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Diffstat (limited to 'geom_bottleneck/bottleneck/src/ann/kd_split.cpp')
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diff --git a/geom_bottleneck/bottleneck/src/ann/kd_split.cpp b/geom_bottleneck/bottleneck/src/ann/kd_split.cpp deleted file mode 100644 index 7979aaa..0000000 --- a/geom_bottleneck/bottleneck/src/ann/kd_split.cpp +++ /dev/null @@ -1,632 +0,0 @@ -//---------------------------------------------------------------------- -// File: kd_split.cpp -// Programmer: Sunil Arya and David Mount -// Description: Methods for splitting kd-trees -// Last modified: 01/04/05 (Version 1.0) -//---------------------------------------------------------------------- -// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and -// David Mount. All Rights Reserved. -// -// This software and related documentation is part of the Approximate -// Nearest Neighbor Library (ANN). This software is provided under -// the provisions of the Lesser GNU Public License (LGPL). See the -// file ../ReadMe.txt for further information. -// -// The University of Maryland (U.M.) and the authors make no -// representations about the suitability or fitness of this software for -// any purpose. It is provided "as is" without express or implied -// warranty. -//---------------------------------------------------------------------- -// History: -// Revision 0.1 03/04/98 -// Initial release -// Revision 1.0 04/01/05 -//---------------------------------------------------------------------- - -#include "kd_tree.h" // kd-tree definitions -#include "kd_util.h" // kd-tree utilities -#include "kd_split.h" // splitting functions - -namespace geom_bt { -//---------------------------------------------------------------------- -// Constants -//---------------------------------------------------------------------- - -const double ERR = 0.001; // a small value -const double FS_ASPECT_RATIO = 3.0; // maximum allowed aspect ratio - // in fair split. Must be >= 2. - -//---------------------------------------------------------------------- -// NOTE: Virtually all point indexing is done through an index (i.e. -// permutation) array pidx. Consequently, a reference to the d-th -// coordinate of the i-th point is pa[pidx[i]][d]. The macro PA(i,d) -// is a shorthand for this. -//---------------------------------------------------------------------- - // standard 2-d indirect indexing -#define PA(i,d) (pa[pidx[(i)]][(d)]) - // accessing a single point -#define PP(i) (pa[pidx[(i)]]) - - -//---------------------------------------------------------------------- -// kd_split - Bentley's standard splitting routine for kd-trees -// Find the dimension of the greatest spread, and split -// just before the median point along this dimension. -//---------------------------------------------------------------------- - -void kd_split( - ANNpointArray pa, // point array (permuted on return) - ANNidxArray pidx, // point indices - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo) // num of points on low side (returned) -{ - // find dimension of maximum spread - cut_dim = annMaxSpread(pa, pidx, n, dim); - n_lo = n/2; // median rank - // split about median - annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); -} - -//---------------------------------------------------------------------- -// midpt_split - midpoint splitting rule for box-decomposition trees -// -// This is the simplest splitting rule that guarantees boxes -// of bounded aspect ratio. It simply cuts the box with the -// longest side through its midpoint. If there are ties, it -// selects the dimension with the maximum point spread. -// -// WARNING: This routine (while simple) doesn't seem to work -// well in practice in high dimensions, because it tends to -// generate a large number of trivial and/or unbalanced splits. -// Either kd_split(), sl_midpt_split(), or fair_split() are -// recommended, instead. -//---------------------------------------------------------------------- - -void midpt_split( - ANNpointArray pa, // point array - ANNidxArray pidx, // point indices (permuted on return) - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo) // num of points on low side (returned) -{ - int d; - - ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; - for (d = 1; d < dim; d++) { // find length of longest box side - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (length > max_length) { - max_length = length; - } - } - ANNcoord max_spread = -1; // find long side with most spread - for (d = 0; d < dim; d++) { - // is it among longest? - if (double(bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { - // compute its spread - ANNcoord spr = annSpread(pa, pidx, n, d); - if (spr > max_spread) { // is it max so far? - max_spread = spr; - cut_dim = d; - } - } - } - // split along cut_dim at midpoint - cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim]) / 2; - // permute points accordingly - int br1, br2; - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - //------------------------------------------------------------------ - // On return: pa[0..br1-1] < cut_val - // pa[br1..br2-1] == cut_val - // pa[br2..n-1] > cut_val - // - // We can set n_lo to any value in the range [br1..br2]. - // We choose split so that points are most evenly divided. - //------------------------------------------------------------------ - if (br1 > n/2) n_lo = br1; - else if (br2 < n/2) n_lo = br2; - else n_lo = n/2; -} - -//---------------------------------------------------------------------- -// sl_midpt_split - sliding midpoint splitting rule -// -// This is a modification of midpt_split, which has the nonsensical -// name "sliding midpoint". The idea is that we try to use the -// midpoint rule, by bisecting the longest side. If there are -// ties, the dimension with the maximum spread is selected. If, -// however, the midpoint split produces a trivial split (no points -// on one side of the splitting plane) then we slide the splitting -// (maintaining its orientation) until it produces a nontrivial -// split. For example, if the splitting plane is along the x-axis, -// and all the data points have x-coordinate less than the x-bisector, -// then the split is taken along the maximum x-coordinate of the -// data points. -// -// Intuitively, this rule cannot generate trivial splits, and -// hence avoids midpt_split's tendency to produce trees with -// a very large number of nodes. -// -//---------------------------------------------------------------------- - -void sl_midpt_split( - ANNpointArray pa, // point array - ANNidxArray pidx, // point indices (permuted on return) - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo) // num of points on low side (returned) -{ - int d; - - ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; - for (d = 1; d < dim; d++) { // find length of longest box side - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (length > max_length) { - max_length = length; - } - } - ANNcoord max_spread = -1; // find long side with most spread - for (d = 0; d < dim; d++) { - // is it among longest? - if ((bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { - // compute its spread - ANNcoord spr = annSpread(pa, pidx, n, d); - if (spr > max_spread) { // is it max so far? - max_spread = spr; - cut_dim = d; - } - } - } - // ideal split at midpoint - ANNcoord ideal_cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim])/2; - - ANNcoord min, max; - annMinMax(pa, pidx, n, cut_dim, min, max); // find min/max coordinates - - if (ideal_cut_val < min) // slide to min or max as needed - cut_val = min; - else if (ideal_cut_val > max) - cut_val = max; - else - cut_val = ideal_cut_val; - - // permute points accordingly - int br1, br2; - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - //------------------------------------------------------------------ - // On return: pa[0..br1-1] < cut_val - // pa[br1..br2-1] == cut_val - // pa[br2..n-1] > cut_val - // - // We can set n_lo to any value in the range [br1..br2] to satisfy - // the exit conditions of the procedure. - // - // if ideal_cut_val < min (implying br2 >= 1), - // then we select n_lo = 1 (so there is one point on left) and - // if ideal_cut_val > max (implying br1 <= n-1), - // then we select n_lo = n-1 (so there is one point on right). - // Otherwise, we select n_lo as close to n/2 as possible within - // [br1..br2]. - //------------------------------------------------------------------ - if (ideal_cut_val < min) n_lo = 1; - else if (ideal_cut_val > max) n_lo = n-1; - else if (br1 > n/2) n_lo = br1; - else if (br2 < n/2) n_lo = br2; - else n_lo = n/2; -} - -//---------------------------------------------------------------------- -// fair_split - fair-split splitting rule -// -// This is a compromise between the kd-tree splitting rule (which -// always splits data points at their median) and the midpoint -// splitting rule (which always splits a box through its center. -// The goal of this procedure is to achieve both nicely balanced -// splits, and boxes of bounded aspect ratio. -// -// A constant FS_ASPECT_RATIO is defined. Given a box, those sides -// which can be split so that the ratio of the longest to shortest -// side does not exceed