| 1 | """Classes implementing general 2D geometrical mesh of triangles. |
|---|
| 2 | |
|---|
| 3 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
|---|
| 4 | Geoscience Australia, 2004 |
|---|
| 5 | """ |
|---|
| 6 | |
|---|
| 7 | |
|---|
| 8 | class Mesh: |
|---|
| 9 | """Collection of triangular elements (purely geometric) |
|---|
| 10 | |
|---|
| 11 | A triangular element is defined in terms of three vertex ids, |
|---|
| 12 | ordered counter clock-wise, |
|---|
| 13 | each corresponding to a given coordinate set. |
|---|
| 14 | Vertices from different elements can point to the same |
|---|
| 15 | coordinate set. |
|---|
| 16 | |
|---|
| 17 | Coordinate sets are implemented as an N x 2 Numeric array containing |
|---|
| 18 | x and y coordinates. |
|---|
| 19 | |
|---|
| 20 | |
|---|
| 21 | To instantiate: |
|---|
| 22 | Mesh(points, vertices) |
|---|
| 23 | |
|---|
| 24 | where |
|---|
| 25 | |
|---|
| 26 | points is either a list of 2-tuples or an Mx2 Numeric array of |
|---|
| 27 | floats representing all x, y coordinates in the mesh. |
|---|
| 28 | |
|---|
| 29 | vertices is either a list of 3-tuples or an Nx3 Numeric array of |
|---|
| 30 | integers representing indices of all vertices in the mesh. |
|---|
| 31 | Each vertex is identified by its index i in [0, M-1]. |
|---|
| 32 | |
|---|
| 33 | |
|---|
| 34 | Example: |
|---|
| 35 | a = [0.0, 0.0] |
|---|
| 36 | b = [0.0, 2.0] |
|---|
| 37 | c = [2.0,0.0] |
|---|
| 38 | e = [2.0, 2.0] |
|---|
| 39 | |
|---|
| 40 | points = [a, b, c, e] |
|---|
| 41 | vertices = [ [1,0,2], [1,2,3] ] #bac, bce |
|---|
| 42 | mesh = Mesh(points, vertices) |
|---|
| 43 | |
|---|
| 44 | #creates two triangles: bac and bce |
|---|
| 45 | |
|---|
| 46 | |
|---|
| 47 | Mesh takes the optional third argument boundary which is a |
|---|
| 48 | dictionary mapping from (element_id, edge_id) to boundary tag. |
|---|
| 49 | The default value is None which will assign the defualt_boundary_tag |
|---|
| 50 | as specified in config.py to all boundary edges. |
|---|
| 51 | """ |
|---|
| 52 | |
|---|
| 53 | def __init__(self, coordinates, vertices, boundary = None): |
|---|
| 54 | """ |
|---|
| 55 | Build triangles from x,y coordinates (sequence of 2-tuples or |
|---|
| 56 | Mx2 Numeric array of floats) and vertices (sequence of 3-tuples |
|---|
| 57 | or Nx3 Numeric array of non-negative integers). |
|---|
| 58 | """ |
|---|
| 59 | |
|---|
| 60 | from Numeric import array, zeros, Int, Float, maximum, sqrt, sum |
|---|
| 61 | |
|---|
| 62 | self.vertices = array(vertices).astype(Int) |
|---|
| 63 | self.coordinates = array(coordinates) |
|---|
| 64 | |
|---|
| 65 | #Input checks |
|---|
| 66 | msg = 'Vertices must an Nx2 Numeric array or a sequence of 2-tuples' |
|---|
| 67 | assert len(self.vertices.shape) == 2, msg |
|---|
| 68 | |
|---|
| 69 | msg = 'Coordinates must an Mx2 Numeric array or a sequence of 2-tuples' |
|---|
| 70 | assert len(self.coordinates.shape) == 2, msg |
|---|
| 71 | |
|---|
| 72 | msg = 'Vertex indices reference non-existing coordinate sets' |
|---|
| 73 | assert max(max(self.vertices)) <= self.coordinates.shape[0], msg |
|---|
| 74 | |
|---|
| 75 | |
|---|
