418 lines
16 KiB
Text
418 lines
16 KiB
Text
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//----------------------------------------------------------------------
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// File: bd_tree.cpp
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// Programmer: David Mount
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// Description: Basic methods for bd-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 l.0 04/01/05
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// Fixed centroid shrink threshold condition to depend on the
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// dimension.
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// Moved dump routine to kd_dump.cpp.
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//----------------------------------------------------------------------
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#include "bd_tree.h" // bd-tree declarations
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#include "kd_util.h" // kd-tree utilities
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#include "kd_split.h" // kd-tree splitting rules
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#include <ANN/ANNperf.h> // performance evaluation
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//----------------------------------------------------------------------
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// Printing a bd-tree
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// These routines print a bd-tree. See the analogous procedure
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// in kd_tree.cpp for more information.
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//----------------------------------------------------------------------
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void ANNbd_shrink::print( // print shrinking 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_OUT]->print(level+1, out); // print out-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 << "Shrink";
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for (int j = 0; j < n_bnds; j++) { // print sides, 2 per line
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if (j % 2 == 0) {
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out << "\n"; // newline and indentation
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for (int i = 0; i < level+2; i++) out << " ";
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}
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out << " ([" << bnds[j].cd << "]"
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<< (bnds[j].sd > 0 ? ">=" : "< ")
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<< bnds[j].cv << ")";
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}
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out << "\n";
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child[ANN_IN]->print(level+1, out); // print in-child
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}
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//----------------------------------------------------------------------
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// kd_tree statistics utility (for performance evaluation)
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// This routine computes various statistics information for
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// shrinking nodes. See file kd_tree.cpp for more information.
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//----------------------------------------------------------------------
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void ANNbd_shrink::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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ANNorthRect inner_box(dim); // inner box of shrink
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annBnds2Box(bnd_box, // enclosing box
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dim, // dimension
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n_bnds, // number of bounds
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bnds, // bounds array
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inner_box); // inner box (modified)
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// get stats for inner child
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ch_stats.reset(); // reset
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child[ANN_IN]->getStats(dim, ch_stats, inner_box);
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st.merge(ch_stats); // merge them
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// get stats for outer child
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ch_stats.reset(); // reset
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child[ANN_OUT]->getStats(dim, ch_stats, bnd_box);
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st.merge(ch_stats); // merge them
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st.depth++; // increment depth
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st.n_shr++; // increment number of shrinks
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}
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//----------------------------------------------------------------------
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// bd-tree constructor
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// This is the main constructor for bd-trees given a set of points.
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// It first builds a skeleton kd-tree as a basis, then computes the
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// bounding box of the data points, and then invokes rbd_tree() to
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// actually build the tree, passing it the appropriate splitting
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// and shrinking information.
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//----------------------------------------------------------------------
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ANNkd_ptr rbd_tree( // recursive construction of bd-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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ANNshrinkRule shrink); // shrinking rule
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ANNbd_tree::ANNbd_tree( // construct from point array
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ANNpointArray pa, // point array (with at least n pts)
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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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ANNsplitRule split, // splitting rule
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ANNshrinkRule shrink) // shrinking rule
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: ANNkd_tree(n, dd, bs) // build skeleton base tree
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{
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pts = pa; // where the points are
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if (n == 0) return; // no points--no sweat
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ANNorthRect bnd_box(dd); // bounding box for points
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// construct bounding rectangle
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annEnclRect(pa, pidx, n, dd, bnd_box);
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// copy to tree structure
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bnd_box_lo = annCopyPt(dd, bnd_box.lo);
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bnd_box_hi = annCopyPt(dd, bnd_box.hi);
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switch (split) { // build by rule
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case ANN_KD_STD: // standard kd-splitting rule
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root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, kd_split, shrink);
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break;
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case ANN_KD_MIDPT: // midpoint split
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root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, midpt_split, shrink);
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break;
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case ANN_KD_SUGGEST: // best (in our opinion)
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case ANN_KD_SL_MIDPT: // sliding midpoint split
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root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, sl_midpt_split, shrink);
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break;
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case ANN_KD_FAIR: // fair split
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root = rbd_tree(pa, pidx, n, dd, bs, bnd_box, fair_split, shrink);
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break;
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case ANN_KD_SL_FAIR: // sliding fair split
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root = rbd_tree(pa, pidx, n, dd, bs,
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bnd_box, sl_fair_split, shrink);
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break;
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default:
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annError("Illegal splitting method", ANNabort);
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}
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}
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//----------------------------------------------------------------------
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// Shrinking rules
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//----------------------------------------------------------------------
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enum ANNdecomp {SPLIT, SHRINK}; // decomposition methods
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//----------------------------------------------------------------------
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// trySimpleShrink - Attempt a simple shrink
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//
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// We compute the tight bounding box of the points, and compute
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// the 2*dim ``gaps'' between the sides of the tight box and the
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// bounding box. If any of the gaps is large enough relative to
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// the longest side of the tight bounding box, then we shrink
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// all sides whose gaps are large enough. (The reason for
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// comparing against the tight bounding box, is that after
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// shrinking the longest box size will decrease, and if we use
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// the standard bounding box, we may decide to shrink twice in
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// a row. Since the tight box is fixed, we cannot shrink twice
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// consecutively.)