ASPECT_RATIO are identified. Among these -// sides, we select the one in which the points have the largest -// spread. We then split the points in a manner which most evenly -// distributes the points on either side of the splitting plane, -// subject to maintaining the bound on the ratio of long to short -// sides. To determine that the aspect ratio will be preserved, -// we determine the longest side (other than this side), and -// determine how narrowly we can cut this side, without causing the -// aspect ratio bound to be exceeded (small_piece). -// -// This procedure is more robust than either kd_split or midpt_split, -// but is more complicated as well. When point distribution is -// extremely skewed, this degenerates to midpt_split (actually -// 1/3 point split), and when the points are most evenly distributed, -// this degenerates to kd-split. -//---------------------------------------------------------------------- - -void fair_split( - ANNpointArray pa, // point array - ANNidxArray pidx, // point indices (permuted on return) - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo) // num of points on low side (returned) -{ - int d; - ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; - cut_dim = 0; - for (d = 1; d < dim; d++) { // find length of longest box side - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (length > max_length) { - max_length = length; - cut_dim = d; - } - } - - ANNcoord max_spread = 0; // find legal cut with max spread - cut_dim = 0; - for (d = 0; d < dim; d++) { - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - // is this side midpoint splitable - // without violating aspect ratio? - if (((double) max_length)*2.0/((double) length) <= FS_ASPECT_RATIO) { - // compute spread along this dim - ANNcoord spr = annSpread(pa, pidx, n, d); - if (spr > max_spread) { // best spread so far - max_spread = spr; - cut_dim = d; // this is dimension to cut - } - } - } - - max_length = 0; // find longest side other than cut_dim - for (d = 0; d < dim; d++) { - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (d != cut_dim && length > max_length) - max_length = length; - } - // consider most extreme splits - ANNcoord small_piece = max_length / FS_ASPECT_RATIO; - ANNcoord lo_cut = bnds.lo[cut_dim] + small_piece;// lowest legal cut - ANNcoord hi_cut = bnds.hi[cut_dim] - small_piece;// highest legal cut - - int br1, br2; - // is median below lo_cut ? - if (annSplitBalance(pa, pidx, n, cut_dim, lo_cut) >= 0) { - cut_val = lo_cut; // cut at lo_cut - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - n_lo = br1; - } - // is median above hi_cut? - else if (annSplitBalance(pa, pidx, n, cut_dim, hi_cut) <= 0) { - cut_val = hi_cut; // cut at hi_cut - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - n_lo = br2; - } - else { // median cut preserves asp ratio - n_lo = n/2; // split about median - annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); - } -} - -//---------------------------------------------------------------------- -// sl_fair_split - sliding fair split splitting rule -// -// Sliding fair split is a splitting rule that combines the -// strengths of both fair split with sliding midpoint split. -// Fair split tends to produce balanced splits when the points -// are roughly uniformly distributed, but it can produce many -// trivial splits when points are highly clustered. Sliding -// midpoint never produces trivial splits, and shrinks boxes -// nicely if points are highly clustered, but it may produce -// rather unbalanced splits when points are unclustered but not -// quite uniform. -// -// Sliding fair split is based on the theory that there are two -// types of splits that are "good": balanced splits that produce -// fat boxes, and unbalanced splits provided the cell with fewer -// points is fat. -// -// This splitting rule operates by first computing the longest -// side of the current bounding box. Then it asks which sides -// could be split (at the midpoint) and still satisfy the aspect -// ratio bound with respect to this side. Among these, it selects -// the side with the largest spread (as fair split would). It -// then considers the most extreme cuts that would be allowed by -// the aspect ratio bound. This is done by dividing the longest -// side of the box by the aspect ratio bound. If the median cut -// lies between these extreme cuts, then we use the median cut. -// If not, then consider the extreme cut that is closer to the -// median. If all the points lie to one side of this cut, then -// we slide the cut until it hits the first point. This may -// violate the aspect ratio bound, but