1 | """quad.py - quad tree data structure for fast indexing of points in the plane |
---|
2 | |
---|
3 | |
---|
4 | """ |
---|
5 | |
---|
6 | from treenode import TreeNode |
---|
7 | import string, types, sys |
---|
8 | |
---|
9 | #FIXME verts are added one at a time. |
---|
10 | #FIXME add max min x y in general_mesh |
---|
11 | |
---|
12 | class Cell(TreeNode): |
---|
13 | """class Cell |
---|
14 | |
---|
15 | One cell in the plane delimited by southern, northern, |
---|
16 | western, eastern boundaries. |
---|
17 | |
---|
18 | Public Methods: |
---|
19 | prune() |
---|
20 | insert(point) |
---|
21 | search(x, y) |
---|
22 | collapse() |
---|
23 | split() |
---|
24 | store() |
---|
25 | retrieve() |
---|
26 | count() |
---|
27 | """ |
---|
28 | |
---|
29 | def __init__(self, southern, northern, western, eastern, |
---|
30 | name = 'cell', |
---|
31 | max_points_per_cell = 4): |
---|
32 | |
---|
33 | # Initialise base classes |
---|
34 | TreeNode.__init__(self, string.lower(name)) |
---|
35 | |
---|
36 | # Initialise cell |
---|
37 | self.southern = round(southern,5) |
---|
38 | self.northern = round(northern,5) |
---|
39 | self.western = round(western,5) |
---|
40 | self.eastern = round(eastern,5) |
---|
41 | |
---|
42 | # The points in this cell |
---|
43 | self.points = [] |
---|
44 | |
---|
45 | self.max_points_per_cell = max_points_per_cell |
---|
46 | |
---|
47 | |
---|
48 | def __repr__(self): |
---|
49 | return self.name |
---|
50 | |
---|
51 | |
---|
52 | def spawn(self): |
---|
53 | """Create four child cells unless they already exist |
---|
54 | """ |
---|
55 | |
---|
56 | if self.children: |
---|
57 | return |
---|
58 | else: |
---|
59 | self.children = [] |
---|
60 | |
---|
61 | # convenience variables |
---|
62 | cs = self.southern |
---|
63 | cn = self.northern |
---|
64 | cw = self.western |
---|
65 | ce = self.eastern |
---|
66 | |
---|
67 | # create 4 child cells |
---|
68 | self.AddChild(Cell((cn+cs)/2,cn,cw,(cw+ce)/2,self.name+'_nw')) |
---|
69 | self.AddChild(Cell((cn+cs)/2,cn,(cw+ce)/2,ce,self.name+'_ne')) |
---|
70 | self.AddChild(Cell(cs,(cn+cs)/2,(cw+ce)/2,ce,self.name+'_se')) |
---|
71 | self.AddChild(Cell(cs,(cn+cs)/2,cw,(cw+ce)/2,self.name+'_sw')) |
---|
72 | |
---|
73 | |
---|
74 | def search(self, x, y): |
---|
75 | #def search_new(self, x, y): |
---|
76 | """Find all point indices sharing the same cell as point (x, y) |
---|
77 | """ |
---|
78 | branch = [] |
---|
79 | points = [] |
---|
80 | if self.children: |
---|
81 | for child in self: |
---|
82 | if child.contains(x,y): |
---|
83 | brothers = list(self.children) |
---|
84 | brothers.remove(child) |
---|
85 | branch.append(brothers) |
---|
86 | points, branch = child.search_branch(x,y, branch) |
---|
87 | else: |
---|
88 | # Leaf node: Get actual waypoints |
---|
89 | points = self.retrieve() |
---|
90 | |
---|
91 | self.branch = branch |
---|
92 | return points |
---|
93 | |
---|
94 | |
---|
95 | def search_branch(self, x, y, branch): |
---|
96 | """Find all point indices sharing the same cell as point (x, y) |
---|
97 | """ |
---|
98 | points = [] |
---|
99 | if self.children: |
---|
100 | for child in self: |
---|
101 | if child.contains(x,y): |
---|
102 | brothers = list(self.children) |
---|
103 | brothers.remove(child) |
---|
104 | branch.append(brothers) |
---|
105 | points, branch = child.search_branch(x,y, branch) |
---|
106 | |
---|
107 | else: |
---|
108 | # Leaf node: Get actual waypoints |
---|
109 | points = self.retrieve() |
---|
110 | return points, branch |
---|
111 | |
---|
112 | |
---|
113 | def expand_search(self): |
---|
114 | """Find all point indices 'up' one cell from the last search |
