[4955] | 1 | """Alpha shape |
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| 2 | Determine the shape of a set of points. |
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| 3 | |
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| 4 | From website by Kaspar Fischer: |
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| 5 | As mentionned in Edelsbrunner's and Muecke's paper, one can |
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| 6 | intuitively think of an alpha-shape as the following: |
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| 7 | |
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| 8 | Imagine a huge mass of ice-cream making up the space and containing |
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| 9 | the points S as ``hard'' chocolate pieces. Using one of these |
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| 10 | sphere-formed ice-cream spoons we carve out all parts of the ice-cream |
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| 11 | block we can reach without bumping into chocolate pieces, even |
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| 12 | carving out holes in the inside (eg. parts not reachable by simply |
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| 13 | moving the spoon from the outside). We will eventually end up with a |
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| 14 | (not necessarily convex) object bounded by caps, arcs and points. If |
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| 15 | we now straighten all ``round'' faces to triangles and line segments, |
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| 16 | we have an intuitive description of what is called the alpha-shape. |
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| 17 | |
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| 18 | Author: Vanessa Robins, ANU |
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| 19 | """ |
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| 20 | |
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| 21 | import exceptions |
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| 22 | import random |
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| 23 | |
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| 24 | from load_mesh.loadASCII import export_boundary_file |
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| 25 | from anuga.geospatial_data.geospatial_data import Geospatial_data |
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| 26 | |
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[6304] | 27 | import numpy as num |
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[6147] | 28 | |
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| 29 | |
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[4955] | 30 | class AlphaError(exceptions.Exception):pass |
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| 31 | class PointError(AlphaError): pass |
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| 32 | class FlagError(AlphaError): pass |
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| 33 | |
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| 34 | OUTPUT_FILE_TITLE = "# The alpha shape boundary defined by point index pairs of edges" |
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| 35 | INF = pow(10,9) |
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| 36 | EPSILON = 1.0e-12 |
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| 37 | |
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| 38 | def alpha_shape_via_files(point_file, boundary_file, alpha= None): |
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| 39 | """ |
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| 40 | Load a point file and return the alpha shape boundary as a boundary file. |
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| 41 | |
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| 42 | Inputs: |
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| 43 | point_file: File location of the input file, points format (.csv or .pts) |
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| 44 | boundary_file: File location of the generated output file |
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| 45 | alpha: The alpha value can be optionally specified. If it is not specified |
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| 46 | the optimum alpha value will be used. |
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| 47 | """ |
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| 48 | geospatial = Geospatial_data(point_file) |
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| 49 | points = geospatial.get_data_points(absolute=False) |
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| 50 | |
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| 51 | AS = Alpha_Shape(points, alpha) |
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| 52 | AS.write_boundary(boundary_file) |
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| 53 | |
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| 54 | |
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| 55 | class Alpha_Shape: |
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| 56 | |
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| 57 | def __init__(self, points, alpha = None): |
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| 58 | """ |
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| 59 | An Alpha_Shape requires input of a set of points. Other class routines |
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| 60 | return the alpha shape boundary. |
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| 61 | |
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| 62 | Inputs: |
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| 63 | points: List of coordinate pairs [[x1, y1],[x2, y2]..] |
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| 64 | alpha: The alpha value can be optionally specified. If it is |
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| 65 | not specified the optimum alpha value will be used. |
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| 66 | """ |
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| 67 | self._set_points(points) |
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| 68 | self._alpha_shape_algorithm(alpha) |
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| 69 | |
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| 70 | def _set_points(self, points): |
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| 71 | """ |
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| 72 | Create self.points array, do Error checking |
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| 73 | Inputs: |
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| 74 | points: List of coordinate pairs [[x1, y1],[x2, y2]..] |
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| 75 | """ |
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| 76 | # print "setting points" |
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| 77 | if len (points) <= 2: |
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| 78 | raise PointError, "Too few points to find an alpha shape" |
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| 79 | if len(points)==3: |
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| 80 | #check not in a straight line |
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| 81 | # FIXME check points 1,2,3 if straingt, check if points 2,3,4, ect |
