| 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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