1 | //---------------------------------------------------------------------- |
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2 | // File: bd_tree.cpp |
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3 | // Programmer: David Mount |
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4 | // Description: Basic methods for bd-trees. |
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5 | // Last modified: 01/04/05 (Version 1.0) |
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6 | //---------------------------------------------------------------------- |
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7 | // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and |
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8 | // David Mount. All Rights Reserved. |
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9 | // |
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10 | // This software and related documentation is part of the Approximate |
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11 | // Nearest Neighbor Library (ANN). This software is provided under |
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12 | // the provisions of the Lesser GNU Public License (LGPL). See the |
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13 | // file ../ReadMe.txt for further information. |
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14 | // |
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15 | // The University of Maryland (U.M.) and the authors make no |
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16 | // representations about the suitability or fitness of this software for |
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17 | // any purpose. It is provided "as is" without express or implied |
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18 | // warranty. |
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19 | //---------------------------------------------------------------------- |
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20 | // History: |
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21 | // Revision 0.1 03/04/98 |
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22 | // Initial release |
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23 | // Revision l.0 04/01/05 |
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24 | // Fixed centroid shrink threshold condition to depend on the |
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25 | // dimension. |
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26 | // Moved dump routine to kd_dump.cpp. |
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27 | //---------------------------------------------------------------------- |
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28 | |
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29 | #include "bd_tree.h" // bd-tree declarations |
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30 | #include "kd_util.h" // kd-tree utilities |
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31 | #include "kd_split.h" // kd-tree splitting rules |
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32 | |
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33 | #include <ANN/ANNperf.h> // performance evaluation |
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34 | |
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35 | //---------------------------------------------------------------------- |
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36 | // Printing a bd-tree |
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37 | // These routines print a bd-tree. See the analogous procedure |
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38 | // in kd_tree.cpp for more information. |
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39 | //---------------------------------------------------------------------- |
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40 | |
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41 | void ANNbd_shrink::print( // print shrinking node |
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42 | int level, // depth of node in tree |
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43 | ostream &out) // output stream |
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44 | { |
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45 | child[ANN_OUT]->print(level+1, out); // print out-child |
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46 | |
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47 | out << " "; |
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48 | for (int i = 0; i < level; i++) // print indentation |
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49 | out << ".."; |
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50 | out << "Shrink"; |
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51 | for (int j = 0; j < n_bnds; j++) { // print sides, 2 per line |
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52 | if (j % 2 == 0) { |
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53 | out << "\n"; // newline and indentation |
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54 | for (int i = 0; i < level+2; i++) out << " "; |
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55 | } |
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56 | out << " ([" << bnds[j].cd << "]" |
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57 | << (bnds[j].sd > 0 ? ">=" : "< ") |
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58 | << bnds[j].cv << ")"; |
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59 | } |
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60 | out << "\n"; |
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61 | |
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62 | child[ANN_IN]->print(level+1, out); // print in-child |
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63 | } |
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64 | |
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65 | //---------------------------------------------------------------------- |
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66 | // kd_tree statistics utility (for performance evaluation) |
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67 | // This routine computes various statistics information for |
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68 | // shrinking nodes. See file kd_tree.cpp for more information. |
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69 | //---------------------------------------------------------------------- |
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70 | |
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71 | void ANNbd_shrink::getStats( // get subtree statistics |
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72 | int dim, // dimension of space |
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73 | ANNkdStats &st, // stats (modified) |
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74 | ANNorthRect &bnd_box) // bounding box |
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75 | { |
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76 | ANNkdStats ch_stats; // stats for children |
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77 | ANNorthRect inner_box(dim); // inner box of shrink |
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78 | |
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79 | annBnds2Box(bnd_box, // enclosing box |
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80 | dim, // dimension |
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81 | n_bnds, // number of bounds |
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82 | bnds, // bounds array |
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83 | inner_box); // inner box (modified) |
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84 | // get stats for inner child |
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85 | ch_stats.reset(); // reset |
