406 lines
15 KiB
Text
406 lines
15 KiB
Text
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//----------------------------------------------------------------------
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// File: kd_tree.cpp
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// Programmer: Sunil Arya and David Mount
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// Description: Basic methods for kd-trees.
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// Last modified: 01/04/05 (Version 1.0)
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//----------------------------------------------------------------------
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// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and
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// David Mount. All Rights Reserved.
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//
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// This software and related documentation is part of the Approximate
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// Nearest Neighbor Library (ANN). This software is provided under
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// the provisions of the Lesser GNU Public License (LGPL). See the
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// file ../ReadMe.txt for further information.
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//
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// The University of Maryland (U.M.) and the authors make no
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// representations about the suitability or fitness of this software for
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// any purpose. It is provided "as is" without express or implied
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// warranty.
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//----------------------------------------------------------------------
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// History:
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// Revision 0.1 03/04/98
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// Initial release
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// Revision 1.0 04/01/05
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// Increased aspect ratio bound (ANN_AR_TOOBIG) from 100 to 1000.
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// Fixed leaf counts to count trivial leaves.
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// Added optional pa, pi arguments to Skeleton kd_tree constructor
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// for use in load constructor.
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// Added annClose() to eliminate KD_TRIVIAL memory leak.
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//----------------------------------------------------------------------
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#include "kd_tree.h" // kd-tree declarations
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#include "kd_split.h" // kd-tree splitting rules
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#include "kd_util.h" // kd-tree utilities
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#include <ANN/ANNperf.h> // performance evaluation
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//----------------------------------------------------------------------
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// Global data
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//
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// For some splitting rules, especially with small bucket sizes,
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// it is possible to generate a large number of empty leaf nodes.
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// To save storage we allocate a single trivial leaf node which
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// contains no points. For messy coding reasons it is convenient
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// to have it reference a trivial point index.
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//
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// KD_TRIVIAL is allocated when the first kd-tree is created. It
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// must *never* deallocated (since it may be shared by more than
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// one tree).
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//----------------------------------------------------------------------
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static int IDX_TRIVIAL[] = {0}; // trivial point index
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ANNkd_leaf *KD_TRIVIAL = NULL; // trivial leaf node
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//----------------------------------------------------------------------
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// Printing the kd-tree
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// These routines print a kd-tree in reverse inorder (high then
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// root then low). (This is so that if you look at the output
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// from the right side it appear from left to right in standard
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// inorder.) When outputting leaves we output only the point
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// indices rather than the point coordinates. There is an option
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// to print the point coordinates separately.
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//
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// The tree printing routine calls the printing routines on the
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// individual nodes of the tree, passing in the level or depth
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// in the tree. The level in the tree is used to print indentation
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// for readability.
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//----------------------------------------------------------------------
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void ANNkd_split::print( // print splitting node
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int level, // depth of node in tree
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ostream &out) // output stream
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{
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child[ANN_HI]->print(level+1, out); // print high child
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out << " ";
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for (int i = 0; i < level; i++) // print indentation
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out << "..";
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out << "Split cd=" << cut_dim << " cv=" << cut_val;
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out << " lbnd=" << cd_bnds[ANN_LO];
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out << " hbnd=" << cd_bnds[ANN_HI];
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out << "\n";
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child[ANN_LO]->print(level+1, out); // print low child
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}
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void ANNkd_leaf::print( // print leaf node
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int level, // depth of node in tree
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ostream &out) // output stream
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{
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out << " ";
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for (int i = 0; i < level; i++) // print indentation
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out << "..";
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if (this == KD_TRIVIAL) { // canonical trivial leaf node
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out << "Leaf (trivial)\n";
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}
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else{
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out << "Leaf n=" << n_pts << " <";
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for (int j = 0; j < n_pts; j++) {
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out << bkt[j];
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if (j < n_pts-1) out << ",";
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}
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out << ">\n";
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}
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}
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void ANNkd_tree::Print( // print entire tree
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ANNbool with_pts, // print points as well?
