| 1 | """quad.py - quad tree data structure for fast indexing of points in the plane |
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| 2 | |
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| 3 | |
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| 4 | """ |
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| 5 | |
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| 6 | from treenode import TreeNode |
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| 7 | import string, types, sys |
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| 8 | |
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| 9 | #FIXME verts are added one at a time. |
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| 10 | #FIXME add max min x y in general_mesh |
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| 11 | |
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| 12 | class Cell(TreeNode): |
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| 13 | """class Cell |
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| 14 | |
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| 15 | One cell in the plane delimited by southern, northern, |
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| 16 | western, eastern boundaries. |
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| 17 | |
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| 18 | Public Methods: |
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| 19 | prune() |
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| 20 | insert(point) |
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| 21 | search(x, y) |
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| 22 | collapse() |
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| 23 | split() |
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| 24 | store() |
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| 25 | retrieve() |
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| 26 | count() |
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| 27 | """ |
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| 28 | |
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| 29 | def __init__(self, southern, northern, western, eastern, |
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| 30 | name = 'cell', |
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| 31 | max_points_per_cell = 4): |
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| 32 | |
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| 33 | # Initialise base classes |
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| 34 | TreeNode.__init__(self, string.lower(name)) |
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| 35 | |
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| 36 | # Initialise cell |
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| 37 | self.southern = round(southern,5) |
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| 38 | self.northern = round(northern,5) |
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| 39 | self.western = round(western,5) |
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| 40 | self.eastern = round(eastern,5) |
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| 41 | |
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| 42 | # The points in this cell |
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| 43 | self.points = [] |
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| 44 | |
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| 45 | self.max_points_per_cell = max_points_per_cell |
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| 46 | |
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| 47 | |
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| 48 | def __repr__(self): |
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| 49 | return self.name |
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| 50 | |
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| 51 | |
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| 52 | def spawn(self): |
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| 53 | """Create four child cells unless they already exist |
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| 54 | """ |
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| 55 | |
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| 56 | if self.children: |
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| 57 | return |
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| 58 | else: |
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| 59 | self.children = [] |
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| 60 | |
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| 61 | # convenience variables |
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| 62 | cs = self.southern |
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| 63 | cn = self.northern |
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| 64 | cw = self.western |
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| 65 | ce = self.eastern |
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| 66 | |
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| 67 | # create 4 child cells |
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| 68 | self.AddChild(Cell((cn+cs)/2,cn,cw,(cw+ce)/2,self.name+'_nw')) |
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| 69 | self.AddChild(Cell((cn+cs)/2,cn,(cw+ce)/2,ce,self.name+'_ne')) |
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| 70 | self.AddChild(Cell(cs,(cn+cs)/2,(cw+ce)/2,ce,self.name+'_se')) |
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| 71 | self.AddChild(Cell(cs,(cn+cs)/2,cw,(cw+ce)/2,self.name+'_sw')) |
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| 72 | |
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| 73 | |
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| 74 | def search(self, x, y, get_vertices=False): |
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| 75 | """Find all point indices sharing the same cell as point (x, y) |
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| 76 | """ |
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| 77 | branch = [] |
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| 78 | points = [] |
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| 79 | if self.children: |
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| 80 | for child in self: |
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| 81 | if child.contains(x,y): |
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| 82 | brothers = list(self.children) |
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| 83 | brothers.remove(child) |
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| 84 | branch.append(brothers) |
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| 85 | points, branch = child.search_branch(x,y, branch, |
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| 86 | get_vertices=get_vertices) |
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| 87 | else: |
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| 88 | # Leaf node: Get actual waypoints |
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| 89 | points = self.retrieve(get_vertices=get_vertices) |
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| 90 | self.branch = branch |
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| 91 | return points |
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| 92 | |
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| 93 | |
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| 94 | def search_branch(self, x, y, branch, get_vertices=False): |
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| 95 | """Find all point indices sharing the same cell as point (x, y) |
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| 96 | """ |
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| 97 | points = [] |