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86 | child[ANN_IN]->getStats(dim, ch_stats, inner_box); |
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87 | st.merge(ch_stats); // merge them |
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88 | // get stats for outer child |
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89 | ch_stats.reset(); // reset |
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90 | child[ANN_OUT]->getStats(dim, ch_stats, bnd_box); |
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91 | st.merge(ch_stats); // merge them |
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92 | |
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93 | st.depth++; // increment depth |
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94 | st.n_shr++; // increment number of shrinks |
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95 | } |
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96 | |
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97 | //---------------------------------------------------------------------- |
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98 | // bd-tree constructor |
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99 | // This is the main constructor for bd-trees given a set of points. |
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100 | // It first builds a skeleton kd-tree as a basis, then computes the |
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101 | // bounding box of the data points, and then invokes rbd_tree() to |
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102 | // actually build the tree, passing it the appropriate splitting |
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103 | // and shrinking information. |
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104 | //---------------------------------------------------------------------- |
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105 | |
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106 | ANNkd_ptr rbd_tree( // recursive construction of bd-tree |
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107 | ANNpointArray pa, // point array |
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108 | ANNidxArray pidx, // point indices to store in subtree |
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109 | int n, // number of points |
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110 | int dim, // dimension of space |
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111 | int bsp, // bucket space |
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112 | ANNorthRect &bnd_box, // bounding box for current node |
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113 | ANNkd_splitter splitter, // splitting routine |
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114 | ANNshrinkRule shrink); // shrinking rule |
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115 | |
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116 | ANNbd_tree::ANNbd_tree( // construct from point array |
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117 | ANNpointArray pa, // point array (with at least n pts) |
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118 | int n, // number of points |
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119 | int dd, // dimension |
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120 | int bs, // bucket size |
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121 | ANNsplitRule split, // splitting rule |
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122 | ANNshrinkRule shrink) // shrinking rule |
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123 | : ANNkd_tree(n, dd, bs) // build skeleton base tree |
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124 | { |
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125 | pts = pa; // where the points are |
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126 | if (n == 0) return; // no points--no sweat |
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127 | |
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128 | ANNorthRect bnd_box(dd); // bounding box for points |
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129 | // construct bounding rectangle |
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130 | annEnclRect(pa, pidx, n, dd, bnd_box); |
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131 | // copy to tree structure |
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132 | bnd_box_lo = annCopyPt(dd, bnd_box.lo); |
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133 | bnd_box_hi = annCopyPt(dd, bnd_box.hi); |
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134 | |
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135 | switch (split) { // build by rule |
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136 | case ANN_KD_STD: // standard kd-splitting rule |
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137 | root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split, shrink); |
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138 | break; |
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139 | case ANN_KD_MIDPT: // midpoint split |
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140 | root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split, shrink); |
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141 | break; |
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142 | case ANN_KD_SUGGEST: // best (in our opinion) |
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143 | case ANN_KD_SL_MIDPT: // sliding midpoint split |
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144 | root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split, shrink); |
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145 | break; |
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146 | case ANN_KD_FAIR: // fair split |
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147 | root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split, shrink); |
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148 | break; |
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149 | case ANN_KD_SL_FAIR: // sliding fair split |
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150 | root = rbd_tree(pa, pidx, n, dd, bs, |
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151 | bnd_box, sl_fair_split, shrink); |
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152 | break; |
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153 | default: |
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154 | annError("Illegal splitting method", ANNabort); |
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155 | } |
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156 | } |
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157 | |
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158 | //---------------------------------------------------------------------- |
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159 | // Shrinking rules |
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160 | //---------------------------------------------------------------------- |
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161 | |
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162 | enum ANNdecomp {SPLIT, SHRINK}; // decomposition methods |
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163 | |
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164 | //---------------------------------------------------------------------- |
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165 | // trySimpleShrink - Attempt a simple shrink |
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166 | // |
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167 | // We compute the tight bounding box of the points, and compute |
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168 | // the 2*dim ``gaps'' between the sides of the tight box and the |