| 76 | #Register number of elements (N) |
|---|
| 77 | self.number_of_elements = N = self.vertices.shape[0] |
|---|
| 78 | |
|---|
| 79 | #Allocate space for geometric quantities |
|---|
| 80 | self.centroids = zeros((N, 2), Float) |
|---|
| 81 | #FIXME: Should be renamed to centroid_coordinates |
|---|
| 82 | |
|---|
| 83 | self.areas = zeros(N, Float) |
|---|
| 84 | self.radii = zeros(N, Float) |
|---|
| 85 | self.edgelengths = zeros((N, 3), Float) |
|---|
| 86 | |
|---|
| 87 | self.neighbours = zeros((N, 3), Int) |
|---|
| 88 | self.neighbour_edges = zeros((N, 3), Int) |
|---|
| 89 | self.number_of_boundaries = zeros(N, Int) |
|---|
| 90 | self.surrogate_neighbours = zeros((N, 3), Int) |
|---|
| 91 | |
|---|
| 92 | self.normals = zeros((N, 6), Float) |
|---|
| 93 | |
|---|
| 94 | #Get x,y coordinates for all vertices for all triangles |
|---|
| 95 | #and store |
|---|
| 96 | self.vertex_coordinates = V = self.compute_vertex_coordinates() |
|---|
| 97 | |
|---|
| 98 | |
|---|
| 99 | ##print 'Initialise mesh' |
|---|
| 100 | #Initialise each triangle |
|---|
| 101 | for i in range(N): |
|---|
| 102 | #if i % (N/10) == 0: print '(%d/%d)' %(i, N) |
|---|
| 103 | |
|---|
| 104 | x0 = V[i, 0]; y0 = V[i, 1] |
|---|
| 105 | x1 = V[i, 2]; y1 = V[i, 3] |
|---|
| 106 | x2 = V[i, 4]; y2 = V[i, 5] |
|---|
| 107 | |
|---|
| 108 | #Compute centroid |
|---|
| 109 | centroid = array([(x0 + x1 + x2)/3, (y0 + y1 + y2)/3]) |
|---|
| 110 | self.centroids[i] = centroid |
|---|
| 111 | |
|---|
| 112 | #Area |
|---|
| 113 | self.areas[i] = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
|---|
| 114 | |
|---|
| 115 | msg = 'Triangle (%f,%f), (%f,%f), (%f, %f)' %(x0,y0,x1,y1,x2,y2) |
|---|
| 116 | msg += ' is degenerate: area == %f' %self.areas[i] |
|---|
| 117 | assert self.areas[i] > 0.0, msg |
|---|
| 118 | |
|---|
| 119 | #Midpoints |
|---|
| 120 | m0 = array([(x1 + x2)/2, (y1 + y2)/2]) |
|---|
| 121 | m1 = array([(x0 + x2)/2, (y0 + y2)/2]) |
|---|
| 122 | m2 = array([(x1 + x0)/2, (y1 + y0)/2]) |
|---|
| 123 | |
|---|
| 124 | #The radius is the distance from the centroid of |
|---|
| 125 | #a triangle to the midpoint of the side of the triangle |
|---|
| 126 | #closest to the centroid |
|---|
| 127 | d0 = sqrt(sum( (centroid-m0)**2 )) |
|---|
| 128 | d1 = sqrt(sum( (centroid-m1)**2 )) |
|---|
| 129 | d2 = sqrt(sum( (centroid-m2)**2 )) |
|---|
| 130 | |
|---|
| 131 | self.radii[i] = min(d0, d1, d2) |
|---|
| 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 | #Initialise Neighbours (-1 means that it is a boundary neighbour) |
|---|
| 166 | self.neighbours[i, :] = [-1, -1, -1] |
|---|
| 167 | |
|---|
| 168 | #Initialise edge ids of neighbours |
|---|
| 169 | #In case of boundaries this slot is not used |
|---|
| 170 | self.neighbour_edges[i, :] = [-1, -1, -1] |
|---|
| 171 | |
|---|
| 172 | |
|---|
| 173 | #Build neighbour structure |
|---|
| 174 | self.build_neighbour_structure() |
|---|
| 175 | |
|---|
| 176 | #Build vertex list |
|---|
| 177 | self.build_vertexlist() |
|---|
| 178 | |
|---|
| 179 | #Build surrogate neighbour structure |
|---|
| 180 | self.build_surrogate_neighbour_structure() |
|---|
| 181 | |
|---|