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| 98 | if self.children: |
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| 99 | for child in self: |
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| 100 | if child.contains(x,y): |
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| 101 | brothers = list(self.children) |
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| 102 | brothers.remove(child) |
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| 103 | branch.append(brothers) |
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| 104 | points, branch = child.search_branch(x,y, branch, |
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| 105 | get_vertices=get_vertices) |
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| 106 | |
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| 107 | else: |
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| 108 | # Leaf node: Get actual waypoints |
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| 109 | points = self.retrieve(get_vertices=get_vertices) |
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| 110 | return points, branch |
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| 111 | |
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| 112 | |
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| 113 | def expand_search(self, get_vertices=False): |
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| 114 | """Find all point indices 'up' one cell from the last search |
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| 115 | """ |
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| 116 | points = [] |
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| 117 | if self.branch == []: |
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| 118 | points = [] |
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| 119 | else: |
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| 120 | three_cells = self.branch.pop() |
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| 121 | for cell in three_cells: |
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| 122 | #print "cell ", cell.show() |
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| 123 | points += cell.retrieve(get_vertices=get_vertices) |
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| 124 | return points, self.branch |
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| 125 | |
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| 126 | |
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| 127 | def contains(*args): |
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| 128 | """True only if P's coordinates lie within cell boundaries |
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| 129 | This methods has two forms: |
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| 130 | |
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| 131 | cell.contains(index) |
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| 132 | #True if cell contains indexed point |
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| 133 | cell.contains(x, y) |
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| 134 | #True if cell contains point (x,y) |
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| 135 | |
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| 136 | """ |
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| 137 | |
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| 138 | self = args[0] |
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| 139 | if len(args) == 2: |
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| 140 | point_id = int(args[1]) |
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| 141 | x, y = self.__class__.mesh.get_nodes()[point_id] |
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| 142 | |
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| 143 | #print point_id, x, y |
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| 144 | elif len(args) == 3: |
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| 145 | x = float(args[1]) |
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| 146 | y = float(args[2]) |
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| 147 | else: |
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| 148 | msg = 'Number of arguments to method must be two or three' |
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| 149 | raise msg |
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| 150 | |
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| 151 | if y < self.southern: return False |
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| 152 | if y >= self.northern: return False |
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| 153 | if x < self.western: return False |
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| 154 | if x >= self.eastern: return False |
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| 155 | return True |
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| 156 | |
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| 157 | |
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| 158 | def insert(self, points, split = False): |
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| 159 | """insert point(s) in existing tree structure below self |
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| 160 | and split if requested |
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| 161 | """ |
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| 162 | |
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| 163 | # Call insert for each element of a list of points |
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| 164 | if type(points) == types.ListType: |
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| 165 | for point in points: |
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| 166 | self.insert(point, split) |
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| 167 | else: |
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| 168 | #Only one point given as argument |
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| 169 | point = points |
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| 170 | |
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| 171 | # Find appropriate cell |
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| 172 | if self.children is not None: |
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| 173 | for child in self: |
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| 174 | if child.contains(point): |
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| 175 | child.insert(point, split) |
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| 176 | break |
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| 177 | else: |
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| 178 | # self is a leaf cell: insert point into cell |
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| 179 | if self.contains(point): |
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| 180 | self.store(point) |
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| 181 | else: |
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| 182 | x = self.__class__.mesh.coordinates[point][0] |
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| 183 | y = self.__class__.mesh.coordinates[point][1] |
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| 184 | print "(" + str(x) + "," + str(y) + ")" |
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| 185 | raise 'point not in region: %s' %str(point) |
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| 186 | |
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| 187 | |
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| 188 | #Split datastructure if requested |
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| 189 | if split is True: |
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| 190 | self.split() |
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| 191 | |