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//----------------------------------------------------------------------
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const float BD_GAP_THRESH = 0.5; // gap threshold (must be < 1)
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const int BD_CT_THRESH = 2; // min number of shrink sides
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ANNdecomp trySimpleShrink( // try a simple shrink
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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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const ANNorthRect &bnd_box, // current bounding box
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ANNorthRect &inner_box) // inner box if shrinking (returned)
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{
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int i;
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// compute tight bounding box
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annEnclRect(pa, pidx, n, dim, inner_box);
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ANNcoord max_length = 0; // find longest box side
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for (i = 0; i < dim; i++) {
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ANNcoord length = inner_box.hi[i] - inner_box.lo[i];
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if (length > max_length) {
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max_length = length;
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}
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}
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int shrink_ct = 0; // number of sides we shrunk
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for (i = 0; i < dim; i++) { // select which sides to shrink
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// gap between boxes
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ANNcoord gap_hi = bnd_box.hi[i] - inner_box.hi[i];
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// big enough gap to shrink?
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if (gap_hi < max_length*BD_GAP_THRESH)
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inner_box.hi[i] = bnd_box.hi[i]; // no - expand
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else shrink_ct++; // yes - shrink this side
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// repeat for high side
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ANNcoord gap_lo = inner_box.lo[i] - bnd_box.lo[i];
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if (gap_lo < max_length*BD_GAP_THRESH)
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inner_box.lo[i] = bnd_box.lo[i]; // no - expand
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else shrink_ct++; // yes - shrink this side
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}
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if (shrink_ct >= BD_CT_THRESH) // did we shrink enough sides?
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return SHRINK;
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else return SPLIT;
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}
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//----------------------------------------------------------------------
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// tryCentroidShrink - Attempt a centroid shrink
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//
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// We repeatedly apply the splitting rule, always to the larger subset
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// of points, until the number of points decreases by the constant
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// fraction BD_FRACTION. If this takes more than dim*BD_MAX_SPLIT_FAC
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// splits for this to happen, then we shrink to the final inner box
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// Otherwise we split.
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//----------------------------------------------------------------------
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const float BD_MAX_SPLIT_FAC = 0.5; // maximum number of splits allowed
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const float BD_FRACTION = 0.5; // ...to reduce points by this fraction
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// ...This must be < 1.
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ANNdecomp tryCentroidShrink( // try a centroid shrink
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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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const ANNorthRect &bnd_box, // current bounding box
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ANNkd_splitter splitter, // splitting procedure
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ANNorthRect &inner_box) // inner box if shrinking (returned)
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{
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int n_sub = n; // number of points in subset
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int n_goal = (int) (n*BD_FRACTION); // number of point in goal
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int n_splits = 0; // number of splits needed
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// initialize inner box to bounding box
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annAssignRect(dim, inner_box, bnd_box);
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while (n_sub > n_goal) { // keep splitting until goal reached
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int cd; // cut dim from splitter (ignored)
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ANNcoord cv; // cut value from splitter (ignored)
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int n_lo; // number of points on low side
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// invoke splitting procedure
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(*splitter)(pa, pidx, inner_box, n_sub, dim, cd, cv, n_lo);
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n_splits++; // increment split count
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if (n_lo >= n_sub/2) { // most points on low side
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inner_box.hi[cd] = cv; // collapse high side
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n_sub = n_lo; // recurse on lower points
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}
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else { // most points on high side
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inner_box.lo[cd] = cv; // collapse low side
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pidx += n_lo; // recurse on higher points
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n_sub -= n_lo;
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}
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}
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if (n_splits > dim*BD_MAX_SPLIT_FAC)// took too many splits
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return SHRINK; // shrink to final subset
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else
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return SPLIT;
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}
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//----------------------------------------------------------------------
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// selectDecomp - select which decomposition to use
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//----------------------------------------------------------------------
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ANNdecomp selectDecomp( // select decomposition method
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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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const ANNorthRect &bnd_box, // current bounding box
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ANNkd_splitter splitter, // splitting procedure
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ANNshrinkRule shrink, // shrinking rule
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ANNorthRect &inner_box) // inner box if shrinking (returned)
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{
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ANNdecomp decomp = SPLIT; // decomposition
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switch (shrink) { // check shrinking rule
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case ANN_BD_NONE: // no shrinking allowed
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decomp = SPLIT;
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break;
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case ANN_BD_SUGGEST: // author's suggestion
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case ANN_BD_SIMPLE: // simple shrink
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decomp = trySimpleShrink(
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pa, pidx, // points and indices
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n, dim, // number of points and dimension
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bnd_box, // current bounding box
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inner_box); // inner box if shrinking (returned)
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break;
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case ANN_BD_CENTROID: // centroid shrink
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decomp = tryCentroidShrink(
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pa, pidx, // points and indices
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n, dim, // number of points and dimension
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bnd_box, // current bounding box
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splitter, // splitting procedure
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inner_box); // inner box if shrinking (returned)
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break;
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default:
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annError("Illegal shrinking rule", ANNabort);
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}
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return decomp;
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}
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//----------------------------------------------------------------------
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// rbd_tree - recursive procedure to build a bd-tree
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//
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// This is analogous to rkd_tree, but for bd-trees. See the
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// procedure rkd_tree() in kd_split.cpp for more information.