| 182 | #Build boundary dictionary mapping (id, edge) to symbolic tags |
|---|
| 183 | self.build_boundary_dictionary(boundary) |
|---|
| 184 | |
|---|
| 185 | #Update boundary indices |
|---|
| 186 | self.build_boundary_structure() |
|---|
| 187 | |
|---|
| 188 | |
|---|
| 189 | def __len__(self): |
|---|
| 190 | return self.number_of_elements |
|---|
| 191 | |
|---|
| 192 | def __repr__(self): |
|---|
| 193 | return 'Mesh: %d vertices, %d elements, %d boundary segments'\ |
|---|
| 194 | %(self.coordinates.shape[0], len(self), len(self.boundary)) |
|---|
| 195 | |
|---|
| 196 | |
|---|
| 197 | def build_neighbour_structure(self): |
|---|
| 198 | """Update all registered triangles to point to their neighbours. |
|---|
| 199 | |
|---|
| 200 | Also, keep a tally of the number of boundaries for each triangle |
|---|
| 201 | |
|---|
| 202 | Postconditions: |
|---|
| 203 | neighbours and neighbour_edges is populated |
|---|
| 204 | number_of_boundaries integer array is defined. |
|---|
| 205 | """ |
|---|
| 206 | |
|---|
| 207 | #Step 1: |
|---|
| 208 | #Build dictionary mapping from segments (2-tuple of points) |
|---|
| 209 | #to left hand side edge (facing neighbouring triangle) |
|---|
| 210 | |
|---|
| 211 | N = self.number_of_elements |
|---|
| 212 | neighbourdict = {} |
|---|
| 213 | for i in range(N): |
|---|
| 214 | |
|---|
| 215 | #Register all segments as keys mapping to current triangle |
|---|
| 216 | #and segment id |
|---|
| 217 | a = self.vertices[i, 0] |
|---|
| 218 | b = self.vertices[i, 1] |
|---|
| 219 | c = self.vertices[i, 2] |
|---|
| 220 | neighbourdict[a,b] = (i, 2) #(id, edge) |
|---|
| 221 | neighbourdict[b,c] = (i, 0) #(id, edge) |
|---|
| 222 | neighbourdict[c,a] = (i, 1) #(id, edge) |
|---|
| 223 | |
|---|
| 224 | |
|---|
| 225 | #Step 2: |
|---|
| 226 | #Go through triangles again, but this time |
|---|
| 227 | #reverse direction of segments and lookup neighbours. |
|---|
| 228 | for i in range(N): |
|---|
| 229 | a = self.vertices[i, 0] |
|---|
| 230 | b = self.vertices[i, 1] |
|---|
| 231 | c = self.vertices[i, 2] |
|---|
| 232 | |
|---|
| 233 | self.number_of_boundaries[i] = 3 |
|---|
| 234 | if neighbourdict.has_key((b,a)): |
|---|
| 235 | self.neighbours[i, 2] = neighbourdict[b,a][0] |
|---|
| 236 | self.neighbour_edges[i, 2] = neighbourdict[b,a][1] |
|---|
| 237 | self.number_of_boundaries[i] -= 1 |
|---|
| 238 | |
|---|
| 239 | if neighbourdict.has_key((c,b)): |
|---|
| 240 | self.neighbours[i, 0] = neighbourdict[c,b][0] |
|---|
| 241 | self.neighbour_edges[i, 0] = neighbourdict[c,b][1] |
|---|
| 242 | self.number_of_boundaries[i] -= 1 |
|---|
| 243 | |
|---|
| 244 | if neighbourdict.has_key((a,c)): |
|---|
| 245 | self.neighbours[i, 1] = neighbourdict[a,c][0] |
|---|
| 246 | self.neighbour_edges[i, 1] = neighbourdict[a,c][1] |
|---|
| 247 | self.number_of_boundaries[i] -= 1 |
|---|
| 248 | |
|---|
| 249 | |
|---|
| 250 | |
|---|
| 251 | def build_vertexlist(self): |
|---|
| 252 | """Build vertexlist index by vertex ids and for each entry (point id) |
|---|
| 253 | build a list of (triangles, vertex_id) pairs that use the point |
|---|
| 254 | as vertex. |
|---|
| 255 | |
|---|
| 256 | Preconditions: |