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| 82 | x01 = points[0][0] - points[1][0] |
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| 83 | y01 = points[0][1] - points[1][1] |
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| 84 | x12 = points[1][0] - points[2][0] |
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| 85 | y12 = points[1][1] - points[2][1] |
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| 86 | crossprod = x01*y12 - x12*y01 |
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| 87 | if crossprod==0: |
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| 88 | raise PointError, "Three points on a straight line" |
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| 89 | |
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[6304] | 90 | #Convert input to numeric arrays |
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| 91 | self.points = num.array(points, num.float) |
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[4955] | 92 | |
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| 93 | |
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| 94 | def write_boundary(self,file_name): |
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| 95 | """ |
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| 96 | Write the boundary to a file |
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| 97 | """ |
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| 98 | #print " this info will be in the file" |
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| 99 | export_boundary_file(file_name, self.get_boundary(), |
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| 100 | OUTPUT_FILE_TITLE, delimiter = ',') |
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| 101 | |
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| 102 | def get_boundary(self): |
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| 103 | """ |
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| 104 | Return a list of tuples. |
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| 105 | Each tuple represents a segment in the boundary |
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| 106 | by the index of its two end points. |
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| 107 | The list of tuples represents the alpha shape boundary. |
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| 108 | """ |
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| 109 | return self.boundary |
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| 110 | |
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| 111 | def set_boundary_type(self,raw_boundary=True, |
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| 112 | remove_holes=False, |
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| 113 | smooth_indents=False, |
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| 114 | expand_pinch=False, |
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| 115 | boundary_points_fraction=0.2): |
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| 116 | """ |
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| 117 | Use the flags to set constraints on the boundary: |
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| 118 | raw_boundary Return raw boundary i.e. the regular edges of the |
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| 119 | alpha shape. |
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| 120 | remove_holes filter to remove small holes |
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| 121 | (small is defined by boundary_points_fraction ) |
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| 122 | smooth_indents remove sharp triangular indents in boundary |
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| 123 | expand_pinch test for pinch-off and correct |
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| 124 | i.e. a boundary vertex with more than two edges. |
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| 125 | """ |
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| 126 | |
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| 127 | if raw_boundary: |
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| 128 | # reset alpha shape boundary |
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| 129 | reg_edge = self.get_regular_edges(self.alpha) |
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| 130 | self.boundary = [self.edge[k] for k in reg_edge] |
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| 131 | self._init_boundary_triangles() |
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| 132 | if remove_holes: |
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| 133 | #remove small holes |
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| 134 | self.boundary = self._remove_holes(boundary_points_fraction) |
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| 135 | if smooth_indents: |
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| 136 | #remove sharp triangular indents |
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| 137 | self.boundary = self._smooth_indents() |
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| 138 | if expand_pinch: |
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| 139 | #deal with pinch-off |
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| 140 | self.boundary = self._expand_pinch() |
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| 141 | |
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| 142 | |
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| 143 | def get_delaunay(self): |
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| 144 | """ |
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| 145 | """ |
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| 146 | return self.deltri |
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| 147 | |
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| 148 | def get_optimum_alpha(self): |
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| 149 | """ |
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| 150 | """ |
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| 151 | return self.optimum_alpha |
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| 152 | |
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| 153 | def get_alpha(self): |
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| 154 | """ |
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| 155 | Return current alpha value. |
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| 156 | """ |
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| 157 | return self.alpha |
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| 158 | |
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| 159 | def set_alpha(self,alpha): |
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| 160 | """ |
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| 161 | Set alpha and update alpha-boundary. |
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| 162 | """ |
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| 163 | self.alpha = alpha |
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| 164 | reg_edge = self.get_regular_edges(alpha) |
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| 165 | self.boundary = [self.edge[k] for k in reg_edge] |
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| 166 | self._init_boundary_triangles() |