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| 192 | |
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| 193 | |
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| 194 | def store(self,objects): |
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| 195 | |
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| 196 | if type(objects) not in [types.ListType,types.TupleType]: |
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| 197 | self.points.append(objects) |
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| 198 | else: |
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| 199 | self.points.extend(objects) |
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| 200 | |
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| 201 | |
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| 202 | def retrieve_triangles(self): |
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| 203 | """return a list of lists. For the inner lists, |
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| 204 | The first element is the triangle index, |
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| 205 | the second element is a list.for this list |
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| 206 | the first element is a list of three (x, y) vertices, |
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| 207 | the following elements are the three triangle normals. |
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| 208 | |
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| 209 | This info is used in searching for a triangle that a point is in. |
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| 210 | """ |
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| 211 | # FIXME Tidy up the structure that is returned. |
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| 212 | # if the triangles att has been made |
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| 213 | # return it. |
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| 214 | if not hasattr(self,'triangles'): |
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| 215 | # use a dictionary to remove duplicates |
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| 216 | triangles = {} |
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| 217 | verts = self.retrieve_vertices() |
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| 218 | # print "verts", verts |
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| 219 | for vert in verts: |
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| 220 | triangle_list = self.__class__.mesh.get_triangles_and_vertices_per_node(vert) |
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| 221 | for k, _ in triangle_list: |
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| 222 | if not triangles.has_key(k): |
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| 223 | # print 'k',k |
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| 224 | tri = self.__class__.mesh.get_vertex_coordinates(k) |
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| 225 | n0 = self.__class__.mesh.get_normal(k, 0) |
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| 226 | n1 = self.__class__.mesh.get_normal(k, 1) |
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| 227 | n2 = self.__class__.mesh.get_normal(k, 2) |
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| 228 | triangles[k]=(tri, (n0, n1, n2)) |
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| 229 | self.triangles = triangles.items() |
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| 230 | return self.triangles |
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| 231 | |
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| 232 | def retrieve_vertices(self): |
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| 233 | objects = [] |
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| 234 | if self.children is None: |
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| 235 | objects = self.points |
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| 236 | else: |
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| 237 | for child in self: |
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| 238 | objects += child.retrieve() |
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| 239 | return objects |
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| 240 | |
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| 241 | |
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| 242 | def retrieve(self, get_vertices=True): |
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| 243 | if get_vertices is True: |
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| 244 | return self.retrieve_vertices() |
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| 245 | else: |
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| 246 | return self.retrieve_triangles() |
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| 247 | |
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| 248 | |
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| 249 | def count(self, keywords=None): |
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| 250 | """retrieve number of stored objects beneath this node inclusive |
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| 251 | """ |
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| 252 | |
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| 253 | num_waypoint = 0 |
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| 254 | if self.children: |
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| 255 | for child in self: |
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| 256 | num_waypoint = num_waypoint + child.count() |
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| 257 | else: |
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| 258 | num_waypoint = len(self.points) |
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| 259 | return num_waypoint |
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| 260 | |
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| 261 | |
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| 262 | def clear(self): |
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| 263 | self.Prune() # TreeNode method |
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| 264 | |
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| 265 | |
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| 266 | def clear_leaf_node(self): |
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| 267 | """Clears storage in leaf node. |
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| 268 | Called from Treenod. |
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| 269 | Must exist. |
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| 270 | """ |
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| 271 | self.points = [] |
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| 272 | |
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| 273 | |
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| 274 | def clear_internal_node(self): |
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| 275 | """Called from Treenode. |
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| 276 | Must exist. |
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| 277 | """ |
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| 278 | pass |
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| 279 | |
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| 280 | |
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| 281 | |
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| 282 | def split(self, threshold=None): |
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| 283 | """ |
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| 284 | Partition cell when number of contained waypoints exceeds |