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169 | // bounding box. If any of the gaps is large enough relative to |
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170 | // the longest side of the tight bounding box, then we shrink |
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171 | // all sides whose gaps are large enough. (The reason for |
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172 | // comparing against the tight bounding box, is that after |
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173 | // shrinking the longest box size will decrease, and if we use |
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174 | // the standard bounding box, we may decide to shrink twice in |
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175 | // a row. Since the tight box is fixed, we cannot shrink twice |
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176 | // consecutively.) |
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177 | //---------------------------------------------------------------------- |
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178 | const float BD_GAP_THRESH = 0.5; // gap threshold (must be < 1) |
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179 | const int BD_CT_THRESH = 2; // min number of shrink sides |
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180 | |
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181 | ANNdecomp trySimpleShrink( // try a simple shrink |
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182 | ANNpointArray pa, // point array |
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183 | ANNidxArray pidx, // point indices to store in subtree |
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184 | int n, // number of points |
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185 | int dim, // dimension of space |
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186 | const ANNorthRect &bnd_box, // current bounding box |
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187 | ANNorthRect &inner_box) // inner box if shrinking (returned) |
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188 | { |
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189 | int i; |
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190 | // compute tight bounding box |
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191 | annEnclRect(pa, pidx, n, dim, inner_box); |
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192 | |
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193 | ANNcoord max_length = 0; // find longest box side |
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194 | for (i = 0; i < dim; i++) { |
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195 | ANNcoord length = inner_box.hi[i] - inner_box.lo[i]; |
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196 | if (length > max_length) { |
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197 | max_length = length; |
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198 | } |
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199 | } |
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200 | |
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201 | int shrink_ct = 0; // number of sides we shrunk |
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202 | for (i = 0; i < dim; i++) { // select which sides to shrink |
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203 | // gap between boxes |
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204 | ANNcoord gap_hi = bnd_box.hi[i] - inner_box.hi[i]; |
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205 | // big enough gap to shrink? |
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206 | if (gap_hi < max_length*BD_GAP_THRESH) |
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207 | inner_box.hi[i] = bnd_box.hi[i]; // no - expand |
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208 | else shrink_ct++; // yes - shrink this side |
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209 | |
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210 | // repeat for high side |
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211 | ANNcoord gap_lo = inner_box.lo[i] - bnd_box.lo[i]; |
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212 | if (gap_lo < max_length*BD_GAP_THRESH) |
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213 | inner_box.lo[i] = bnd_box.lo[i]; // no - expand |
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214 | else shrink_ct++; // yes - shrink this side |
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215 | } |
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216 | |
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217 | if (shrink_ct >= BD_CT_THRESH) // did we shrink enough sides? |
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218 | return SHRINK; |
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219 | else return SPLIT; |
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220 | } |
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221 | |
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222 | //---------------------------------------------------------------------- |
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223 | // tryCentroidShrink - Attempt a centroid shrink |
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224 | // |
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225 | // We repeatedly apply the splitting rule, always to the larger subset |
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226 | // of points, until the number of points decreases by the constant |
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227 | // fraction BD_FRACTION. If this takes more than dim*BD_MAX_SPLIT_FAC |
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228 | // splits for this to happen, then we shrink to the final inner box |
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229 | // Otherwise we split. |
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230 | //---------------------------------------------------------------------- |
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231 | |
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232 | const float BD_MAX_SPLIT_FAC = 0.5; // maximum number of splits allowed |
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233 | const float BD_FRACTION = 0.5; // ...to reduce points by this fraction |
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234 | // ...This must be < 1. |
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235 | |
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236 | ANNdecomp tryCentroidShrink( // try a centroid shrink |
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237 | ANNpointArray pa, // point array |
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238 | ANNidxArray pidx, // point indices to store in subtree |
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239 | int n, // number of points |
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240 | int dim, // dimension of space |
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241 | const ANNorthRect &bnd_box, // current bounding box |
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242 | ANNkd_splitter splitter, // splitting procedure |
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243 | ANNorthRect &inner_box) // inner box if shrinking (returned) |
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244 | { |
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245 | int n_sub = n; // number of points in subset |
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246 | int n_goal = (int) (n*BD_FRACTION); // number of point in goal |
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247 | int n_splits = 0; // number of splits needed |
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248 | // initialize inner box to bounding box |
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249 | annAssignRect(dim, inner_box, bnd_box); |