|---|
| 257 | self.coordinates and self.vertices are defined |
|---|
| 258 | |
|---|
| 259 | Postcondition: |
|---|
| 260 | self.vertexlist is build |
|---|
| 261 | """ |
|---|
| 262 | |
|---|
| 263 | vertexlist = [None]*len(self.coordinates) |
|---|
| 264 | for i in range(self.number_of_elements): |
|---|
| 265 | |
|---|
| 266 | a = self.vertices[i, 0] |
|---|
| 267 | b = self.vertices[i, 1] |
|---|
| 268 | c = self.vertices[i, 2] |
|---|
| 269 | |
|---|
| 270 | #Register the vertices v as lists of |
|---|
| 271 | #(triangle_id, vertex_id) tuples associated with them |
|---|
| 272 | #This is used for smoothing |
|---|
| 273 | for vertex_id, v in enumerate([a,b,c]): |
|---|
| 274 | if vertexlist[v] is None: |
|---|
| 275 | vertexlist[v] = [] |
|---|
| 276 | |
|---|
| 277 | vertexlist[v].append( (i, vertex_id) ) |
|---|
| 278 | |
|---|
| 279 | self.vertexlist = vertexlist |
|---|
| 280 | |
|---|
| 281 | |
|---|
| 282 | def build_surrogate_neighbour_structure(self): |
|---|
| 283 | """Build structure where each triangle edge points to its neighbours |
|---|
| 284 | if they exist. Otherwise point to the triangle itself. |
|---|
| 285 | |
|---|
| 286 | The surrogate neighbour structure is useful for computing gradients |
|---|
| 287 | based on centroid values of neighbours. |
|---|
| 288 | |
|---|
| 289 | Precondition: Neighbour structure is defined |
|---|
| 290 | Postcondition: |
|---|
| 291 | Surrogate neighbour structure is defined: |
|---|
| 292 | surrogate_neighbours: i0, i1, i2 where all i_k >= 0 point to |
|---|
| 293 | triangles. |
|---|
| 294 | |
|---|
| 295 | """ |
|---|
| 296 | |
|---|
| 297 | N = self.number_of_elements |
|---|
| 298 | for i in range(N): |
|---|
| 299 | #Find all neighbouring volumes that are not boundaries |
|---|
| 300 | for k in range(3): |
|---|
| 301 | if self.neighbours[i, k] < 0: |
|---|
| 302 | self.surrogate_neighbours[i, k] = i #Point this triangle |
|---|
| 303 | else: |
|---|
| 304 | self.surrogate_neighbours[i, k] = self.neighbours[i, k] |
|---|
| 305 | |
|---|
| 306 | |
|---|
| 307 | |
|---|
| 308 | def build_boundary_dictionary(self, boundary = None): |
|---|
| 309 | """Build or input the dictionary of boundary tags. |
|---|
| 310 | self.boundary is a dictionary of tags, |
|---|
| 311 | keyed by volume id and edge: |
|---|
| 312 | { (id, edge): tag, ... } |
|---|
| 313 | |
|---|
| 314 | Postconditions: |
|---|
| 315 | self.boundary is defined. |
|---|
| 316 | """ |
|---|
| 317 | |
|---|
| 318 | from config import default_boundary_tag |
|---|
| 319 | |
|---|
| 320 | if boundary is None: |
|---|
| 321 | boundary = {} |
|---|
| 322 | for vol_id in range(self.number_of_elements): |
|---|
| 323 | for edge_id in range(0, 3): |
|---|
| 324 | if self.neighbours[vol_id, edge_id] < 0: |
|---|
| 325 | boundary[(vol_id, edge_id)] = default_boundary_tag |
|---|
| 326 | else: |
|---|
| 327 | #Check that all keys in given boundary exist |
|---|
| 328 | for vol_id, edge_id in boundary.keys(): |
|---|
| 329 | msg = 'Segment (%d, %d) does not exist' %(vol_id, edge_id) |
|---|
| 330 | a, b = self.neighbours.shape |
|---|
| 331 | assert vol_id < a and edge_id < b, msg |
|---|
| 332 | |
|---|
