1 | //---------------------------------------------------------------------- |
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2 | // File: kd_pr_search.cpp |
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3 | // Programmer: Sunil Arya and David Mount |
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4 | // Description: Priority search 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 | //---------------------------------------------------------------------- |
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24 | |
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25 | #include "kd_pr_search.h" // kd priority search declarations |
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26 | |
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27 | //---------------------------------------------------------------------- |
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28 | // Approximate nearest neighbor searching by priority search. |
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29 | // The kd-tree is searched for an approximate nearest neighbor. |
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30 | // The point is returned through one of the arguments, and the |
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31 | // distance returned is the SQUARED distance to this point. |
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32 | // |
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33 | // The method used for searching the kd-tree is called priority |
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34 | // search. (It is described in Arya and Mount, ``Algorithms for |
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35 | // fast vector quantization,'' Proc. of DCC '93: Data Compression |
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36 | // Conference}, eds. J. A. Storer and M. Cohn, IEEE Press, 1993, |
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37 | // 381--390.) |
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38 | // |
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39 | // The cell of the kd-tree containing the query point is located, |
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40 | // and cells are visited in increasing order of distance from the |
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41 | // query point. This is done by placing each subtree which has |
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42 | // NOT been visited in a priority queue, according to the closest |
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43 | // distance of the corresponding enclosing rectangle from the |
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44 | // query point. The search stops when the distance to the nearest |
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45 | // remaining rectangle exceeds the distance to the nearest point |
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46 | // seen by a factor of more than 1/(1+eps). (Implying that any |
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47 | // point found subsequently in the search cannot be closer by more |
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48 | // than this factor.) |
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49 | // |
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50 | // The main entry point is annkPriSearch() which sets things up and |
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51 | // then call the recursive routine ann_pri_search(). This is a |
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52 | // recursive routine which performs the processing for one node in |
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53 | // the kd-tree. There are two versions of this virtual procedure, |
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54 | // one for splitting nodes and one for leaves. When a splitting node |
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55 | // is visited, we determine which child to continue the search on |
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56 | // (the closer one), and insert the other child into the priority |
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57 | // queue. When a leaf is visited, we compute the distances to the |
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58 | // points in the buckets, and update information on the closest |
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59 | // points. |
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60 | // |
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61 | // Some trickery is used to incrementally update the distance from |
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62 | // a kd-tree rectangle to the query point. This comes about from |
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63 | // the fact that which each successive split, only one component |
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64 | // (along the dimension that is split) of the squared distance to |
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65 | // the child rectangle is different from the squared distance to |
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66 | // the parent rectangle. |
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67 | //---------------------------------------------------------------------- |
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68 | |
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69 | //---------------------------------------------------------------------- |
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70 | // To keep argument lists short, a number of global variables |
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71 | // are maintained which are common to all the recursive calls. |
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72 | // These are given below. |
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73 | //---------------------------------------------------------------------- |
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74 | |
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75 | double ANNprEps; // the error bound |
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76 | int ANNprDim; // dimension of space |
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77 | ANNpoint ANNprQ; // query point |
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78 | double ANNprMaxErr; // max tolerable squared error |
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79 | ANNpointArray ANNprPts; // the points |
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80 | ANNpr_queue *ANNprBoxPQ; // priority queue for boxes |
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81 | ANNmin_k *ANNprPointMK; // set of k closest points |
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82 | |
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83 | //---------------------------------------------------------------------- |
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84 | // annkPriSearch - priority search for k nearest neighbors |
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85 | //---------------------------------------------------------------------- |
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86 | |
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87 | void ANNkd_tree::annkPriSearch( |
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88 | ANNpoint q, // query point |
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89 | int k, // number of near neighbors to return |
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90 | ANNidxArray nn_idx, // nearest neighbor indices (returned) |
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91 | ANNdistArray dd, // dist to near neighbors (returned) |
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92 | double eps) // error bound (ignored) |
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93 | { |
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94 | // max tolerable squared error |
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95 | ANNprMaxErr = ANN_POW(1.0 + eps); |
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96 | ANN_FLOP(2) // increment floating ops |
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97 | |
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98 | ANNprDim = dim; // copy arguments to static equivs |
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99 | ANNprQ = q; |
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100 | ANNprPts = pts; |
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101 | ANNptsVisited = 0; // initialize count of points visited |
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102 | |
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103 | ANNprPointMK = new ANNmin_k(k); // create set for closest k points |
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104 | |
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105 | // distance to root box |
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106 | ANNdist box_dist = annBoxDistance(q, |
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107 | bnd_box_lo, bnd_box_hi, dim); |
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108 | |
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109 | ANNprBoxPQ = new ANNpr_queue(n_pts);// create priority queue for boxes |
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110 | ANNprBoxPQ->insert(box_dist, root); // insert root in priority queue |
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111 | |
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112 | while (ANNprBoxPQ->non_empty() && |
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113 | (!(ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited))) { |