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250 | |
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251 | while (n_sub > n_goal) { // keep splitting until goal reached |
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252 | int cd; // cut dim from splitter (ignored) |
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253 | ANNcoord cv; // cut value from splitter (ignored) |
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254 | int n_lo; // number of points on low side |
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255 | // invoke splitting procedure |
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256 | (*splitter)(pa, pidx, inner_box, n_sub, dim, cd, cv, n_lo); |
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257 | n_splits++; // increment split count |
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258 | |
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259 | if (n_lo >= n_sub/2) { // most points on low side |
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260 | inner_box.hi[cd] = cv; // collapse high side |
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261 | n_sub = n_lo; // recurse on lower points |
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262 | } |
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263 | else { // most points on high side |
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264 | inner_box.lo[cd] = cv; // collapse low side |
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265 | pidx += n_lo; // recurse on higher points |
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266 | n_sub -= n_lo; |
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267 | } |
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268 | } |
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269 | if (n_splits > dim*BD_MAX_SPLIT_FAC)// took too many splits |
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270 | return SHRINK; // shrink to final subset |
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271 | else |
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272 | return SPLIT; |
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273 | } |
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274 | |
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275 | //---------------------------------------------------------------------- |
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276 | // selectDecomp - select which decomposition to use |
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277 | //---------------------------------------------------------------------- |
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278 | |
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279 | ANNdecomp selectDecomp( // select decomposition method |
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280 | ANNpointArray pa, // point array |
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281 | ANNidxArray pidx, // point indices to store in subtree |
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282 | int n, // number of points |
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283 | int dim, // dimension of space |
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284 | const ANNorthRect &bnd_box, // current bounding box |
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285 | ANNkd_splitter splitter, // splitting procedure |
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286 | ANNshrinkRule shrink, // shrinking rule |
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287 | ANNorthRect &inner_box) // inner box if shrinking (returned) |
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288 | { |
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289 | ANNdecomp decomp = SPLIT; // decomposition |
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290 | |
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291 | switch (shrink) { // check shrinking rule |
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292 | case ANN_BD_NONE: // no shrinking allowed |
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293 | decomp = SPLIT; |
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294 | break; |
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295 | case ANN_BD_SUGGEST: // author's suggestion |
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296 | case ANN_BD_SIMPLE: // simple shrink |
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297 | decomp = trySimpleShrink( |
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298 | pa, pidx, // points and indices |
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299 | n, dim, // number of points and dimension |
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300 | bnd_box, // current bounding box |
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301 | inner_box); // inner box if shrinking (returned) |
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302 | break; |
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303 | case ANN_BD_CENTROID: // centroid shrink |
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304 | decomp = tryCentroidShrink( |
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305 | pa, pidx, // points and indices |
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306 | n, dim, // number of points and dimension |
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307 | bnd_box, // current bounding box |
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308 | splitter, // splitting procedure |
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309 | inner_box); // inner box if shrinking (returned) |
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310 | break; |
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311 | default: |
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312 | annError("Illegal shrinking rule", ANNabort); |
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313 | } |
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314 | return decomp; |
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315 | } |
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316 | |
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317 | //---------------------------------------------------------------------- |
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318 | // rbd_tree - recursive procedure to build a bd-tree |
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319 | // |
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320 | // This is analogous to rkd_tree, but for bd-trees. See the |
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321 | // procedure rkd_tree() in kd_split.cpp for more information. |
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322 | // |
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323 | // If the number of points falls below the bucket size, then a |
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324 | // leaf node is created for the points. Otherwise we invoke the |
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325 | // procedure selectDecomp() which determines whether we are to |
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326 | // split or shrink. If splitting is chosen, then we essentially |
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327 | // do exactly as rkd_tree() would, and invoke the specified |
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328 | // splitting procedure to the points. Otherwise, the selection |
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329 | // procedure returns a bounding box, from which we extract the |
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330 | // appropriate shrinking bounds, and create a shrinking node. |
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331 | // Finally the points are subdivided, and the procedure is |
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332 | // invoked recursively on the two subsets to form the children. |
