1 | //---------------------------------------------------------------------- |
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2 | // File: kd_tree.cpp |
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3 | // Programmer: Sunil Arya and David Mount |
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4 | // Description: Basic methods for kd-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 1.0 04/01/05 |
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24 | // Increased aspect ratio bound (ANN_AR_TOOBIG) from 100 to 1000. |
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25 | // Fixed leaf counts to count trivial leaves. |
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26 | // Added optional pa, pi arguments to Skeleton kd_tree constructor |
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27 | // for use in load constructor. |
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28 | // Added annClose() to eliminate KD_TRIVIAL memory leak. |
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29 | //---------------------------------------------------------------------- |
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30 | |
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31 | #include "kd_tree.h" // kd-tree declarations |
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32 | #include "kd_split.h" // kd-tree splitting rules |
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33 | #include "kd_util.h" // kd-tree utilities |
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34 | #include <ANN/ANNperf.h> // performance evaluation |
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35 | |
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36 | //---------------------------------------------------------------------- |
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37 | // Global data |
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38 | // |
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39 | // For some splitting rules, especially with small bucket sizes, |
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40 | // it is possible to generate a large number of empty leaf nodes. |
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41 | // To save storage we allocate a single trivial leaf node which |
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42 | // contains no points. For messy coding reasons it is convenient |
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43 | // to have it reference a trivial point index. |
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44 | // |
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45 | // KD_TRIVIAL is allocated when the first kd-tree is created. It |
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46 | // must *never* deallocated (since it may be shared by more than |
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47 | // one tree). |
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48 | //---------------------------------------------------------------------- |
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49 | static int IDX_TRIVIAL[] = {0}; // trivial point index |
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50 | ANNkd_leaf *KD_TRIVIAL = NULL; // trivial leaf node |
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51 | |
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52 | //---------------------------------------------------------------------- |
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53 | // Printing the kd-tree |
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54 | // These routines print a kd-tree in reverse inorder (high then |
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55 | // root then low). (This is so that if you look at the output |
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56 | // from the right side it appear from left to right in standard |
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57 | // inorder.) When outputting leaves we output only the point |
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58 | // indices rather than the point coordinates. There is an option |
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59 | // to print the point coordinates separately. |
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60 | // |
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61 | // The tree printing routine calls the printing routines on the |
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62 | // individual nodes of the tree, passing in the level or depth |
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63 | // in the tree. The level in the tree is used to print indentation |
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64 | // for readability. |
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65 | //---------------------------------------------------------------------- |
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66 | |
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67 | void ANNkd_split::print( // print splitting node |
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68 | int level, // depth of node in tree |
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69 | ostream &out) // output stream |
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70 | { |
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71 | child[ANN_HI]->print(level+1, out); // print high child |
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72 | out << " "; |
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73 | for (int i = 0; i < level; i++) // print indentation |
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74 | out << ".."; |
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75 | out << "Split cd=" << cut_dim << " cv=" << cut_val; |
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76 | out << " lbnd=" << cd_bnds[ANN_LO]; |
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77 | out << " hbnd=" << cd_bnds[ANN_HI]; |
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78 | out << "\n"; |
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79 | child[ANN_LO]->print(level+1, out); // print low child |
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80 | } |
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81 | |
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82 | void ANNkd_leaf::print( // print leaf node |
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83 | int level, // depth of node in tree |
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84 | ostream &out) // output stream |
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85 | { |
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86 | |
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87 | out << " "; |
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88 | for (int i = 0; i < level; i++) // print indentation |
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89 | out << ".."; |
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90 | |
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91 | if (this == KD_TRIVIAL) { // canonical trivial leaf node |
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92 | out << "Leaf (trivial)\n"; |
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93 | } |
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94 | else{ |
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95 | out << "Leaf n=" << n_pts << " <"; |
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96 | for (int j = 0; j < n_pts; j++) { |
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97 | out << bkt[j]; |
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98 | if (j < n_pts-1) out << ","; |
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99 | } |
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100 | out << ">\n"; |
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101 | } |
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102 | } |
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103 | |
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104 | void ANNkd_tree::Print( // print entire tree |
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105 | ANNbool with_pts, // print points as well? |
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106 | ostream &out) // output stream |
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107 | { |
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108 | out << "ANN Version " << ANNversion << "\n"; |
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109 | if (with_pts) { // print point coordinates |
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110 | out << " Points:\n"; |
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111 | for (int i = 0; i < n_pts; i++) { |
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112 | out << "\t" << i << ": "; |
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113 | annPrintPt(pts[i], dim, out); |
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114 | out << "\n"; |
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115 | } |
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116 | } |