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| 167 | |
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| 168 | |
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| 169 | def _alpha_shape_algorithm(self, alpha=None): |
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| 170 | """ |
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| 171 | Given a set of points (self.points) and an optional alpha value |
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| 172 | determines the alpha shape boundary (stored in self.boundary, |
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| 173 | accessed by get_boundary). |
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| 174 | |
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| 175 | Inputs: |
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| 176 | alpha: The alpha value can be optionally specified. If it is |
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| 177 | not specified the optimum alpha value will be used. |
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| 178 | """ |
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| 179 | |
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| 180 | #print "starting alpha shape algorithm" |
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| 181 | |
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| 182 | self.alpha = alpha |
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| 183 | |
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| 184 | ## Build Delaunay triangulation |
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| 185 | from anuga.mesh_engine.mesh_engine import generate_mesh |
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| 186 | points = [] |
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| 187 | seglist = [] |
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| 188 | holelist = [] |
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| 189 | regionlist = [] |
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| 190 | pointattlist = [] |
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| 191 | segattlist = [] |
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| 192 | |
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| 193 | points = [(pt[0], pt[1]) for pt in self.points] |
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| 194 | pointattlist = [ [] for i in range(len(points)) ] |
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| 195 | mode = "Qzcn" |
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| 196 | #print "computing delaunay triangulation ... \n" |
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| 197 | tridata = generate_mesh(points,seglist,holelist,regionlist, |
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| 198 | pointattlist,segattlist,mode) |
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| 199 | #print tridata |
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| 200 | #print "point attlist: ", tridata['generatedpointattributelist'],"\n" |
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| 201 | #print "hull segments: ", tridata['generatedsegmentlist'], "\n" |
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| 202 | self.deltri = tridata['generatedtrianglelist'] |
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| 203 | self.deltrinbr = tridata['generatedtriangleneighborlist'] |
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| 204 | self.hulledges = tridata['generatedsegmentlist'] |
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| 205 | |
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| 206 | #print "Number of delaunay triangles: ", len(self.deltri), "\n" |
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| 207 | #print "deltrinbrs: ", self.deltrinbr, "\n" |
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| 208 | |
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| 209 | ## Build Alpha table |
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| 210 | ## the following routines determine alpha thresholds for the |
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| 211 | ## triangles, edges, and vertices of the delaunay triangulation |
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| 212 | self._tri_circumradius() |
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| 213 | # print "Largest circumradius ", max(self.triradius) |
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| 214 | self._edge_intervals() |
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| 215 | self._vertex_intervals() |
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| 216 | |
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| 217 | if alpha==None: |
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| 218 | # Find optimum alpha |
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| 219 | # Ken Clarkson's hull program uses smallest alpha so that |
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| 220 | # every vertex is non-singular so... |
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| 221 | self.optimum_alpha = max([iv[0] for iv in self.vertexinterval \ |
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| 222 | if iv!=[] ]) |
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| 223 | # print "optimum alpha ", self.optimum_alpha |
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| 224 | alpha = self.optimum_alpha |
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| 225 | self.alpha = alpha |
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| 226 | reg_edge = self.get_regular_edges(self.alpha) |
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| 227 | self.boundary = [self.edge[k] for k in reg_edge] |
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| 228 | #print "alpha boundary edges ", self.boundary |
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| 229 | self._init_boundary_triangles() |
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| 230 | |
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| 231 | return |
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| 232 | |
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| 233 | def _tri_circumradius(self): |
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| 234 | """ |
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| 235 | Compute circumradii of the delaunay triangles |
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| 236 | """ |
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| 237 | |
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| 238 | x = self.points[:,0] |
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| 239 | y = self.points[:,1] |
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| 240 | ind1 = [self.deltri[j][0] for j in range(len(self.deltri))] |
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| 241 | ind2 = [self.deltri[j][1] for j in range(len(self.deltri))] |
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| 242 | ind3 = [self.deltri[j][2] for j in range(len(self.deltri))] |
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| 243 | |
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[6174] | 244 | x1 = num.array([x[j] for j in ind1]) |
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| 245 | y1 = num.array([y[j] for j in ind1]) |
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| 246 | x2 = num.array([x[j] for j in ind2]) |
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| 247 | y2 = num.array([y[j] for j in ind2]) |