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ostream &out) // output stream
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{
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out << "ANN Version " << ANNversion << "\n";
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if (with_pts) { // print point coordinates
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out << " Points:\n";
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for (int i = 0; i < n_pts; i++) {
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out << "\t" << i << ": ";
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annPrintPt(pts[i], dim, out);
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out << "\n";
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}
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}
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if (root == NULL) // empty tree?
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out << " Null tree.\n";
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else {
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root->print(0, out); // invoke printing at root
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}
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}
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//----------------------------------------------------------------------
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// kd_tree statistics (for performance evaluation)
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// This routine compute various statistics information for
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// a kd-tree. It is used by the implementors for performance
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// evaluation of the data structure.
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//----------------------------------------------------------------------
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#define MAX(a,b) ((a) > (b) ? (a) : (b))
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void ANNkdStats::merge(const ANNkdStats &st) // merge stats from child
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{
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n_lf += st.n_lf; n_tl += st.n_tl;
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n_spl += st.n_spl; n_shr += st.n_shr;
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depth = MAX(depth, st.depth);
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sum_ar += st.sum_ar;
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}
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//----------------------------------------------------------------------
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// Update statistics for nodes
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//----------------------------------------------------------------------
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const double ANN_AR_TOOBIG = 1000; // too big an aspect ratio
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void ANNkd_leaf::getStats( // get subtree statistics
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int dim, // dimension of space
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ANNkdStats &st, // stats (modified)
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ANNorthRect &bnd_box) // bounding box
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{
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st.reset();
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st.n_lf = 1; // count this leaf
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if (this == KD_TRIVIAL) st.n_tl = 1; // count trivial leaf
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double ar = annAspectRatio(dim, bnd_box); // aspect ratio of leaf
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// incr sum (ignore outliers)
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st.sum_ar += float(ar < ANN_AR_TOOBIG ? ar : ANN_AR_TOOBIG);
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}
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void ANNkd_split::getStats( // get subtree statistics
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int dim, // dimension of space
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ANNkdStats &st, // stats (modified)
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ANNorthRect &bnd_box) // bounding box
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{
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ANNkdStats ch_stats; // stats for children
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// get stats for low child
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ANNcoord hv = bnd_box.hi[cut_dim]; // save box bounds
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bnd_box.hi[cut_dim] = cut_val; // upper bound for low child
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ch_stats.reset(); // reset
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child[ANN_LO]->getStats(dim, ch_stats, bnd_box);
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st.merge(ch_stats); // merge them
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bnd_box.hi[cut_dim] = hv; // restore bound
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// get stats for high child
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ANNcoord lv = bnd_box.lo[cut_dim]; // save box bounds
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bnd_box.lo[cut_dim] = cut_val; // lower bound for high child
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ch_stats.reset(); // reset
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child[ANN_HI]->getStats(dim, ch_stats, bnd_box);
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st.merge(ch_stats); // merge them
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bnd_box.lo[cut_dim] = lv; // restore bound
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st.depth++; // increment depth
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st.n_spl++; // increment number of splits
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}
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//----------------------------------------------------------------------
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// getStats
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// Collects a number of statistics related to kd_tree or
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// bd_tree.
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//----------------------------------------------------------------------
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void ANNkd_tree::getStats( // get tree statistics
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ANNkdStats &st) // stats (modified)
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{
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st.reset(dim, n_pts, bkt_size); // reset stats
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// create bounding box
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ANNorthRect bnd_box(dim, bnd_box_lo, bnd_box_hi);
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if (root != NULL) { // if nonempty tree
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root->getStats(dim, st, bnd_box); // get statistics
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st.avg_ar = st.sum_ar / st.n_lf; // average leaf asp ratio
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}
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}
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//----------------------------------------------------------------------
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// kd_tree destructor
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// The destructor just frees the various elements that were
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// allocated in the construction process.