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117 | if (root == NULL) // empty tree? |
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118 | out << " Null tree.\n"; |
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119 | else { |
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120 | root->print(0, out); // invoke printing at root |
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121 | } |
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122 | } |
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123 | |
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124 | //---------------------------------------------------------------------- |
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125 | // kd_tree statistics (for performance evaluation) |
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126 | // This routine compute various statistics information for |
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127 | // a kd-tree. It is used by the implementors for performance |
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128 | // evaluation of the data structure. |
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129 | //---------------------------------------------------------------------- |
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130 | |
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131 | #define MAX(a,b) ((a) > (b) ? (a) : (b)) |
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132 | |
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133 | void ANNkdStats::merge(const ANNkdStats &st) // merge stats from child |
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134 | { |
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135 | n_lf += st.n_lf; n_tl += st.n_tl; |
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136 | n_spl += st.n_spl; n_shr += st.n_shr; |
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137 | depth = MAX(depth, st.depth); |
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138 | sum_ar += st.sum_ar; |
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139 | } |
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140 | |
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141 | //---------------------------------------------------------------------- |
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142 | // Update statistics for nodes |
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143 | //---------------------------------------------------------------------- |
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144 | |
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145 | const double ANN_AR_TOOBIG = 1000; // too big an aspect ratio |
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146 | |
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147 | void ANNkd_leaf::getStats( // get subtree statistics |
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148 | int dim, // dimension of space |
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149 | ANNkdStats &st, // stats (modified) |
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150 | ANNorthRect &bnd_box) // bounding box |
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151 | { |
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152 | st.reset(); |
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153 | st.n_lf = 1; // count this leaf |
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154 | if (this == KD_TRIVIAL) st.n_tl = 1; // count trivial leaf |
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155 | double ar = annAspectRatio(dim, bnd_box); // aspect ratio of leaf |
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156 | // incr sum (ignore outliers) |
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157 | st.sum_ar += float(ar < ANN_AR_TOOBIG ? ar : ANN_AR_TOOBIG); |
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158 | } |
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159 | |
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160 | void ANNkd_split::getStats( // get subtree statistics |
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161 | int dim, // dimension of space |
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162 | ANNkdStats &st, // stats (modified) |
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163 | ANNorthRect &bnd_box) // bounding box |
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164 | { |
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165 | ANNkdStats ch_stats; // stats for children |
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166 | // get stats for low child |
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167 | ANNcoord hv = bnd_box.hi[cut_dim]; // save box bounds |
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168 | bnd_box.hi[cut_dim] = cut_val; // upper bound for low child |
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169 | ch_stats.reset(); // reset |
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170 | child[ANN_LO]->getStats(dim, ch_stats, bnd_box); |
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171 | st.merge(ch_stats); // merge them |
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172 | bnd_box.hi[cut_dim] = hv; // restore bound |
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173 | // get stats for high child |
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174 | ANNcoord lv = bnd_box.lo[cut_dim]; // save box bounds |
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175 | bnd_box.lo[cut_dim] = cut_val; // lower bound for high child |
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176 | ch_stats.reset(); // reset |
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177 | child[ANN_HI]->getStats(dim, ch_stats, bnd_box); |
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178 | st.merge(ch_stats); // merge them |
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179 | bnd_box.lo[cut_dim] = lv; // restore bound |
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180 | |
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181 | st.depth++; // increment depth |
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182 | st.n_spl++; // increment number of splits |
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183 | } |
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184 | |
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185 | //---------------------------------------------------------------------- |
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186 | // getStats |
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187 | // Collects a number of statistics related to kd_tree or |
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188 | // bd_tree. |
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189 | //---------------------------------------------------------------------- |
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190 | |
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191 | void ANNkd_tree::getStats( // get tree statistics |
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192 | ANNkdStats &st) // stats (modified) |
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193 | { |
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194 | st.reset(dim, n_pts, bkt_size); // reset stats |
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195 | // create bounding box |
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196 | ANNorthRect bnd_box(dim, bnd_box_lo, bnd_box_hi); |
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197 | if (root != NULL) { // if nonempty tree |
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198 | root->getStats(dim, st, bnd_box); // get statistics |
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199 | st.avg_ar = st.sum_ar / st.n_lf; // average leaf asp ratio |
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200 | } |
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201 | } |
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202 | |
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203 | //---------------------------------------------------------------------- |
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204 | // kd_tree destructor |
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205 | // The destructor just frees the various elements that were |
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206 | // allocated in the construction process. |
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207 | //---------------------------------------------------------------------- |
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208 | |
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209 | ANNkd_tree::~ANNkd_tree() // tree destructor |
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210 | { |
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211 | if (root != NULL) delete root; |
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212 | if (pidx != NULL) delete [] pidx; |
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213 | if (bnd_box_lo != NULL) annDeallocPt(bnd_box_lo); |
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214 | if (bnd_box_hi != NULL) annDeallocPt(bnd_box_hi); |