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| 248 | x3 = num.array([x[j] for j in ind3]) |
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| 249 | y3 = num.array([y[j] for j in ind3]) |
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[4955] | 250 | |
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| 251 | x21 = x2-x1 |
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| 252 | x31 = x3-x1 |
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| 253 | y21 = y2-y1 |
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| 254 | y31 = y3-y1 |
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| 255 | |
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| 256 | dist21 = x21*x21 + y21*y21 |
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| 257 | dist31 = x31*x31 + y31*y31 |
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| 258 | |
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| 259 | denom = x21*y31 - x31*y21 |
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| 260 | #print "denom = ", denom |
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| 261 | |
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| 262 | # dx/2, dy/2 give circumcenter relative to x1,y1. |
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| 263 | # dx = (y31*dist21 - y21*dist31)/denom |
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| 264 | # dy = (x21*dist31 - x31*dist21)/denom |
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| 265 | # first need to check for near-zero values of denom |
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| 266 | delta = 0.00000001 |
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| 267 | zeroind = [k for k in range(len(denom)) if \ |
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| 268 | (denom[k]< EPSILON and denom[k] > -EPSILON)] |
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| 269 | # if some denom values are close to zero, |
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| 270 | # we perturb the associated vertices and recalculate |
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| 271 | while zeroind!=[]: |
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| 272 | random.seed() |
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| 273 | print "Warning: degenerate triangles found in alpha_shape.py, results may be inaccurate." |
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| 274 | for d in zeroind: |
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| 275 | x1[d] = x1[d]+delta*(random.random()-0.5) |
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| 276 | x2[d] = x2[d]+delta*(random.random()-0.5) |
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| 277 | x3[d] = x3[d]+delta*(random.random()-0.5) |
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| 278 | y1[d] = y1[d]+delta*(random.random()-0.5) |
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| 279 | y2[d] = y2[d]+delta*(random.random()-0.5) |
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| 280 | y3[d] = y3[d]+delta*(random.random()-0.5) |
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| 281 | x21 = x2-x1 |
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| 282 | x31 = x3-x1 |
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| 283 | y21 = y2-y1 |
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| 284 | y31 = y3-y1 |
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| 285 | dist21 = x21*x21 + y21*y21 |
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| 286 | dist31 = x31*x31 + y31*y31 |
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| 287 | denom = x21*y31 - x31*y21 |
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| 288 | zeroind = [k for k in range(len(denom)) if \ |
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| 289 | (denom[k]< EPSILON and denom[k] > -EPSILON)] |
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[6304] | 290 | |
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| 291 | if num.any(denom == 0.0): |
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| 292 | raise AlphaError |
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| 293 | |
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| 294 | dx = num.divide(y31*dist21 - y21*dist31, denom) |
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| 295 | dy = num.divide(x21*dist31 - x31*dist21, denom) |
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| 296 | |
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[6147] | 297 | self.triradius = 0.5*num.sqrt(dx*dx + dy*dy) |
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[4955] | 298 | #print "triangle radii", self.triradius |
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| 299 | |
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| 300 | def _edge_intervals(self): |
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| 301 | """ |
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| 302 | for each edge, find triples |
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| 303 | (length/2, min_adj_triradius, max_adj_triradius) if unattached |
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| 304 | (min_adj_triradius, min_adj_triradius, max_adj_triradius) if attached. |
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| 305 | An edge is attached if it is opposite an obtuse angle |
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| 306 | """ |
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| 307 | |
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| 308 | # It should be possible to rewrite this routine in an array-friendly |
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| 309 | # form like _tri_circumradius() if we need to speed things up. |
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| 310 | # Hard to do though. |
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| 311 | |
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| 312 | edges = [] |
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| 313 | edgenbrs = [] |
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| 314 | edgeinterval = [] |
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| 315 | for t in range(len(self.deltri)): |
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| 316 | tri = self.deltri[t] |
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| 317 | trinbr = self.deltrinbr[t] |
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[6147] | 318 | dx = num.array([self.points[tri[(i+1)%3],0] - |
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| 319 | self.points[tri[(i+2)%3],0] for i in [0,1,2]]) |
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| 320 | dy = num.array([self.points[tri[(i+1)%3],1] - |
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| 321 | self.points[tri[(i+2)%3],1] for i in [0,1,2]]) |
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| 322 | elen = num.sqrt(dx*dx+dy*dy) |
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[4955] | 323 | # really only need sign - not angle value: |
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[6147] | 324 | anglesign = num.array([(-dx[(i+1)%3]*dx[(i+2)%3]- |
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| 325 | dy[(i+1)%3]*dy[(i+2)%3]) for i in [0,1,2]]) |
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[4955] | 326 | |
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| 327 | #print "dx ",dx,"\n" |