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333 | //---------------------------------------------------------------------- |
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334 | |
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335 | ANNkd_ptr rbd_tree( // recursive construction of bd-tree |
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336 | ANNpointArray pa, // point array |
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337 | ANNidxArray pidx, // point indices to store in subtree |
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338 | int n, // number of points |
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339 | int dim, // dimension of space |
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340 | int bsp, // bucket space |
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341 | ANNorthRect &bnd_box, // bounding box for current node |
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342 | ANNkd_splitter splitter, // splitting routine |
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343 | ANNshrinkRule shrink) // shrinking rule |
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344 | { |
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345 | ANNdecomp decomp; // decomposition method |
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346 | |
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347 | ANNorthRect inner_box(dim); // inner box (if shrinking) |
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348 | |
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349 | if (n <= bsp) { // n small, make a leaf node |
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350 | if (n == 0) // empty leaf node |
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351 | return KD_TRIVIAL; // return (canonical) empty leaf |
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352 | else // construct the node and return |
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353 | return new ANNkd_leaf(n, pidx); |
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354 | } |
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355 | |
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356 | decomp = selectDecomp( // select decomposition method |
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357 | pa, pidx, // points and indices |
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358 | n, dim, // number of points and dimension |
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359 | bnd_box, // current bounding box |
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360 | splitter, shrink, // splitting/shrinking methods |
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361 | inner_box); // inner box if shrinking (returned) |
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362 | |
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363 | if (decomp == SPLIT) { // split selected |
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364 | int cd; // cutting dimension |
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365 | ANNcoord cv; // cutting value |
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366 | int n_lo; // number on low side of cut |
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367 | // invoke splitting procedure |
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368 | (*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo); |
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369 | |
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370 | ANNcoord lv = bnd_box.lo[cd]; // save bounds for cutting dimension |
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371 | ANNcoord hv = bnd_box.hi[cd]; |
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372 | |
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373 | bnd_box.hi[cd] = cv; // modify bounds for left subtree |
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374 | ANNkd_ptr lo = rbd_tree( // build left subtree |
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375 | pa, pidx, n_lo, // ...from pidx[0..n_lo-1] |
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376 | dim, bsp, bnd_box, splitter, shrink); |
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377 | bnd_box.hi[cd] = hv; // restore bounds |
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378 | |
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379 | bnd_box.lo[cd] = cv; // modify bounds for right subtree |
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380 | ANNkd_ptr hi = rbd_tree( // build right subtree |
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381 | pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1] |
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382 | dim, bsp, bnd_box, splitter, shrink); |
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383 | bnd_box.lo[cd] = lv; // restore bounds |
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384 | // create the splitting node |
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385 | return new ANNkd_split(cd, cv, lv, hv, lo, hi); |
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386 | } |
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387 | else { // shrink selected |
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388 | int n_in; // number of points in box |
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389 | int n_bnds; // number of bounding sides |
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390 | |
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391 | annBoxSplit( // split points around inner box |
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392 | pa, // points to split |
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393 | pidx, // point indices |
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394 | n, // number of points |
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395 | dim, // dimension |
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396 | inner_box, // inner box |
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397 | n_in); // number of points inside (returned) |
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398 | |
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399 | ANNkd_ptr in = rbd_tree( // build inner subtree pidx[0..n_in-1] |
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400 | pa, pidx, n_in, dim, bsp, inner_box, splitter, shrink); |
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401 | ANNkd_ptr out = rbd_tree( // build outer subtree pidx[n_in..n] |
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402 | pa, pidx+n_in, n - n_in, dim, bsp, bnd_box, splitter, shrink); |
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403 | |
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404 | ANNorthHSArray bnds = NULL; // bounds (alloc in Box2Bnds and |
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405 | // ...freed in bd_shrink destroyer) |
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406 | |
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407 | annBox2Bnds( // convert inner box to bounds |
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408 | inner_box, // inner box |
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409 | bnd_box, // enclosing box |
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410 | dim, // dimension |
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411 | n_bnds, // number of bounds (returned) |
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412 | bnds); // bounds array (modified) |
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413 | |
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414 | // return shrinking node |
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415 | return new ANNbd_shrink(n_bnds, bnds, in, out); |
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416 | } |
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417 | } |
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