| 333 | msg = 'Segment (%d, %d) is not a boundary' %(vol_id, edge_id) |
|---|
| 334 | assert self.neighbours[vol_id, edge_id] < 0, msg |
|---|
| 335 | |
|---|
| 336 | #Check that all boundary segments are assigned a value |
|---|
| 337 | for vol_id in range(self.number_of_elements): |
|---|
| 338 | for edge_id in range(0, 3): |
|---|
| 339 | if self.neighbours[vol_id, edge_id] < 0: |
|---|
| 340 | if not boundary.has_key( (vol_id, edge_id) ): |
|---|
| 341 | msg = 'WARNING: Given boundary does not contain ' |
|---|
| 342 | msg += 'tags for edge (%d, %d). '\ |
|---|
| 343 | %(vol_id, edge_id) |
|---|
| 344 | msg += 'Assigning default tag (%s).'\ |
|---|
| 345 | %default_boundary_tag |
|---|
| 346 | |
|---|
| 347 | #FIXME: Print only as per verbosity |
|---|
| 348 | #print msg |
|---|
| 349 | boundary[ (vol_id, edge_id) ] =\ |
|---|
| 350 | default_boundary_tag |
|---|
| 351 | |
|---|
| 352 | |
|---|
| 353 | |
|---|
| 354 | self.boundary = boundary |
|---|
| 355 | |
|---|
| 356 | |
|---|
| 357 | def build_boundary_structure(self): |
|---|
| 358 | """Traverse boundary and |
|---|
| 359 | enumerate neighbour indices from -1 and |
|---|
| 360 | counting down. |
|---|
| 361 | |
|---|
| 362 | Precondition: |
|---|
| 363 | self.boundary is defined. |
|---|
| 364 | Post condition: |
|---|
| 365 | neighbour array has unique negative indices for boundary |
|---|
| 366 | boundary_segments array imposes an ordering on segments |
|---|
| 367 | (not otherwise available from the dictionary) |
|---|
| 368 | """ |
|---|
| 369 | |
|---|
| 370 | if self.boundary is None: |
|---|
| 371 | msg = 'Boundary dictionary must be defined before ' |
|---|
| 372 | msg += 'building boundary structure' |
|---|
| 373 | raise msg |
|---|
| 374 | |
|---|
| 375 | |
|---|
| 376 | self.boundary_segments = self.boundary.keys() |
|---|
| 377 | self.boundary_segments.sort() |
|---|
| 378 | |
|---|
| 379 | index = -1 |
|---|
| 380 | for id, edge in self.boundary_segments: |
|---|
| 381 | self.neighbours[id, edge] = index |
|---|
| 382 | index -= 1 |
|---|
| 383 | |
|---|
| 384 | |
|---|
| 385 | def get_boundary_tags(self): |
|---|
| 386 | """Return list of available boundary tags |
|---|
| 387 | """ |
|---|
| 388 | |
|---|
| 389 | tags = {} |
|---|
| 390 | for v in self.boundary.values(): |
|---|
| 391 | tags[v] = 1 |
|---|
| 392 | |
|---|
| 393 | return tags.keys() |
|---|
| 394 | |
|---|
| 395 | |
|---|
| 396 | |
|---|
| 397 | def check_integrity(self): |
|---|
| 398 | """Check that triangles are internally consistent e.g. |
|---|
| 399 | that area corresponds to edgelengths, that vertices |
|---|
| 400 | are arranged in a counter-clockwise order, etc etc |
|---|
| 401 | Neighbour structure will be checked by class Mesh |
|---|
| 402 | """ |
|---|
| 403 | |
|---|
| 404 | from config import epsilon |
|---|
| 405 | from math import pi |
|---|
| 406 | from util import anglediff |
|---|
| 407 | |
|---|
| 408 | N = self.number_of_elements |
|---|
| 409 | |
|---|
| 410 | #Get x,y coordinates for all vertices for all triangles |
|---|
| 411 | V = self.get_vertex_coordinates() |
|---|
| 412 | |
|---|
| 413 | #Check each triangle |
|---|
| 414 | for i in range(N): |
|---|