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//----------------------------------------------------------------------
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ANNkd_tree::~ANNkd_tree() // tree destructor
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{
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if (root != NULL) delete root;
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if (pidx != NULL) delete [] pidx;
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if (bnd_box_lo != NULL) annDeallocPt(bnd_box_lo);
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if (bnd_box_hi != NULL) annDeallocPt(bnd_box_hi);
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}
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//----------------------------------------------------------------------
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// This is called with all use of ANN is finished. It eliminates the
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// minor memory leak caused by the allocation of KD_TRIVIAL.
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//----------------------------------------------------------------------
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void annClose() // close use of ANN
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{
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if (KD_TRIVIAL != NULL) {
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delete KD_TRIVIAL;
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KD_TRIVIAL = NULL;
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}
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}
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//----------------------------------------------------------------------
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// kd_tree constructors
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// There is a skeleton kd-tree constructor which sets up a
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// trivial empty tree. The last optional argument allows
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// the routine to be passed a point index array which is
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// assumed to be of the proper size (n). Otherwise, one is
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// allocated and initialized to the identity. Warning: In
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// either case the destructor will deallocate this array.
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//
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// As a kludge, we need to allocate KD_TRIVIAL if one has not
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// already been allocated. (This is because I'm too dumb to
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// figure out how to cause a pointer to be allocated at load
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// time.)
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//----------------------------------------------------------------------
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void ANNkd_tree::SkeletonTree( // construct skeleton tree
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int n, // number of points
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int dd, // dimension
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int bs, // bucket size
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ANNpointArray pa, // point array
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ANNidxArray pi) // point indices
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{
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dim = dd; // initialize basic elements
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n_pts = n;
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bkt_size = bs;
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pts = pa; // initialize points array
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root = NULL; // no associated tree yet
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if (pi == NULL) { // point indices provided?
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pidx = new ANNidx[n]; // no, allocate space for point indices
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for (int i = 0; i < n; i++) {
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pidx[i] = i; // initially identity
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}
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}
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else {
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pidx = pi; // yes, use them
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}
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bnd_box_lo = bnd_box_hi = NULL; // bounding box is nonexistent
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if (KD_TRIVIAL == NULL) // no trivial leaf node yet?
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KD_TRIVIAL = new ANNkd_leaf(0, IDX_TRIVIAL); // allocate it
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}
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ANNkd_tree::ANNkd_tree( // basic constructor
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int n, // number of points
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int dd, // dimension
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int bs) // bucket size
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{ SkeletonTree(n, dd, bs); } // construct skeleton tree
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//----------------------------------------------------------------------
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// rkd_tree - recursive procedure to build a kd-tree
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//
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// Builds a kd-tree for points in pa as indexed through the
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// array pidx[0..n-1] (typically a subarray of the array used in
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// the top-level call). This routine permutes the array pidx,
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// but does not alter pa[].
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//
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// The construction is based on a standard algorithm for constructing
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// the kd-tree (see Friedman, Bentley, and Finkel, ``An algorithm for
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// finding best matches in logarithmic expected time,'' ACM Transactions
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// on Mathematical Software, 3(3):209-226, 1977). The procedure
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// operates by a simple divide-and-conquer strategy, which determines
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// an appropriate orthogonal cutting plane (see below), and splits
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// the points. When the number of points falls below the bucket size,
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// we simply store the points in a leaf node's bucket.
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//
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// One of the arguments is a pointer to a splitting routine,
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// whose prototype is:
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//
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// void split(
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// ANNpointArray pa, // complete point array
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// ANNidxArray pidx, // point array (permuted on return)
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// ANNorthRect &bnds, // bounds of current cell
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// int n, // number of points
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// int dim, // dimension of space
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// int &cut_dim, // cutting dimension
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// ANNcoord &cut_val, // cutting value
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// int &n_lo) // no. of points on low side of cut
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//
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// This procedure selects a cutting dimension and cutting value,
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// partitions pa about these values, and returns the number of
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// points on the low side of the cut.