---|
115 | """ |
---|
116 | points = [] |
---|
117 | if self.branch == []: |
---|
118 | points = [] |
---|
119 | else: |
---|
120 | three_cells = self.branch.pop() |
---|
121 | for cell in three_cells: |
---|
122 | #print "cell ", cell.show() |
---|
123 | points += cell.retrieve() |
---|
124 | return points, self.branch |
---|
125 | |
---|
126 | |
---|
127 | def contains(*args): |
---|
128 | """True only if P's coordinates lie within cell boundaries |
---|
129 | This methods has two forms: |
---|
130 | |
---|
131 | cell.contains(index) |
---|
132 | #True if cell contains indexed point |
---|
133 | cell.contains(x, y) |
---|
134 | #True if cell contains point (x,y) |
---|
135 | |
---|
136 | """ |
---|
137 | |
---|
138 | self = args[0] |
---|
139 | if len(args) == 2: |
---|
140 | point_id = int(args[1]) |
---|
141 | x = self.__class__.mesh.coordinates[point_id][0] |
---|
142 | y = self.__class__.mesh.coordinates[point_id][1] |
---|
143 | |
---|
144 | #print point_id, x, y |
---|
145 | elif len(args) == 3: |
---|
146 | x = float(args[1]) |
---|
147 | y = float(args[2]) |
---|
148 | else: |
---|
149 | msg = 'Number of arguments to method must be two or three' |
---|
150 | raise msg |
---|
151 | |
---|
152 | if y < self.southern: return False |
---|
153 | if y >= self.northern: return False |
---|
154 | if x < self.western: return False |
---|
155 | if x >= self.eastern: return False |
---|
156 | return True |
---|
157 | |
---|
158 | |
---|
159 | def insert(self, points, split = False): |
---|
160 | """insert point(s) in existing tree structure below self |
---|
161 | and split if requested |
---|
162 | """ |
---|
163 | |
---|
164 | # Call insert for each element of a list of points |
---|
165 | if type(points) == types.ListType: |
---|
166 | for point in points: |
---|
167 | self.insert(point, split) |
---|
168 | else: |
---|
169 | #Only one point given as argument |
---|
170 | point = points |
---|
171 | |
---|
172 | # Find appropriate cell |
---|
173 | if self.children is not None: |
---|
174 | for child in self: |
---|
175 | if child.contains(point): |
---|
176 | child.insert(point, split) |
---|
177 | break |
---|
178 | else: |
---|
179 | # self is a leaf cell: insert point into cell |
---|
180 | if self.contains(point): |
---|
181 | self.store(point) |
---|
182 | else: |
---|
183 | x = self.__class__.mesh.coordinates[point][0] |
---|
184 | y = self.__class__.mesh.coordinates[point][1] |
---|
185 | print "(" + str(x) + "," + str(y) + ")" |
---|
186 | raise 'point not in region: %s' %str(point) |
---|
187 | |
---|
188 | |
---|
189 | #Split datastructure if requested |
---|
190 | if split is True: |
---|
191 | self.split() |
---|
192 | |
---|
193 | |
---|
194 | |
---|
195 | def store(self,objects): |
---|
196 | |
---|
197 | if type(objects) not in [types.ListType,types.TupleType]: |
---|
198 | self.points.append(objects) |
---|
199 | else: |
---|
200 | self.points.extend(objects) |
---|
201 | |
---|
202 | |
---|
203 | def retrieve(self): |
---|
204 | objects = [] |
---|
205 | if self.children is None: |
---|
206 | objects = self.points |
---|
207 | else: |
---|
208 | for child in self: |
---|
209 | objects += child.retrieve() |
---|
210 | return objects |
---|
211 | |
---|
212 | |
---|
213 | def count(self, keywords=None): |
---|
214 | """retrieve number of stored objects beneath this node inclusive |
---|
215 | """ |
---|
216 | |
---|
217 | num_waypoint = 0 |
---|
218 | if self.children: |
---|
219 | for child in self: |
---|
220 | num_waypoint = num_waypoint + child.count() |
---|
221 | else: |
---|
222 | num_waypoint = len(self.points) |
---|
223 | return num_waypoint |
---|
224 | |
---|