| 415 | x0 = V[i, 0]; y0 = V[i, 1] |
|---|
| 416 | x1 = V[i, 2]; y1 = V[i, 3] |
|---|
| 417 | x2 = V[i, 4]; y2 = V[i, 5] |
|---|
| 418 | |
|---|
| 419 | #Check that area hasn't been compromised |
|---|
| 420 | area = self.areas[i] |
|---|
| 421 | ref = abs((x1*y0-x0*y1)+(x2*y1-x1*y2)+(x0*y2-x2*y0))/2 |
|---|
| 422 | msg = 'Wrong area for vertex coordinates: %f %f %f %f %f %f'\ |
|---|
| 423 | %(x0,y0,x1,y1,x2,y2) |
|---|
| 424 | assert abs((area - ref)/area) < epsilon, msg |
|---|
| 425 | |
|---|
| 426 | #Check that points are arranged in counter clock-wise order |
|---|
| 427 | v0 = [x1-x0, y1-y0] |
|---|
| 428 | v1 = [x2-x1, y2-y1] |
|---|
| 429 | v2 = [x0-x2, y0-y2] |
|---|
| 430 | |
|---|
| 431 | a0 = anglediff(v1, v0) |
|---|
| 432 | a1 = anglediff(v2, v1) |
|---|
| 433 | a2 = anglediff(v0, v2) |
|---|
| 434 | |
|---|
| 435 | msg = '''Vertices (%s,%s), (%s,%s), (%s,%s) are not arranged |
|---|
| 436 | in counter clockwise order''' %(x0, y0, x1, y1, x2, y2) |
|---|
| 437 | assert a0 < pi and a1 < pi and a2 < pi, msg |
|---|
| 438 | |
|---|
| 439 | #Check that normals are orthogonal to edge vectors |
|---|
| 440 | #Note that normal[k] lies opposite vertex k |
|---|
| 441 | |
|---|
| 442 | normal0 = self.normals[i, 0:2] |
|---|
| 443 | normal1 = self.normals[i, 2:4] |
|---|
| 444 | normal2 = self.normals[i, 4:6] |
|---|
| 445 | |
|---|
| 446 | for u, v in [ (v0, normal2), (v1, normal0), (v2, normal1) ]: |
|---|
| 447 | assert u[0]*v[0] + u[1]*v[1] < epsilon |
|---|
| 448 | |
|---|
| 449 | |
|---|
| 450 | #Check integrity of neighbour structure |
|---|
| 451 | for i in range(N): |
|---|
| 452 | for v in self.vertices[i, :]: |
|---|
| 453 | #Check that all vertices have been registered |
|---|
| 454 | assert self.vertexlist[v] is not None |
|---|
| 455 | |
|---|
| 456 | #Check that this triangle is listed with at least one vertex |
|---|
| 457 | assert (i, 0) in self.vertexlist[v] or\ |
|---|
| 458 | (i, 1) in self.vertexlist[v] or\ |
|---|
| 459 | (i, 2) in self.vertexlist[v] |
|---|
| 460 | |
|---|
| 461 | |
|---|
| 462 | |
|---|
| 463 | #Check neighbour structure |
|---|
| 464 | for k, neighbour_id in enumerate(self.neighbours[i,:]): |
|---|
| 465 | |
|---|
| 466 | #Assert that my neighbour's neighbour is me |
|---|
| 467 | #Boundaries need not fulfill this |
|---|
| 468 | if neighbour_id >= 0: |
|---|
| 469 | edge = self.neighbour_edges[i, k] |
|---|
| 470 | assert self.neighbours[neighbour_id, edge] == i |
|---|
| 471 | |
|---|
| 472 | |
|---|
| 473 | |
|---|
| 474 | #Check that all boundaries have |
|---|
| 475 | # unique, consecutive, negative indices |
|---|
| 476 | L = len(self.boundary) |
|---|
| 477 | for i in range(L): |
|---|
| 478 | id, edge = self.boundary_segments[i] |
|---|
| 479 | assert self.neighbours[id, edge] == -i-1 |
|---|
| 480 | |
|---|
| 481 | |
|---|
| 482 | #NOTE: This assert doesn't hold true if there are internal boundaries |
|---|
| 483 | #FIXME: Look into this further. |
|---|
| 484 | #for id, edge in self.boundary: |
|---|
| 485 | # assert self.neighbours[id,edge] < 0 |
|---|
| 486 | |
|---|
| 487 | |
|---|
| 488 | |
|---|
| 489 | |
|---|
| 490 | def get_normals(self): |
|---|