will never generate empty -// cells. However the sibling of every such skinny cell is fat, -// and hence packing arguments still apply. -// -//---------------------------------------------------------------------- - -void sl_fair_split( - ANNpointArray pa, // point array - ANNidxArray pidx, // point indices (permuted on return) - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo) // num of points on low side (returned) -{ - int d; - ANNcoord min, max; // min/max coordinates - int br1, br2; // split break points - - ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; - cut_dim = 0; - for (d = 1; d < dim; d++) { // find length of longest box side - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (length > max_length) { - max_length = length; - cut_dim = d; - } - } - - ANNcoord max_spread = 0; // find legal cut with max spread - cut_dim = 0; - for (d = 0; d < dim; d++) { - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - // is this side midpoint splitable - // without violating aspect ratio? - if (((double) max_length)*2.0/((double) length) <= FS_ASPECT_RATIO) { - // compute spread along this dim - ANNcoord spr = annSpread(pa, pidx, n, d); - if (spr > max_spread) { // best spread so far - max_spread = spr; - cut_dim = d; // this is dimension to cut - } - } - } - - max_length = 0; // find longest side other than cut_dim - for (d = 0; d < dim; d++) { - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (d != cut_dim && length > max_length) - max_length = length; - } - // consider most extreme splits - ANNcoord small_piece = max_length / FS_ASPECT_RATIO; - ANNcoord lo_cut = bnds.lo[cut_dim] + small_piece;// lowest legal cut - ANNcoord hi_cut = bnds.hi[cut_dim] - small_piece;// highest legal cut - // find min and max along cut_dim - annMinMax(pa, pidx, n, cut_dim, min, max); - // is median below lo_cut? - if (annSplitBalance(pa, pidx, n, cut_dim, lo_cut) >= 0) { - if (max > lo_cut) { // are any points above lo_cut? - cut_val = lo_cut; // cut at lo_cut - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - n_lo = br1; // balance if there are ties - } - else { // all points below lo_cut - cut_val = max; // cut at max value - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - n_lo = n-1; - } - } - // is median above hi_cut? - else if (annSplitBalance(pa, pidx, n, cut_dim, hi_cut) <= 0) { - if (min < hi_cut) { // are any points below hi_cut? - cut_val = hi_cut; // cut at hi_cut - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - n_lo = br2; // balance if there are ties - } - else { // all points above hi_cut - cut_val = min; // cut at min value - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - n_lo = 1; - } - } - else { // median cut is good enough - n_lo = n/2; // split about median - annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); - } -} - - -///////////////////////////////////////////////////////////////////////////////// -// for kd-trees with deletion -// -//---------------------------------------------------------------------- -// kd_split - Bentley's standard splitting routine for kd-trees -// Find the dimension of the greatest spread, and split -// just before the median point along this dimension. -//---------------------------------------------------------------------- - -void kd_split_wd( - ANNpointArray pa, // point array (permuted on return) - ANNidxArray pidx, // point indices - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo, // num of points on low side (returned) - int &cut_pt_idx) // index of cutting point (returned) -{ - // find dimension of maximum spread - cut_dim = annMaxSpread(pa, pidx, n, dim); - n_lo = n/2; // median rank - // split about median - annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); - cut_pt_idx = n_lo; - cut_val = PA(cut_pt_idx, cut_dim); -} - -//---------------------------------------------------------------------- -// midpt_split - midpoint splitting rule for box-decomposition trees -// -// This is the simplest splitting rule that guarantees boxes -// of bounded aspect ratio. It simply cuts the box with the -// longest side through its midpoint. If there are ties, it -// selects the dimension with the maximum point spread. -// -// WARNING: This routine (while simple) doesn't seem to work -// well in practice in high dimensions, because it tends to -// generate a large number of trivial and/or unbalanced splits. -// Either kd_split(), sl_midpt_split(), or fair_split() are -// recommended, instead. -//---------------------------------------------------------------------- - -void midpt_split_wd( - ANNpointArray pa, // point array - ANNidxArray pidx, // point