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215 | } |
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216 | |
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217 | //---------------------------------------------------------------------- |
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218 | // This is called with all use of ANN is finished. It eliminates the |
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219 | // minor memory leak caused by the allocation of KD_TRIVIAL. |
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220 | //---------------------------------------------------------------------- |
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221 | void annClose() // close use of ANN |
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222 | { |
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223 | if (KD_TRIVIAL != NULL) { |
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224 | delete KD_TRIVIAL; |
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225 | KD_TRIVIAL = NULL; |
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226 | } |
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227 | } |
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228 | |
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229 | //---------------------------------------------------------------------- |
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230 | // kd_tree constructors |
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231 | // There is a skeleton kd-tree constructor which sets up a |
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232 | // trivial empty tree. The last optional argument allows |
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233 | // the routine to be passed a point index array which is |
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234 | // assumed to be of the proper size (n). Otherwise, one is |
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235 | // allocated and initialized to the identity. Warning: In |
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236 | // either case the destructor will deallocate this array. |
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237 | // |
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238 | // As a kludge, we need to allocate KD_TRIVIAL if one has not |
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239 | // already been allocated. (This is because I'm too dumb to |
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240 | // figure out how to cause a pointer to be allocated at load |
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241 | // time.) |
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242 | //---------------------------------------------------------------------- |
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243 | |
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244 | void ANNkd_tree::SkeletonTree( // construct skeleton tree |
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245 | int n, // number of points |
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246 | int dd, // dimension |
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247 | int bs, // bucket size |
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248 | ANNpointArray pa, // point array |
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249 | ANNidxArray pi) // point indices |
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250 | { |
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251 | dim = dd; // initialize basic elements |
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252 | n_pts = n; |
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253 | bkt_size = bs; |
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254 | pts = pa; // initialize points array |
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255 | |
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256 | root = NULL; // no associated tree yet |
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257 | |
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258 | if (pi == NULL) { // point indices provided? |
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259 | pidx = new ANNidx[n]; // no, allocate space for point indices |
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260 | for (int i = 0; i < n; i++) { |
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261 | pidx[i] = i; // initially identity |
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262 | } |
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263 | } |
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264 | else { |
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265 | pidx = pi; // yes, use them |
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266 | } |
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267 | |
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268 | bnd_box_lo = bnd_box_hi = NULL; // bounding box is nonexistent |
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269 | if (KD_TRIVIAL == NULL) // no trivial leaf node yet? |
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270 | KD_TRIVIAL = new ANNkd_leaf(0, IDX_TRIVIAL); // allocate it |
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271 | } |
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272 | |
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273 | ANNkd_tree::ANNkd_tree( // basic constructor |
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274 | int n, // number of points |
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275 | int dd, // dimension |
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276 | int bs) // bucket size |
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277 | { SkeletonTree(n, dd, bs); } // construct skeleton tree |
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278 | |
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279 | //---------------------------------------------------------------------- |
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280 | // rkd_tree - recursive procedure to build a kd-tree |
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281 | // |
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282 | // Builds a kd-tree for points in pa as indexed through the |
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283 | // array pidx[0..n-1] (typically a subarray of the array used in |
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284 | // the top-level call). This routine permutes the array pidx, |
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285 | // but does not alter pa[]. |
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286 | // |
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287 | // The construction is based on a standard algorithm for constructing |
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288 | // the kd-tree (see Friedman, Bentley, and Finkel, ``An algorithm for |
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289 | // finding best matches in logarithmic expected time,'' ACM Transactions |
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290 | // on Mathematical Software, 3(3):209-226, 1977). The procedure |
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291 | // operates by a simple divide-and-conquer strategy, which determines |
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292 | // an appropriate orthogonal cutting plane (see below), and splits |
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293 | // the points. When the number of points falls below the bucket size, |
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294 | // we simply store the points in a leaf node's bucket. |
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295 | // |
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296 | // One of the arguments is a pointer to a splitting routine, |
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297 | // whose prototype is: |
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298 | // |
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299 | // void split( |
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300 | // ANNpointArray pa, // complete point array |
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301 | // ANNidxArray pidx, // point array (permuted on return) |
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302 | // ANNorthRect &bnds, // bounds of current cell |
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303 | // int n, // number of points |
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304 | // int dim, // dimension of space |
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305 | // int &cut_dim, // cutting dimension |
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306 | // ANNcoord &cut_val, // cutting value |
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307 | // int &n_lo) // no. of points on low side of cut |
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308 | // |
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309 | // This procedure selects a cutting dimension and cutting value, |
