[37] | 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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