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| 328 | #print "dy ",dy,"\n" |
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| 329 | #print "edge lengths of triangle ",t,"\t",elen,"\n" |
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| 330 | #print "angles ",angle,"\n" |
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| 331 | |
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| 332 | for i in [0,1,2]: |
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| 333 | j = (i+1)%3 |
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| 334 | k = (i+2)%3 |
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| 335 | if trinbr[i]==-1: |
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| 336 | edges.append((tri[j], tri[k])) |
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| 337 | edgenbrs.append((t, -1)) |
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| 338 | edgeinterval.append([0.5*elen[i], self.triradius[t], INF]) |
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| 339 | elif (tri[j]<tri[k]): |
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| 340 | edges.append((tri[j], tri[k])) |
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| 341 | edgenbrs.append((t, trinbr[i])) |
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| 342 | edgeinterval.append([0.5*elen[i],\ |
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| 343 | min(self.triradius[t],self.triradius[trinbr[i]]),\ |
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| 344 | max(self.triradius[t],self.triradius[trinbr[i]]) ]) |
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| 345 | else: |
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| 346 | continue |
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| 347 | if anglesign[i] < 0: |
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| 348 | edgeinterval[-1][0] = edgeinterval[-1][1] |
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| 349 | |
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| 350 | self.edge = edges |
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| 351 | self.edgenbr = edgenbrs |
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| 352 | self.edgeinterval = edgeinterval |
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| 353 | #print "edges: ",edges, "\n" |
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| 354 | #print "edge nbrs:", edgenbrs ,"\n" |
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| 355 | #print "edge intervals: ",edgeinterval , "\n" |
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| 356 | |
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| 357 | def _vertex_intervals(self): |
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| 358 | """ |
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| 359 | for each vertex find pairs |
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| 360 | (min_adj_triradius, max_adj_triradius) |
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| 361 | """ |
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| 362 | nv = len(self.points) |
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| 363 | vertexnbrs = [ [] for i in range(nv)] |
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| 364 | vertexinterval = [ [] for i in range(nv)] |
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| 365 | for t in range(len(self.deltri)): |
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| 366 | for j in self.deltri[t]: |
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| 367 | vertexnbrs[int(j)].append(t) |
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| 368 | for h in range(len(self.hulledges)): |
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| 369 | for j in self.hulledges[h]: |
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| 370 | vertexnbrs[int(j)].append(-1) |
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| 371 | |
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| 372 | for i in range(nv): |
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| 373 | radii = [ self.triradius[t] for t in vertexnbrs[i] if t>=0 ] |
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| 374 | try: |
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| 375 | vertexinterval[i] = [min(radii), max(radii)] |
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| 376 | if vertexnbrs[i][-1]==-1: |
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| 377 | vertexinterval[i][1]=INF |
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| 378 | except ValueError: |
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| 379 | raise AlphaError |
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| 380 | |
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| 381 | self.vertexnbr = vertexnbrs |
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| 382 | self.vertexinterval = vertexinterval |
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| 383 | #print "vertex nbrs ", vertexnbrs, "\n" |
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| 384 | #print "vertex intervals ",vertexinterval, "\n" |
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| 385 | |
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| 386 | def get_alpha_triangles(self,alpha): |
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| 387 | """ |
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| 388 | Given an alpha value, |
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| 389 | return indices of triangles in the alpha-shape |
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| 390 | """ |
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| 391 | def tri_rad_lta(k): |
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| 392 | return self.triradius[k]<=alpha |
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| 393 | |
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| 394 | return filter(tri_rad_lta, range(len(self.triradius))) |
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| 395 | |
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| 396 | def get_regular_edges(self,alpha): |
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| 397 | """ |
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| 398 | Given an alpha value, |
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| 399 | return the indices of edges on the boundary of the alpha-shape |
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| 400 | """ |
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| 401 | def reg_edge(k): |
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| 402 | return self.edgeinterval[k][1]<=alpha and \ |
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| 403 | self.edgeinterval[k][2]>alpha |
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| 404 | |
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| 405 | return filter(reg_edge, range(len(self.edgeinterval))) |
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| 406 | |
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| 407 | def get_exposed_vertices(self,alpha): |
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| 408 | """ |
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| 409 | Given an alpha value, |
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| 410 | return the vertices on the boundary of the alpha-shape |
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| 411 | """ |
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| 412 | def exp_vert(k): |