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310 | // partitions pa about these values, and returns the number of |
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311 | // points on the low side of the cut. |
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312 | //---------------------------------------------------------------------- |
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313 | |
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314 | ANNkd_ptr rkd_tree( // recursive construction of kd-tree |
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315 | ANNpointArray pa, // point array |
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316 | ANNidxArray pidx, // point indices to store in subtree |
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317 | int n, // number of points |
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318 | int dim, // dimension of space |
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319 | int bsp, // bucket space |
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320 | ANNorthRect &bnd_box, // bounding box for current node |
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321 | ANNkd_splitter splitter) // splitting routine |
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322 | { |
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323 | if (n <= bsp) { // n small, make a leaf node |
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324 | if (n == 0) // empty leaf node |
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325 | return KD_TRIVIAL; // return (canonical) empty leaf |
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326 | else // construct the node and return |
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327 | return new ANNkd_leaf(n, pidx); |
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328 | } |
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329 | else { // n large, make a splitting node |
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330 | int cd; // cutting dimension |
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331 | ANNcoord cv; // cutting value |
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332 | int n_lo; // number on low side of cut |
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333 | ANNkd_node *lo, *hi; // low and high children |
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334 | |
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335 | // invoke splitting procedure |
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336 | (*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo); |
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337 | |
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338 | ANNcoord lv = bnd_box.lo[cd]; // save bounds for cutting dimension |
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339 | ANNcoord hv = bnd_box.hi[cd]; |
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340 | |
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341 | bnd_box.hi[cd] = cv; // modify bounds for left subtree |
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342 | lo = rkd_tree( // build left subtree |
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343 | pa, pidx, n_lo, // ...from pidx[0..n_lo-1] |
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344 | dim, bsp, bnd_box, splitter); |
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345 | bnd_box.hi[cd] = hv; // restore bounds |
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346 | |
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347 | bnd_box.lo[cd] = cv; // modify bounds for right subtree |
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348 | hi = rkd_tree( // build right subtree |
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349 | pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1] |
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350 | dim, bsp, bnd_box, splitter); |
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351 | bnd_box.lo[cd] = lv; // restore bounds |
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352 | |
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353 | // create the splitting node |
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354 | ANNkd_split *ptr = new ANNkd_split(cd, cv, lv, hv, lo, hi); |
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355 | |
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356 | return ptr; // return pointer to this node |
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357 | } |
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358 | } |
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359 | |
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360 | //---------------------------------------------------------------------- |
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361 | // kd-tree constructor |
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362 | // This is the main constructor for kd-trees given a set of points. |
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363 | // It first builds a skeleton tree, then computes the bounding box |
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364 | // of the data points, and then invokes rkd_tree() to actually |
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365 | // build the tree, passing it the appropriate splitting routine. |
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366 | //---------------------------------------------------------------------- |
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367 | |
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368 | ANNkd_tree::ANNkd_tree( // construct from point array |
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369 | ANNpointArray pa, // point array (with at least n pts) |
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370 | int n, // number of points |
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371 | int dd, // dimension |
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372 | int bs, // bucket size |
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373 | ANNsplitRule split) // splitting method |
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374 | { |
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375 | SkeletonTree(n, dd, bs); // set up the basic stuff |
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376 | pts = pa; // where the points are |
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377 | if (n == 0) return; // no points--no sweat |
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378 | |
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379 | ANNorthRect bnd_box(dd); // bounding box for points |
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380 | annEnclRect(pa, pidx, n, dd, bnd_box);// construct bounding rectangle |
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381 | // copy to tree structure |
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382 | bnd_box_lo = annCopyPt(dd, bnd_box.lo); |
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383 | bnd_box_hi = annCopyPt(dd, bnd_box.hi); |
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384 | |
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385 | switch (split) { // build by rule |
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386 | case ANN_KD_STD: // standard kd-splitting rule |
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387 | root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split); |
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388 | break; |
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389 | case ANN_KD_MIDPT: // midpoint split |
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390 | root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split); |
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391 | break; |
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392 | case ANN_KD_FAIR: // fair split |
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393 | root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split); |
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394 | break; |
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395 | case ANN_KD_SUGGEST: // best (in our opinion) |
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396 | case ANN_KD_SL_MIDPT: // sliding midpoint split |
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397 | root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split); |
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398 | break; |
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399 | case ANN_KD_SL_FAIR: // sliding fair split |
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400 | root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_fair_split); |
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401 | break; |
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402 | default: |
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403 | annError("Illegal splitting method", ANNabort); |
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404 | } |
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405 | } |
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