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| 285 | threshold. All waypoints are then moved into correct |
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| 286 | child cell. |
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| 287 | """ |
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| 288 | if threshold == None: |
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| 289 | threshold = self.max_points_per_cell |
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| 290 | |
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| 291 | #FIXME, mincellsize removed. base it on side length, if needed |
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| 292 | |
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| 293 | #Protect against silly thresholds such as -1 |
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| 294 | if threshold < 1: |
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| 295 | return |
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| 296 | |
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| 297 | if not self.children: # Leaf cell |
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| 298 | if self.count() > threshold : |
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| 299 | #Split is needed |
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| 300 | points = self.retrieve() # Get points from leaf cell |
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| 301 | self.clear() # and remove them from storage |
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| 302 | |
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| 303 | self.spawn() # Spawn child cells and move |
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| 304 | for p in points: # points to appropriate child |
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| 305 | for child in self: |
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| 306 | if child.contains(p): |
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| 307 | child.insert(p) |
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| 308 | break |
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| 309 | |
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| 310 | if self.children: # Parent cell |
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| 311 | for child in self: # split (possibly newly created) |
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| 312 | child.split(threshold) # child cells recursively |
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| 313 | |
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| 314 | |
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| 315 | |
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| 316 | def collapse(self,threshold=None): |
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| 317 | """ |
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| 318 | collapse child cells into immediate parent if total number of contained waypoints |
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| 319 | in subtree below is less than or equal to threshold. |
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| 320 | All waypoints are then moved into parent cell and |
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| 321 | children are removed. If self is a leaf node initially, do nothing. |
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| 322 | """ |
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| 323 | |
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| 324 | if threshold is None: |
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| 325 | threshold = self.max_points_per_cell |
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| 326 | |
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| 327 | |
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| 328 | if self.children: # Parent cell |
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| 329 | if self.count() <= threshold: # collapse |
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| 330 | points = self.retrieve() # Get all points from child cells |
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| 331 | self.clear() # Remove children, self is now a leaf node |
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| 332 | self.insert(points) # Insert all points in local storage |
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| 333 | else: |
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| 334 | for child in self: # Check if any sub tree can be collapsed |
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| 335 | child.collapse(threshold) |
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| 336 | |
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| 337 | |
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| 338 | def Get_tree(self,depth=0): |
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| 339 | """Traverse tree below self |
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| 340 | Print for each node the name and |
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| 341 | if it is a leaf the number of objects |
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| 342 | """ |
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| 343 | s = '' |
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| 344 | if depth == 0: |
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| 345 | s = '\n' |
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| 346 | |
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| 347 | s += "%s%s:" % (' '*depth, self.name) |
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| 348 | if self.children: |
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| 349 | s += '\n' |
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| 350 | for child in self.children: |
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| 351 | s += child.Get_tree(depth+1) |
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| 352 | else: |
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| 353 | s += '(#wp=%d)\n' %(self.count()) |
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| 354 | |
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| 355 | return s |
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| 356 | |
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| 357 | |
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| 358 | def show(self, depth=0): |
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| 359 | """Traverse tree below self |
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| 360 | Print for each node the name and |
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| 361 | if it is a leaf the number of objects |
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| 362 | """ |
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| 363 | if depth == 0: |
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| 364 | print |
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| 365 | print "%s%s" % (' '*depth, self.name), |
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| 366 | if self.children: |
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| 367 | print |
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| 368 | for child in self.children: |
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| 369 | child.show(depth+1) |
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| 370 | else: |
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| 371 | print '(xmin=%.2f, xmax=%.2f, ymin=%.2f, ymax=%.2f): [%d]'\ |
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| 372 | %(self.western, self.eastern, |
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| 373 | self.southern, self.northern, |
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| 374 | self.count()) |
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| 375 | |
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| 376 | |
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| 377 | def show_all(self,depth=0): |
