = concatenate( (V0, V1, V2), axis=1 ) |
---|
221 | |
---|
222 | |
---|
223 | if obj is True: |
---|
224 | |
---|
225 | N = V.shape[0] |
---|
226 | return reshape(V, (3*N, 2)) |
---|
227 | else: |
---|
228 | return V |
---|
229 | |
---|
230 | |
---|
231 | def get_vertex_coordinate(self, i, j, absolute=False): |
---|
232 | """Return coordinates for vertex j of the i'th triangle. |
---|
233 | Return value is the numeric array slice [x, y] |
---|
234 | """ |
---|
235 | |
---|
236 | V = self.get_vertex_coordinates(absolute=absolute) |
---|
237 | return V[i, 2*j:2*j+2] |
---|
238 | |
---|
239 | ##return self.vertex_coordinates[i, 2*j:2*j+2] |
---|
240 | |
---|
241 | |
---|
242 | def compute_vertex_coordinates(self): |
---|
243 | """Return vertex coordinates for all triangles as an Nx6 array |
---|
244 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
---|
245 | """ |
---|
246 | |
---|
247 | #FIXME (Ole): Perhaps they should be ordered as in obj files?? |
---|
248 | #See quantity.get_vertex_values |
---|
249 | #FIXME (Ole) - oh yes they should |
---|
250 | |
---|
251 | N = self.number_of_elements |
---|
252 | vertex_coordinates = zeros((N, 6), Float) |
---|
253 | |
---|
254 | for i in range(N): |
---|
255 | for j in range(3): |
---|
256 | k = self.triangles[i,j] #Index of vertex 0 |
---|
257 | v_k = self.coordinates[k] |
---|
258 | vertex_coordinates[i, 2*j+0] = v_k[0] |
---|
259 | vertex_coordinates[i, 2*j+1] = v_k[1] |
---|
260 | |
---|
261 | return vertex_coordinates |
---|
262 | |
---|
263 | def get_vertices(self, indices=None): |
---|
264 | """Get connectivity |
---|
265 | indices is the set of element ids of interest |
---|
266 | """ |
---|
267 | |
---|
268 | if (indices == None): |
---|
269 | indices = range(len(self)) #len(self)=number of elements |
---|
270 | |
---|
271 | return take(self.triangles, indices) |
---|
272 | |
---|
273 | #FIXME - merge these two (get_vertices and get_triangles) |
---|
274 | def get_triangles(self, obj=False): |
---|
275 | """Get connetivity |
---|
276 | Return triangles (triplets of indices into point coordinates) |
---|
277 | |
---|
278 | If obj is True return structure commensurate with replicated |
---|
279 | points, allowing for discontinuities |
---|
280 | (FIXME: Need good name for this concept) |
---|
281 | """ |
---|
282 | |
---|
283 | if obj is True: |
---|
284 | m = len(self) #Number of triangles |
---|
285 | M = 3*m #Total number of unique vertices |
---|
286 | T = reshape(array(range(M)).astype(Int), (m,3)) |
---|
287 | else: |
---|
288 | T = self.triangles |
---|
289 | |
---|
290 | return T |
---|
291 | |
---|
292 | |
---|
293 | |
---|
294 | def get_unique_vertices(self, indices=None): |
---|
295 | triangles = self.get_vertices(indices=indices) |
---|
296 | unique_verts = {} |
---|
297 | for triangle in triangles: |
---|
298 | unique_verts[triangle[0]] = 0 |
---|
299 | unique_verts[triangle[1]] = 0 |
---|
300 | unique_verts[triangle[2]] = 0 |
---|
301 | return unique_verts.keys() |
---|
302 | |
---|
303 | def build_vertexlist(self): |
---|
304 | """Build vertexlist index by vertex ids and for each entry (point id) |
---|
305 | build a list of (triangles, vertex_id) pairs that use the point |
---|
306 | as vertex. |
---|
307 | |
---|
308 | Preconditions: |
---|
309 | self.coordinates and self.triangles are defined |
---|
310 | |
---|
311 | Postcondition: |
---|
312 | self.vertexlist is built |
---|
313 | """ |
---|
314 | |
---|
315 | vertexlist = [None]*len(self.coordinates) |
---|
316 | for i in range(self.number_of_elements): |
---|
317 | |
---|
318 | a = self.triangles[i, 0] |
---|
319 | b = self.triangles[i, 1] |
---|
320 | c = self.triangles[i, 2] |
---|
321 | |
---|
322 | #Register the vertices v as lists of |
---|
323 | #(triangle_id, vertex_id) tuples associated with them |
---|
324 | #This is used for averaging multiple vertex values. |
---|
325 | for vertex_id, v in enumerate([a,b,c]): |
---|
326 | if vertexlist[v] is None: |
---|
327 | vertexlist[v] = [] |
---|
328 | |
---|
329 | vertexlist[v].append( (i, vertex_id) ) |
---|
330 | |
---|
331 | self.vertexlist = vertexlist |
---|
332 | |
---|
333 | |
---|
334 | def get_extent(self, absolute=False): |
---|
335 | """Return min and max of all x and y coordinates |
---|
336 | |
---|
337 | Boolean keyword argument absolute determines whether coordinates |
---|
338 | are to be made absolute by taking georeference into account |
---|
339 | """ |
---|
340 | |
---|
341 | |
---|
342 | |
---|
343 | C = self.get_vertex_coordinates(absolute=absolute) |
---|
344 | X = C[:,0:6:2].copy() |
---|
345 | Y = C[:,1:6:2].copy() |
---|
346 | |
---|
347 | xmin = min(X.flat) |
---|
348 | xmax = max(X.flat) |
---|
349 | ymin = min(Y.flat) |
---|
350 | ymax = max(Y.flat) |
---|
351 | |
---|
352 | return xmin, xmax, ymin, ymax |
---|
353 | |
---|
354 | |
---|
355 | def get_area(self): |
---|
356 | """Return total area of mesh |
---|
357 | """ |
---|
358 | |
---|
359 | return sum(self.areas) |
---|
360 | |
---|
361 | |
---|