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| 413 | return self.vertexinterval[k][0]<=alpha and \ |
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| 414 | self.vertexinterval[k][1]>alpha |
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| 415 | |
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| 416 | return filter(exp_vert, range(len(self.vertexinterval))) |
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| 417 | |
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| 418 | def _vertices_from_edges(self,elist): |
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| 419 | """ |
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| 420 | Returns the list of unique vertex labels from edges in elist |
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| 421 | """ |
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| 422 | |
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| 423 | v1 = [elist[k][0] for k in range(len(elist))] |
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| 424 | v2 = [elist[k][1] for k in range(len(elist))] |
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| 425 | v = v1+v2 |
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| 426 | v.sort() |
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| 427 | vertices = [v[k] for k in range(len(v)) if v[k]!=v[k-1] ] |
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| 428 | return vertices |
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| 429 | |
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| 430 | def _init_boundary_triangles(self): |
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| 431 | """ |
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| 432 | Creates the initial list of triangle indices |
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| 433 | exterior to and touching the boundary of the alpha shape |
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| 434 | """ |
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| 435 | def tri_rad_gta(k): |
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| 436 | return self.triradius[k]>self.alpha |
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| 437 | |
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| 438 | extrind = filter(tri_rad_gta, range(len(self.triradius))) |
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| 439 | |
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| 440 | bv = self._vertices_from_edges(self.boundary) |
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| 441 | |
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| 442 | btri = [] |
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| 443 | for et in extrind: |
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| 444 | v0 = self.deltri[et][0] |
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| 445 | v1 = self.deltri[et][1] |
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| 446 | v2 = self.deltri[et][2] |
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| 447 | if v0 in bv or v1 in bv or v2 in bv: |
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| 448 | btri.append(et) |
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| 449 | |
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| 450 | self.boundarytriangle = btri |
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| 451 | |
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| 452 | #print "exterior triangles: ", extrind |
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| 453 | |
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| 454 | |
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| 455 | def _remove_holes(self,small): |
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| 456 | """ |
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| 457 | Given the edges in self.boundary, finds the largest components. |
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| 458 | The routine does this by implementing a union-find algorithm. |
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| 459 | """ |
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| 460 | |
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| 461 | #print "running _remove_holes \n" |
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| 462 | |
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| 463 | bdry = self.boundary |
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| 464 | |
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| 465 | def findroot(i): |
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| 466 | if vptr[i] < 0: |
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| 467 | return i |
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| 468 | k = findroot(vptr[i]) |
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| 469 | vptr[i] = k # this produces "path compression" in the |
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| 470 | # union-find tree. |
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| 471 | return k |
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| 472 | |
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| 473 | |
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| 474 | |
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| 475 | # get a list of unique vertex labels: |
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| 476 | verts = self._vertices_from_edges(bdry) |
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| 477 | #print "verts ", verts, "\n" |
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| 478 | |
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| 479 | # vptr represents the union-find tree. |
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| 480 | # if vptr[i] = EMPTY < 0, the vertex verts[i] has not been visited yet |
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| 481 | # if vptr[i] = j > 0, then j verts[j] is the parent of verts[i]. |
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| 482 | # if vptr[i] = n < 0, then verts[i] is a root vertex and |
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| 483 | # represents a connected component of n vertices. |
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| 484 | |
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| 485 | #initialise vptr to negative number outside range |
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| 486 | EMPTY = -max(verts)-len(verts) |
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| 487 | vptr = [EMPTY for k in range(len(verts))] |
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| 488 | #print "vptr init: ", vptr, "\n" |
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| 489 | |
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| 490 | #add edges and maintain union tree |
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| 491 | for i in range(len(bdry)): |
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| 492 | #print "edge ",i,"\t",bdry[i] |
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| 493 | vl = verts.index(bdry[i][0]) |
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| 494 | vr = verts.index(bdry[i][1]) |
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| 495 | rvl = findroot(vl) |
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| 496 | rvr = findroot(vr) |
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| 497 | #print "roots: ",rvl, rvr |
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| 498 | if not(rvl==rvr): |