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| 378 | """Traverse tree below self |
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| 379 | Print for each node the name and if it is a leaf all its objects |
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| 380 | """ |
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| 381 | if depth == 0: |
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| 382 | print |
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| 383 | print "%s%s:" % (' '*depth, self.name), |
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| 384 | if self.children: |
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| 385 | print |
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| 386 | for child in self.children: |
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| 387 | child.show_all(depth+1) |
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| 388 | else: |
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| 389 | print '%s' %self.retrieve() |
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| 390 | |
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| 391 | |
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| 392 | def stats(self,depth=0,min_rad=sys.maxint,max_depth=0,max_points=0): |
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| 393 | """Traverse tree below self and find minimal cell radius, |
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| 394 | maximumtree depth and maximum number of waypoints per leaf. |
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| 395 | """ |
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| 396 | |
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| 397 | if self.children: |
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| 398 | for child in self.children: |
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| 399 | min_rad, max_depth, max_points =\ |
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| 400 | child.Stats(depth+1,min_rad,max_depth,max_points) |
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| 401 | else: |
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| 402 | #FIXME remvoe radius stuff |
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| 403 | #min_rad = sys.maxint |
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| 404 | #if self.radius < min_rad: min_rad = self.radius |
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| 405 | if depth > max_depth: max_depth = depth |
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| 406 | num_points = self.count() |
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| 407 | if num_points > max_points: max_points = num_points |
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| 408 | |
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| 409 | #return min_rad, max_depth, max_points |
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| 410 | return max_depth, max_points |
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| 411 | |
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| 412 | |
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| 413 | #Class initialisation method |
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| 414 | def initialise(cls, mesh): |
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| 415 | cls.mesh = mesh |
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| 416 | |
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| 417 | initialise = classmethod(initialise) |
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| 418 | |
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| 419 | def build_quadtree(mesh, max_points_per_cell = 4): |
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| 420 | """Build quad tree for mesh. |
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| 421 | |
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| 422 | All vertices in mesh are stored in quadtree and a reference to the root is returned. |
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| 423 | """ |
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| 424 | |
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| 425 | from Numeric import minimum, maximum |
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| 426 | |
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| 427 | #Initialise |
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| 428 | Cell.initialise(mesh) |
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| 429 | |
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| 430 | #Make root cell |
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| 431 | #print mesh.coordinates |
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| 432 | |
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| 433 | nodes = mesh.get_nodes() |
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| 434 | xmin = min(nodes[:,0]) |
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| 435 | xmax = max(nodes[:,0]) |
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| 436 | ymin = min(nodes[:,1]) |
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| 437 | ymax = max(nodes[:,1]) |
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| 438 | |
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| 439 | |
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| 440 | #Ensure boundary points are fully contained in region |
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| 441 | #It is a property of the cell structure that points on xmax or ymax of any given cell |
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| 442 | #belong to the neighbouring cell. |
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| 443 | #Hence, the root cell needs to be expanded slightly |
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| 444 | ymax += (ymax-ymin)/10 |
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| 445 | xmax += (xmax-xmin)/10 |
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| 446 | |
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| 447 | # To avoid round off error |
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| 448 | ymin -= (ymax-ymin)/10 |
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| 449 | xmin -= (xmax-xmin)/10 |
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| 450 | |
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| 451 | #print "xmin", xmin |
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| 452 | #print "xmax", xmax |
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| 453 | #print "ymin", ymin |
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| 454 | #print "ymax", ymax |
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| 455 | |
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| 456 | #FIXME: Use mesh.filename if it exists |
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| 457 | root = Cell(ymin, ymax, xmin, xmax, |
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| 458 | #name = .... |
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| 459 | max_points_per_cell = max_points_per_cell) |
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| 460 | |
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| 461 | #root.show() |
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| 462 | |
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| 463 | #Insert indices of all vertices |
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| 464 | root.insert( range(mesh.number_of_nodes) ) |
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| 465 | |
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| 466 | #Build quad tree and return |
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| 467 | root.split() |
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| 468 | |
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| 469 | return root |
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