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//
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// If the number of points falls below the bucket size, then a
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// leaf node is created for the points. Otherwise we invoke the
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// procedure selectDecomp() which determines whether we are to
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// split or shrink. If splitting is chosen, then we essentially
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// do exactly as rkd_tree() would, and invoke the specified
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// splitting procedure to the points. Otherwise, the selection
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// procedure returns a bounding box, from which we extract the
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// appropriate shrinking bounds, and create a shrinking node.
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// Finally the points are subdivided, and the procedure is
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// invoked recursively on the two subsets to form the children.
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//----------------------------------------------------------------------
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ANNkd_ptr rbd_tree( // recursive construction of bd-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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ANNshrinkRule shrink) // shrinking rule
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{
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ANNdecomp decomp; // decomposition method
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ANNorthRect inner_box(dim); // inner box (if shrinking)
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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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||
|
|
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||
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decomp = selectDecomp( // select decomposition method
|
||
|
|
pa, pidx, // points and indices
|
||
|
|
n, dim, // number of points and dimension
|
||
|
|
bnd_box, // current bounding box
|
||
|
|
splitter, shrink, // splitting/shrinking methods
|
||
|
|
inner_box); // inner box if shrinking (returned)
|
||
|
|
|
||
|
|
if (decomp == SPLIT) { // split selected
|
||
|
|
int cd; // cutting dimension
|
||
|
|
ANNcoord cv; // cutting value
|
||
|
|
int n_lo; // number on low side of cut
|
||
|
|
// invoke splitting procedure
|
||
|
|
(*splitter)(pa, pidx, bnd_box, n, dim, cd, cv, n_lo);
|
||
|
|
|
||
|
|
ANNcoord lv = bnd_box.lo[cd]; // save bounds for cutting dimension
|
||
|
|
ANNcoord hv = bnd_box.hi[cd];
|
||
|
|
|
||
|
|
bnd_box.hi[cd] = cv; // modify bounds for left subtree
|
||
|
|
ANNkd_ptr lo = rbd_tree( // build left subtree
|
||
|
|
pa, pidx, n_lo, // ...from pidx[0..n_lo-1]
|
||
|
|
dim, bsp, bnd_box, splitter, shrink);
|
||
|
|
bnd_box.hi[cd] = hv; // restore bounds
|
||
|
|
|
||
|
|
bnd_box.lo[cd] = cv; // modify bounds for right subtree
|
||
|
|
ANNkd_ptr hi = rbd_tree( // build right subtree
|
||
|
|
pa, pidx + n_lo, n-n_lo,// ...from pidx[n_lo..n-1]
|
||
|
|
dim, bsp, bnd_box, splitter, shrink);
|
||
|
|
bnd_box.lo[cd] = lv; // restore bounds
|
||
|
|
// create the splitting node
|
||
|
|
return new ANNkd_split(cd, cv, lv, hv, lo, hi);
|
||
|
|
}
|
||
|
|
else { // shrink selected
|
||
|
|
int n_in; // number of points in box
|
||
|
|
int n_bnds; // number of bounding sides
|
||
|
|
|
||
|
|
annBoxSplit( // split points around inner box
|
||
|
|
pa, // points to split
|
||
|
|
pidx, // point indices
|
||
|
|
n, // number of points
|
||
|
|
dim, // dimension
|
||
|
|
inner_box, // inner box
|
||
|
|
n_in); // number of points inside (returned)
|
||
|
|
|
||
|
|
ANNkd_ptr in = rbd_tree( // build inner subtree pidx[0..n_in-1]
|
||
|
|
pa, pidx, n_in, dim, bsp, inner_box, splitter, shrink);
|
||
|
|
ANNkd_ptr out = rbd_tree( // build outer subtree pidx[n_in..n]
|
||
|
|
pa, pidx+n_in, n - n_in, dim, bsp, bnd_box, splitter, shrink);
|
||
|
|
|
||
|
|
ANNorthHSArray bnds = NULL; // bounds (alloc in Box2Bnds and
|
||
|
|
// ...freed in bd_shrink destroyer)
|
||
|
|
|
||
|
|
annBox2Bnds( // convert inner box to bounds
|
||
|
|
inner_box, // inner box
|
||
|
|
bnd_box, // enclosing box
|
||
|
|
dim, // dimension
|
||
|
|
n_bnds, // number of bounds (returned)
|
||
|
|
bnds); // bounds array (modified)
|
||
|
|
|
||
|
|
// return shrinking node
|
||
|
|
return new ANNbd_shrink(n_bnds, bnds, in, out);
|
||
|
|
}
|
||
|
|
}
|