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| 499 | if (vptr[vl]==EMPTY): |
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| 500 | if (vptr[vr]==EMPTY): |
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| 501 | vptr[vl] = -2 |
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| 502 | vptr[vr] = vl |
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| 503 | else: |
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| 504 | vptr[vl] = rvr |
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| 505 | vptr[rvr] = vptr[rvr]-1 |
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| 506 | else: |
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| 507 | if (vptr[vr]==EMPTY): |
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| 508 | vptr[vr] = rvl |
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| 509 | vptr[rvl] = vptr[rvl]-1 |
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| 510 | else: |
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| 511 | if vptr[rvl] > vptr[rvr]: |
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| 512 | vptr[rvr] = vptr[rvr] + vptr[rvl] |
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| 513 | vptr[rvl] = rvr |
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| 514 | vptr[vl] = rvr |
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| 515 | else: |
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| 516 | vptr[rvl] = vptr[rvl] + vptr[rvr] |
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| 517 | vptr[rvr] = rvl |
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| 518 | vptr[vr] = rvl |
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| 519 | #print "vptr: ", vptr, "\n" |
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| 520 | # end edge loop |
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| 521 | |
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| 522 | if vptr.count(EMPTY): |
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| 523 | raise FlagError, "We didn't hit all the vertices in the boundary" |
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| 524 | |
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| 525 | # print "number of vertices in the connected components: ", [-v for v in vptr if v<0], "\n" |
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| 526 | # print "largest component has: ", -min(vptr), " points. \n" |
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| 527 | # discard the edges in the little components |
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| 528 | # (i.e. those components with less than 'small' fraction of bdry points) |
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| 529 | cutoff = round(small*len(verts)) |
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| 530 | # print "cutoff component size is ", cutoff, "\n" |
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| 531 | largest_component = -min(vptr) |
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| 532 | if cutoff > largest_component: |
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| 533 | cutoff = round((1-small)*largest_component) |
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| 534 | |
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| 535 | # littleind has root indices for small components |
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| 536 | littleind = [k for k in range(len(vptr)) if \ |
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| 537 | (vptr[k]<0 and vptr[k]>-cutoff)] |
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| 538 | if littleind: |
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| 539 | # littlecomp has all vptr indices in the small components |
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| 540 | littlecomp = [k for k in range(len(vptr)) if \ |
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| 541 | findroot(k) in littleind] |
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| 542 | # vdiscard has the vertex indices corresponding to vptr indices |
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| 543 | vdiscard = [verts[k] for k in littlecomp] |
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| 544 | newbdry = [e for e in bdry if \ |
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| 545 | not((e[0] in vdiscard) and (e[1] in vdiscard))] |
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| 546 | |
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| 547 | newverts = self._vertices_from_edges(newbdry) |
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| 548 | # recompute the boundary triangles |
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| 549 | newbt = [] |
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| 550 | for bt in self.boundarytriangle: |
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| 551 | v0 = self.deltri[bt][0] |
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| 552 | v1 = self.deltri[bt][1] |
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| 553 | v2 = self.deltri[bt][2] |
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| 554 | if (v0 in newverts or v1 in newverts or v2 in newverts): |
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| 555 | newbt.append(bt) |
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| 556 | |
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| 557 | self.boundarytriangle = newbt |
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| 558 | else: |
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| 559 | newbdry = bdry |
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| 560 | |
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| 561 | return newbdry |
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| 562 | |
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| 563 | |
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| 564 | def _smooth_indents(self): |
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| 565 | """ |
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| 566 | Given edges in bdry, test for acute-angle triangular indents |
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| 567 | and remove them. |
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| 568 | """ |
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| 569 | |
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| 570 | #print "running _smooth_indents \n" |
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| 571 | |
---|
| 572 | bdry = self.boundary |
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| 573 | bdrytri = self.boundarytriangle |
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| 574 | |
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| 575 | # find boundary triangles that have two edges in bdry |
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| 576 | # v2ind has the place index relative to the triangle deltri[ind] |
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| 577 | # for the bdry vertex where the two edges meet. |
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| 578 | |
---|
| 579 | verts = self._vertices_from_edges(bdry) |
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| 580 | |
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| 581 | b2etri = [] |
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| 582 | for ind in bdrytri: |
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| 583 | bect = 0 |
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| 584 | v2ind = [0,1,2] |
