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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27 | import numpy as num |
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28 | |
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29 | |
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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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90 | #Convert input to numeric arrays |
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91 | self.points = num.array(points, num.float) |
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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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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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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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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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297 | self.triradius = 0.5*num.sqrt(dx*dx + dy*dy) |
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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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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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323 | # really only need sign - not angle value: |
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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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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 | |
---|
547 | newverts = self._vertices_from_edges(newbdry) |
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548 | # recompute the boundary triangles |
---|
549 | newbt = [] |
---|
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 | |
---|
561 | return newbdry |
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562 | |
---|
563 | |
---|
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 | |
---|
570 | #print "running _smooth_indents \n" |
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571 | |
---|
572 | bdry = self.boundary |
---|
573 | bdrytri = self.boundarytriangle |
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574 | |
---|
575 | # find boundary triangles that have two edges in bdry |
---|
576 | # v2ind has the place index relative to the triangle deltri[ind] |
---|
577 | # for the bdry vertex where the two edges meet. |
---|
578 | |
---|
579 | verts = self._vertices_from_edges(bdry) |
---|
580 | |
---|
581 | b2etri = [] |
---|
582 | for ind in bdrytri: |
---|
583 | bect = 0 |
---|
584 | v2ind = [0,1,2] |
---|
585 | for j in [0,1,2]: |
---|
586 | eda = (self.deltri[ind][(j+1)%3], self.deltri[ind][(j+2)%3]) |
---|
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 |
---|
590 | v2ind.remove(j) |
---|
591 | if bect==2: |
---|
592 | b2etri.append((ind,v2ind[0])) |
---|
593 | |
---|
594 | # test the bdrytri triangles for acute angles |
---|
595 | acutetri = [] |
---|
596 | for tind in b2etri: |
---|
597 | tri = self.deltri[tind[0]] |
---|
598 | |
---|
599 | dx = num.array([self.points[tri[(i+1)%3],0] - \ |
---|
600 | self.points[tri[(i+2)%3],0] for i in [0,1,2]]) |
---|
601 | dy = num.array([self.points[tri[(i+1)%3],1] - \ |
---|
602 | self.points[tri[(i+2)%3],1] for i in [0,1,2]]) |
---|
603 | anglesign = num.array([(-dx[(i+1)%3]*dx[(i+2)%3]-\ |
---|
604 | dy[(i+1)%3]*dy[(i+2)%3]) for i in [0,1,2]]) |
---|
605 | # record any triangle that has an acute angle spanned by |
---|
606 | #two edges along the boundary.. |
---|
607 | if anglesign[tind[1]] > 0: |
---|
608 | acutetri.append(tind[0]) |
---|
609 | |
---|
610 | #print "acute boundary triangles ", acutetri |
---|
611 | |
---|
612 | # adjust the bdry edges and triangles by adding |
---|
613 | #in the acutetri triangles |
---|
614 | for pind in acutetri: |
---|
615 | bdrytri.remove(pind) |
---|
616 | tri = self.deltri[pind] |
---|
617 | for i in [0,1,2]: |
---|
618 | bdry.append((tri[(i+1)%3], tri[(i+2)%3])) |
---|
619 | |
---|
620 | newbdry = [] |
---|
621 | for ed in bdry: |
---|
622 | numed = bdry.count(ed)+bdry.count((ed[1],ed[0])) |
---|
623 | if numed%2 == 1: |
---|
624 | newbdry.append(ed) |
---|
625 | |
---|
626 | #print "new boundary ", newbdry |
---|
627 | return newbdry |
---|
628 | |
---|
629 | def _expand_pinch(self): |
---|
630 | """ |
---|
631 | Given edges in bdry, test for vertices with more than 2 incident edges. |
---|
632 | Expand by adding back in associated triangles. |
---|
633 | """ |
---|
634 | #print "running _expand_pinch \n" |
---|
635 | |
---|
636 | bdry = self.boundary |
---|
637 | bdrytri = self.boundarytriangle |
---|
638 | |
---|
639 | v1 = [bdry[k][0] for k in range(len(bdry))] |
---|
640 | v2 = [bdry[k][1] for k in range(len(bdry))] |
---|
641 | v = v1+v2 |
---|
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) ] |
---|
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: |
---|
650 | v0 = self.deltri[ind][0] |
---|
651 | v1 = self.deltri[ind][1] |
---|
652 | v2 = self.deltri[ind][2] |
---|
653 | if v0 in probv or v1 in probv or v2 in probv: |
---|
654 | probtri.append(ind) |
---|
655 | |
---|
656 | #print "problem boundary triangle indices ", probtri |
---|
657 | |
---|
658 | # "add in" the problem triangles |
---|
659 | for pind in probtri: |
---|
660 | bdrytri.remove(pind) |
---|
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])) |
---|
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 | |
---|