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114 | ANNkd_ptr np; // next box from prior queue |
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115 | |
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116 | // extract closest box from queue |
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117 | ANNprBoxPQ->extr_min(box_dist, (void *&) np); |
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118 | |
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119 | ANN_FLOP(2) // increment floating ops |
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120 | if (box_dist*ANNprMaxErr >= ANNprPointMK->max_key()) |
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121 | break; |
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122 | |
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123 | np->ann_pri_search(box_dist); // search this subtree. |
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124 | } |
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125 | |
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126 | for (int i = 0; i < k; i++) { // extract the k-th closest points |
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127 | dd[i] = ANNprPointMK->ith_smallest_key(i); |
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128 | nn_idx[i] = ANNprPointMK->ith_smallest_info(i); |
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129 | } |
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130 | |
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131 | delete ANNprPointMK; // deallocate closest point set |
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132 | delete ANNprBoxPQ; // deallocate priority queue |
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133 | } |
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134 | |
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135 | //---------------------------------------------------------------------- |
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136 | // kd_split::ann_pri_search - search a splitting node |
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137 | //---------------------------------------------------------------------- |
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138 | |
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139 | void ANNkd_split::ann_pri_search(ANNdist box_dist) |
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140 | { |
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141 | ANNdist new_dist; // distance to child visited later |
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142 | // distance to cutting plane |
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143 | ANNcoord cut_diff = ANNprQ[cut_dim] - cut_val; |
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144 | |
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145 | if (cut_diff < 0) { // left of cutting plane |
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146 | ANNcoord box_diff = cd_bnds[ANN_LO] - ANNprQ[cut_dim]; |
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147 | if (box_diff < 0) // within bounds - ignore |
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148 | box_diff = 0; |
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149 | // distance to further box |
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150 | new_dist = (ANNdist) ANN_SUM(box_dist, |
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151 | ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); |
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152 | |
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153 | if (child[ANN_HI] != KD_TRIVIAL)// enqueue if not trivial |
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154 | ANNprBoxPQ->insert(new_dist, child[ANN_HI]); |
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155 | // continue with closer child |
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156 | child[ANN_LO]->ann_pri_search(box_dist); |
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157 | } |
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158 | else { // right of cutting plane |
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159 | ANNcoord box_diff = ANNprQ[cut_dim] - cd_bnds[ANN_HI]; |
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160 | if (box_diff < 0) // within bounds - ignore |
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161 | box_diff = 0; |
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162 | // distance to further box |
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163 | new_dist = (ANNdist) ANN_SUM(box_dist, |
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164 | ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff))); |
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165 | |
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166 | if (child[ANN_LO] != KD_TRIVIAL)// enqueue if not trivial |
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167 | ANNprBoxPQ->insert(new_dist, child[ANN_LO]); |
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168 | // continue with closer child |
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169 | child[ANN_HI]->ann_pri_search(box_dist); |
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170 | } |
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171 | ANN_SPL(1) // one more splitting node visited |
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172 | ANN_FLOP(8) // increment floating ops |
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173 | } |
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174 | |
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175 | //---------------------------------------------------------------------- |
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176 | // kd_leaf::ann_pri_search - search points in a leaf node |
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177 | // |
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178 | // This is virtually identical to the ann_search for standard search. |
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179 | //---------------------------------------------------------------------- |
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180 | |
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181 | void ANNkd_leaf::ann_pri_search(ANNdist box_dist) |
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182 | { |
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183 | register ANNdist dist; // distance to data point |
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184 | register ANNcoord* pp; // data coordinate pointer |
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185 | register ANNcoord* qq; // query coordinate pointer |
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186 | register ANNdist min_dist; // distance to k-th closest point |
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187 | register ANNcoord t; |
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188 | register int d; |
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189 | |
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190 | min_dist = ANNprPointMK->max_key(); // k-th smallest distance so far |
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191 | |
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192 | for (int i = 0; i < n_pts; i++) { // check points in bucket |
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193 | |
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194 | pp = ANNprPts[bkt[i]]; // first coord of next data point |
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195 | qq = ANNprQ; // first coord of query point |
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196 | dist = 0; |
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197 | |
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198 | for(d = 0; d < ANNprDim; d++) { |
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199 | ANN_COORD(1) // one more coordinate hit |
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200 | ANN_FLOP(4) // increment floating ops |
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201 | |
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202 | t = *(qq++) - *(pp++); // compute length and adv coordinate |
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203 | // exceeds dist to k-th smallest? |
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204 | if( (dist = ANN_SUM(dist, ANN_POW(t))) > min_dist) { |
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205 | break; |
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206 | } |
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207 | } |
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208 | |
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209 | if (d >= ANNprDim && // among the k best? |
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210 | (ANN_ALLOW_SELF_MATCH || dist!=0)) { // and no self-match problem |
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211 | // add it to the list |
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212 | ANNprPointMK->insert(dist, bkt[i]); |
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213 | min_dist = ANNprPointMK->max_key(); |
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214 | } |
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215 | } |
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216 | ANN_LEAF(1) // one more leaf node visited |
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217 | ANN_PTS(n_pts) // increment points visited |
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218 | ANNptsVisited += n_pts; // increment number of points visited |
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219 | } |
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