225 | |
---|
226 | def clear(self): |
---|
227 | self.Prune() # TreeNode method |
---|
228 | |
---|
229 | |
---|
230 | def clear_leaf_node(self): |
---|
231 | """Clears storage in leaf node. |
---|
232 | Called from Treenod. |
---|
233 | Must exist. |
---|
234 | """ |
---|
235 | self.points = [] |
---|
236 | |
---|
237 | |
---|
238 | def clear_internal_node(self): |
---|
239 | """Called from Treenode. |
---|
240 | Must exist. |
---|
241 | """ |
---|
242 | pass |
---|
243 | |
---|
244 | |
---|
245 | |
---|
246 | def split(self, threshold=None): |
---|
247 | """ |
---|
248 | Partition cell when number of contained waypoints exceeds |
---|
249 | threshold. All waypoints are then moved into correct |
---|
250 | child cell. |
---|
251 | """ |
---|
252 | if threshold == None: |
---|
253 | threshold = self.max_points_per_cell |
---|
254 | |
---|
255 | #FIXME, mincellsize removed. base it on side length, if needed |
---|
256 | |
---|
257 | #Protect against silly thresholds such as -1 |
---|
258 | if threshold < 1: |
---|
259 | return |
---|
260 | |
---|
261 | if not self.children: # Leaf cell |
---|
262 | if self.count() > threshold : |
---|
263 | #Split is needed |
---|
264 | points = self.retrieve() # Get points from leaf cell |
---|
265 | self.clear() # and remove them from storage |
---|
266 | |
---|
267 | self.spawn() # Spawn child cells and move |
---|
268 | for p in points: # points to appropriate child |
---|
269 | for child in self: |
---|
270 | if child.contains(p): |
---|
271 | child.insert(p) |
---|
272 | break |
---|
273 | |
---|
274 | if self.children: # Parent cell |
---|
275 | for child in self: # split (possibly newly created) |
---|
276 | child.split(threshold) # child cells recursively |
---|
277 | |
---|
278 | |
---|
279 | |
---|
280 | def collapse(self,threshold=None): |
---|
281 | """ |
---|
282 | collapse child cells into immediate parent if total number of contained waypoints |
---|
283 | in subtree below is less than or equal to threshold. |
---|
284 | All waypoints are then moved into parent cell and |
---|
285 | children are removed. If self is a leaf node initially, do nothing. |
---|
286 | """ |
---|
287 | |
---|
288 | if threshold is None: |
---|
289 | threshold = self.max_points_per_cell |
---|
290 | |
---|
291 | |
---|
292 | if self.children: # Parent cell |
---|
293 | if self.count() <= threshold: # collapse |
---|
294 | points = self.retrieve() # Get all points from child cells |
---|
295 | self.clear() # Remove children, self is now a leaf node |
---|
296 | self.insert(points) # Insert all points in local storage |
---|
297 | else: |
---|
298 | for child in self: # Check if any sub tree can be collapsed |
---|
299 | child.collapse(threshold) |
---|
300 | |
---|
301 | |
---|
302 | def Get_tree(self,depth=0): |
---|
303 | """Traverse tree below self |
---|
304 | Print for each node the name and |
---|
305 | if it is a leaf the number of objects |
---|
306 | """ |
---|
307 | s = '' |
---|
308 | if depth == 0: |
---|
309 | s = '\n' |
---|
310 | |
---|
311 | s += "%s%s:" % (' '*depth, self.name) |
---|
312 | if self.children: |
---|
313 | s += '\n' |
---|
314 | for child in self.children: |
---|
315 | s += child.Get_tree(depth+1) |
---|
316 | else: |
---|
317 | s += '(#wp=%d)\n' %(self.count()) |
---|
318 | |
---|
319 | return s |
---|
320 | |
---|
321 | |
---|
322 | def show(self, depth=0): |
---|
323 | """Traverse tree below self |
---|
324 | Print for each node the name and |
---|
325 | if it is a leaf the number of objects |
---|
326 | """ |
---|
327 | if depth == 0: |
---|
328 | print |
---|
329 | print "%s%s" % (' '*depth, self.name), |
---|
330 | if self.children: |