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//----------------------------------------------------------------------
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ANNkd_ptr rkd_tree( // recursive construction of kd-tree
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ANNpointArray pa, // point array
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ANNidxArray pidx, // point indices to store in subtree
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int n, // number of points
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int dim, // dimension of space
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int bsp, // bucket space
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ANNorthRect &bnd_box, // bounding box for current node
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ANNkd_splitter splitter) // splitting routine
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{
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if (n <= bsp) { // n small, make a leaf node
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if (n == 0) // empty leaf node
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return KD_TRIVIAL; // return (canonical) empty leaf
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else // construct the node and return
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return new ANNkd_leaf(n, pidx);
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}
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else { // n large, make a splitting node
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int cd; // cutting dimension
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ANNcoord cv; // cutting value
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int n_lo; // number on low side of cut
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ANNkd_node *lo, *hi; // low and high children
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// invoke splitting procedure
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(*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo);
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ANNcoord lv = bnd_box.lo[cd]; // save bounds for cutting dimension
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ANNcoord hv = bnd_box.hi[cd];
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bnd_box.hi[cd] = cv; // modify bounds for left subtree
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lo = rkd_tree( // build left subtree
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pa, pidx, n_lo, // ...from pidx[0..n_lo-1]
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dim, bsp, bnd_box, splitter);
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bnd_box.hi[cd] = hv; // restore bounds
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bnd_box.lo[cd] = cv; // modify bounds for right subtree
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hi = rkd_tree( // build right subtree
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pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1]
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dim, bsp, bnd_box, splitter);
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bnd_box.lo[cd] = lv; // restore bounds
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// create the splitting node
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ANNkd_split *ptr = new ANNkd_split(cd, cv, lv, hv, lo, hi);
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return ptr; // return pointer to this node
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}
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||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// kd-tree constructor
|
||
|
|
// This is the main constructor for kd-trees given a set of points.
|
||
|
|
// It first builds a skeleton tree, then computes the bounding box
|
||
|
|
// of the data points, and then invokes rkd_tree() to actually
|
||
|
|
// build the tree, passing it the appropriate splitting routine.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
ANNkd_tree::ANNkd_tree( // construct from point array
|
||
|
|
ANNpointArray pa, // point array (with at least n pts)
|
||
|
|
int n, // number of points
|
||
|
|
int dd, // dimension
|
||
|
|
int bs, // bucket size
|
||
|
|
ANNsplitRule split) // splitting method
|
||
|
|
{
|
||
|
|
SkeletonTree(n, dd, bs); // set up the basic stuff
|
||
|
|
pts = pa; // where the points are
|
||
|
|
if (n == 0) return; // no points--no sweat
|
||
|
|
|
||
|
|
ANNorthRect bnd_box(dd); // bounding box for points
|
||
|
|
annEnclRect(pa, pidx, n, dd, bnd_box);// construct bounding rectangle
|
||
|
|
// copy to tree structure
|
||
|
|
bnd_box_lo = annCopyPt(dd, bnd_box.lo);
|
||
|
|
bnd_box_hi = annCopyPt(dd, bnd_box.hi);
|
||
|
|
|
||
|
|
switch (split) { // build by rule
|
||
|
|
case ANN_KD_STD: // standard kd-splitting rule
|
||
|
|
root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split);
|
||
|
|
break;
|
||
|
|
case ANN_KD_MIDPT: // midpoint split
|
||
|
|
root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split);
|
||
|
|
break;
|
||
|
|
case ANN_KD_FAIR: // fair split
|
||
|
|
root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split);
|
||
|
|
break;
|
||
|
|
case ANN_KD_SUGGEST: // best (in our opinion)
|
||
|
|
case ANN_KD_SL_MIDPT: // sliding midpoint split
|
||
|
|
root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split);
|
||
|
|
break;
|
||
|
|
case ANN_KD_SL_FAIR: // sliding fair split
|
||
|
|
root = rkd_tree(pa, pidx, n, dd, bs, bnd_box, sl_fair_split);
|
||
|
|
break;
|
||
|
|
default:
|
||
|
|
annError("Illegal splitting method", ANNabort);
|
||
|
|
}
|
||
|
|
}
|