| 491 | """Return all normal vectors. |
|---|
| 492 | Return normal vectors for all triangles as an Nx6 array |
|---|
| 493 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
|---|
| 494 | """ |
|---|
| 495 | return self.normals |
|---|
| 496 | |
|---|
| 497 | |
|---|
| 498 | def get_normal(self, i, j): |
|---|
| 499 | """Return normal vector j of the i'th triangle. |
|---|
| 500 | Return value is the numeric array slice [x, y] |
|---|
| 501 | """ |
|---|
| 502 | return self.normals[i, 2*j:2*j+2] |
|---|
| 503 | |
|---|
| 504 | |
|---|
| 505 | |
|---|
| 506 | def get_vertex_coordinates(self): |
|---|
| 507 | """Return all vertex coordinates. |
|---|
| 508 | Return all vertex coordinates for all triangles as an Nx6 array |
|---|
| 509 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
|---|
| 510 | """ |
|---|
| 511 | return self.vertex_coordinates |
|---|
| 512 | |
|---|
| 513 | |
|---|
| 514 | def get_vertex_coordinate(self, i, j): |
|---|
| 515 | """Return coordinates for vertex j of the i'th triangle. |
|---|
| 516 | Return value is the numeric array slice [x, y] |
|---|
| 517 | """ |
|---|
| 518 | return self.vertex_coordinates[i, 2*j:2*j+2] |
|---|
| 519 | |
|---|
| 520 | |
|---|
| 521 | def compute_vertex_coordinates(self): |
|---|
| 522 | """Return vertex coordinates for all triangles as an Nx6 array |
|---|
| 523 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
|---|
| 524 | """ |
|---|
| 525 | |
|---|
| 526 | #FIXME: Perhaps they should be ordered as in obj files?? |
|---|
| 527 | #See quantity.get_vertex_values |
|---|
| 528 | |
|---|
| 529 | from Numeric import zeros, Float |
|---|
| 530 | |
|---|
| 531 | N = self.number_of_elements |
|---|
| 532 | vertex_coordinates = zeros((N, 6), Float) |
|---|
| 533 | |
|---|
| 534 | for i in range(N): |
|---|
| 535 | for j in range(3): |
|---|
| 536 | k = self.vertices[i,j] #Index of vertex 0 |
|---|
| 537 | v_k = self.coordinates[k] |
|---|
| 538 | vertex_coordinates[i, 2*j+0] = v_k[0] |
|---|
| 539 | vertex_coordinates[i, 2*j+1] = v_k[1] |
|---|
| 540 | |
|---|
| 541 | return vertex_coordinates |
|---|
| 542 | |
|---|
| 543 | def get_vertices(self, unique=False): |
|---|
| 544 | """Get connectivity |
|---|
| 545 | If unique is True give them only once as stored internally. |
|---|
| 546 | If unique is False return |
|---|
| 547 | """ |
|---|
| 548 | |
|---|
| 549 | if unique is True: |
|---|
| 550 | return self.vertices |
|---|
| 551 | else: |
|---|
| 552 | from Numeric import reshape, array, Int |
|---|
| 553 | |
|---|
| 554 | m = len(self) #Number of volumes |
|---|
| 555 | M = 3*m #Total number of unique vertices |
|---|
| 556 | return reshape(array(range(M)).astype(Int), (m,3)) |
|---|
| 557 | |
|---|
| 558 | #FIXME: May get rid of |
|---|
| 559 | def rectangular_mesh(m, n, len1=1.0, len2=1.0, origin = (0.0, 0.0)): |
|---|
| 560 | from mesh_factory import rectangular |
|---|
| 561 | points, vertices, boundary = rectangular(m, n, len1, len2, origin) |
|---|
| 562 | |
|---|
| 563 | return Mesh(points, vertices, boundary) |
|---|
| 564 | |
|---|
| 565 | |
|---|
| 566 | #FIXME: Get oblique and contracting and circular meshes from Chris |
|---|
| 567 | |
|---|