---|
331 | print |
---|
332 | for child in self.children: |
---|
333 | child.show(depth+1) |
---|
334 | else: |
---|
335 | print '(xmin=%.2f, xmax=%.2f, ymin=%.2f, ymax=%.2f): [%d]'\ |
---|
336 | %(self.western, self.eastern, |
---|
337 | self.southern, self.northern, |
---|
338 | self.count()) |
---|
339 | |
---|
340 | |
---|
341 | def show_all(self,depth=0): |
---|
342 | """Traverse tree below self |
---|
343 | Print for each node the name and if it is a leaf all its objects |
---|
344 | """ |
---|
345 | if depth == 0: |
---|
346 | print |
---|
347 | print "%s%s:" % (' '*depth, self.name), |
---|
348 | if self.children: |
---|
349 | print |
---|
350 | for child in self.children: |
---|
351 | child.show_all(depth+1) |
---|
352 | else: |
---|
353 | print '%s' %self.retrieve() |
---|
354 | |
---|
355 | |
---|
356 | def stats(self,depth=0,min_rad=sys.maxint,max_depth=0,max_points=0): |
---|
357 | """Traverse tree below self and find minimal cell radius, |
---|
358 | maximumtree depth and maximum number of waypoints per leaf. |
---|
359 | """ |
---|
360 | |
---|
361 | if self.children: |
---|
362 | for child in self.children: |
---|
363 | min_rad, max_depth, max_points =\ |
---|
364 | child.Stats(depth+1,min_rad,max_depth,max_points) |
---|
365 | else: |
---|
366 | #FIXME remvoe radius stuff |
---|
367 | #min_rad = sys.maxint |
---|
368 | #if self.radius < min_rad: min_rad = self.radius |
---|
369 | if depth > max_depth: max_depth = depth |
---|
370 | num_points = self.count() |
---|
371 | if num_points > max_points: max_points = num_points |
---|
372 | |
---|
373 | #return min_rad, max_depth, max_points |
---|
374 | return max_depth, max_points |
---|
375 | |
---|
376 | |
---|
377 | #Class initialisation method |
---|
378 | def initialise(cls, mesh): |
---|
379 | cls.mesh = mesh |
---|
380 | |
---|
381 | initialise = classmethod(initialise) |
---|
382 | |
---|
383 | def build_quadtree(mesh, max_points_per_cell = 4): |
---|
384 | """Build quad tree for mesh. |
---|
385 | |
---|
386 | All vertices in mesh are stored in quadtree and a reference to the root is returned. |
---|
387 | """ |
---|
388 | |
---|
389 | from Numeric import minimum, maximum |
---|
390 | |
---|
391 | #Initialise |
---|
392 | Cell.initialise(mesh) |
---|
393 | |
---|
394 | #Make root cell |
---|
395 | #print mesh.coordinates |
---|
396 | |
---|
397 | xmin = min(mesh.coordinates[:,0]) |
---|
398 | xmax = max(mesh.coordinates[:,0]) |
---|
399 | ymin = min(mesh.coordinates[:,1]) |
---|
400 | ymax = max(mesh.coordinates[:,1]) |
---|
401 | |
---|
402 | |
---|
403 | #Ensure boundary points are fully contained in region |
---|
404 | #It is a property of the cell structure that points on xmax or ymax of any given cell |
---|
405 | #belong to the neighbouring cell. |
---|
406 | #Hence, the root cell needs to be expanded slightly |
---|
407 | ymax += (ymax-ymin)/10 |
---|
408 | xmax += (xmax-xmin)/10 |
---|
409 | |
---|
410 | # To avoid round off error |
---|
411 | ymin -= (ymax-ymin)/10 |
---|
412 | xmin -= (xmax-xmin)/10 |
---|
413 | |
---|
414 | #print "xmin", xmin |
---|
415 | #print "xmax", xmax |
---|
416 | #print "ymin", ymin |
---|
417 | #print "ymax", ymax |
---|
418 | |
---|
419 | #FIXME: Use mesh.filename if it exists |
---|
420 | root = Cell(ymin, ymax, xmin, xmax, |
---|
421 | #name = .... |
---|
422 | max_points_per_cell = max_points_per_cell) |
---|
423 | |
---|
424 | #root.show() |
---|
425 | |
---|
426 | #Insert indices of all vertices |
---|
427 | root.insert( range(len(mesh.coordinates)) ) |
---|
428 | |
---|
429 | #Build quad tree and return |
---|
430 | root.split() |
---|
431 | |
---|
432 | return root |
---|