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| 585 | for j in [0,1,2]: |
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| 586 | eda = (self.deltri[ind][(j+1)%3], self.deltri[ind][(j+2)%3]) |
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| 587 | edb = (self.deltri[ind][(j+2)%3], self.deltri[ind][(j+1)%3]) |
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| 588 | if eda in bdry or edb in bdry: |
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| 589 | bect +=1 |
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| 590 | v2ind.remove(j) |
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| 591 | if bect==2: |
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| 592 | b2etri.append((ind,v2ind[0])) |
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| 593 | |
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| 594 | # test the bdrytri triangles for acute angles |
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| 595 | acutetri = [] |
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| 596 | for tind in b2etri: |
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| 597 | tri = self.deltri[tind[0]] |
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| 598 | |
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[6147] | 599 | dx = num.array([self.points[tri[(i+1)%3],0] - \ |
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| 600 | self.points[tri[(i+2)%3],0] for i in [0,1,2]]) |
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| 601 | dy = num.array([self.points[tri[(i+1)%3],1] - \ |
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| 602 | self.points[tri[(i+2)%3],1] for i in [0,1,2]]) |
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| 603 | anglesign = num.array([(-dx[(i+1)%3]*dx[(i+2)%3]-\ |
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| 604 | dy[(i+1)%3]*dy[(i+2)%3]) for i in [0,1,2]]) |
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[4955] | 605 | # record any triangle that has an acute angle spanned by |
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| 606 | #two edges along the boundary.. |
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| 607 | if anglesign[tind[1]] > 0: |
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| 608 | acutetri.append(tind[0]) |
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| 609 | |
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| 610 | #print "acute boundary triangles ", acutetri |
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| 611 | |
---|
| 612 | # adjust the bdry edges and triangles by adding |
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| 613 | #in the acutetri triangles |
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| 614 | for pind in acutetri: |
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| 615 | bdrytri.remove(pind) |
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| 616 | tri = self.deltri[pind] |
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| 617 | for i in [0,1,2]: |
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| 618 | bdry.append((tri[(i+1)%3], tri[(i+2)%3])) |
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| 619 | |
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| 620 | newbdry = [] |
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| 621 | for ed in bdry: |
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| 622 | numed = bdry.count(ed)+bdry.count((ed[1],ed[0])) |
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| 623 | if numed%2 == 1: |
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| 624 | newbdry.append(ed) |
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| 625 | |
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| 626 | #print "new boundary ", newbdry |
---|
| 627 | return newbdry |
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| 628 | |
---|
| 629 | def _expand_pinch(self): |
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| 630 | """ |
---|
| 631 | Given edges in bdry, test for vertices with more than 2 incident edges. |
---|
| 632 | Expand by adding back in associated triangles. |
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| 633 | """ |
---|
| 634 | #print "running _expand_pinch \n" |
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| 635 | |
---|
| 636 | bdry = self.boundary |
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| 637 | bdrytri = self.boundarytriangle |
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| 638 | |
---|
| 639 | v1 = [bdry[k][0] for k in range(len(bdry))] |
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| 640 | v2 = [bdry[k][1] for k in range(len(bdry))] |
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| 641 | v = v1+v2 |
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| 642 | v.sort() |
---|
| 643 | probv = [v[k] for k in range(len(v)) \ |
---|
| 644 | if (v[k]!=v[k-1] and v.count(v[k])>2) ] |
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| 645 | #print "problem vertices: ", probv |
---|
| 646 | |
---|
| 647 | # find boundary triangles that have at least one vertex in probv |
---|
| 648 | probtri = [] |
---|
| 649 | for ind in bdrytri: |
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| 650 | v0 = self.deltri[ind][0] |
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| 651 | v1 = self.deltri[ind][1] |
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| 652 | v2 = self.deltri[ind][2] |
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| 653 | if v0 in probv or v1 in probv or v2 in probv: |
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| 654 | probtri.append(ind) |
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| 655 | |
---|
| 656 | #print "problem boundary triangle indices ", probtri |
---|
| 657 | |
---|
| 658 | # "add in" the problem triangles |
---|
| 659 | for pind in probtri: |
---|
| 660 | bdrytri.remove(pind) |
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| 661 | tri = self.deltri[pind] |
---|
| 662 | for i in [0,1,2]: |
---|
| 663 | bdry.append((tri[(i+1)%3], tri[(i+2)%3])) |
---|
| 664 | |
---|
| 665 | newbdry = [] |
---|
| 666 | for ed in bdry: |
---|
| 667 | numed = bdry.count(ed)+bdry.count((ed[1],ed[0])) |
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| 668 | if numed%2 == 1: |
---|
| 669 | newbdry.append(ed) |
---|
| 670 | |
---|
| 671 | #print "new boundary ", newbdry |
---|
| 672 | return newbdry |
---|
| 673 | |
---|
| 674 | |
---|
| 675 | #------------------------------------------------------------- |
---|
| 676 | if __name__ == "__main__": |
---|
| 677 | """ |
---|
| 678 | Load in a data point file. |
---|
| 679 | Determine the alpha shape boundary |
---|
| 680 | Save the boundary to a file. |
---|
| 681 | |
---|
| 682 | usage: alpha_shape.py point_file.csv boundary_file.bnd [alpha] |
---|
| 683 | |
---|
| 684 | The alpha value is optional. |
---|
| 685 | """ |
---|
| 686 | |
---|
| 687 | import os, sys |
---|
| 688 | usage = "usage: %s point_file.csv boundary_file.bnd [alpha]"%os.path.basename(sys.argv[0]) |
---|
| 689 | if len(sys.argv) < 3: |
---|
| 690 | print usage |
---|
| 691 | else: |
---|
| 692 | point_file = sys.argv[1] |
---|
| 693 | boundary_file = sys.argv[2] |
---|
| 694 | if len(sys.argv) > 4: |
---|
| 695 | alpha = sys.argv[3] |
---|
| 696 | else: |
---|
| 697 | alpha = None |
---|
| 698 | |
---|
| 699 | #print "about to call alpha shape routine \n" |
---|
| 700 | alpha_shape_via_files(point_file, boundary_file, alpha) |
---|
| 701 | |
---|