indices (permuted on return) - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo, // num of points on low side (returned) - int &cut_pt_idx) // index of cutting point (returned) -{ - int d; - - ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; - for (d = 1; d < dim; d++) { // find length of longest box side - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (length > max_length) { - max_length = length; - } - } - ANNcoord max_spread = -1; // find long side with most spread - for (d = 0; d < dim; d++) { - // is it among longest? - if (double(bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { - // compute its spread - ANNcoord spr = annSpread(pa, pidx, n, d); - if (spr > max_spread) { // is it max so far? - max_spread = spr; - cut_dim = d; - } - } - } - // split along cut_dim at midpoint - cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim]) / 2; - // permute points accordingly - int br1, br2; - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - //------------------------------------------------------------------ - // On return: pa[0..br1-1] < cut_val - // pa[br1..br2-1] == cut_val - // pa[br2..n-1] > cut_val - // - // We can set n_lo to any value in the range [br1..br2]. - // We choose split so that points are most evenly divided. - //------------------------------------------------------------------ - if (br1 > n/2) n_lo = br1; - else if (br2 < n/2) n_lo = br2; - else n_lo = n/2; - - cut_pt_idx = n_lo; - cut_val = PA(cut_pt_idx, cut_dim); - -} - -//---------------------------------------------------------------------- -// sl_midpt_split - sliding midpoint splitting rule -// -// This is a modification of midpt_split, which has the nonsensical -// name "sliding midpoint". The idea is that we try to use the -// midpoint rule, by bisecting the longest side. If there are -// ties, the dimension with the maximum spread is selected. If, -// however, the midpoint split produces a trivial split (no points -// on one side of the splitting plane) then we slide the splitting -// (maintaining its orientation) until it produces a nontrivial -// split. For example, if the splitting plane is along the x-axis, -// and all the data points have x-coordinate less than the x-bisector, -// then the split is taken along the maximum x-coordinate of the -// data points. -// -// Intuitively, this rule cannot generate trivial splits, and -// hence avoids midpt_split's tendency to produce trees with -// a very large number of nodes. -// -//---------------------------------------------------------------------- - -void sl_midpt_split_wd( - ANNpointArray pa, // point array - ANNidxArray pidx, // point indices (permuted on return) - const ANNorthRect &bnds, // bounding rectangle for cell - int n, // number of points - int dim, // dimension of space - int &cut_dim, // cutting dimension (returned) - ANNcoord &cut_val, // cutting value (returned) - int &n_lo, // num of points on low side (returned) - int &cut_pt_idx) // index of cutting point (returned) -{ - int d; - - ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; - for (d = 1; d < dim; d++) { // find length of longest box side - ANNcoord length = bnds.hi[d] - bnds.lo[d]; - if (length > max_length) { - max_length = length; - } - } - ANNcoord max_spread = -1; // find long side with most spread - for (d = 0; d < dim; d++) { - // is it among longest? - if ((bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { - // compute its spread - ANNcoord spr = annSpread(pa, pidx, n, d); - if (spr > max_spread) { // is it max so far? - max_spread = spr; - cut_dim = d; - } - } - } - // ideal split at midpoint - ANNcoord ideal_cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim])/2; - - ANNcoord min, max; - annMinMax(pa, pidx, n, cut_dim, min, max); // find min/max coordinates - - if (ideal_cut_val < min) // slide to min or max as needed - cut_val = min; - else if (ideal_cut_val > max) - cut_val = max; - else - cut_val = ideal_cut_val; - - // permute points accordingly - int br1, br2; - annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); - //------------------------------------------------------------------ - // On return: pa[0..br1-1] < cut_val - // pa[br1..br2-1] == cut_val - // pa[br2..n-1] > cut_val - // - // We can set n_lo to any value in the range [br1..br2] to satisfy - // the exit conditions of the procedure. - // - // if ideal_cut_val < min (implying br2 >= 1), - // then we select n_lo = 1 (so there is one point on left) and - // if ideal_cut_val > max (implying br1 <= n-1), - // then we select n_lo = n-1 (so there is one point on right). - // Otherwise, we select n_lo as close to n/2 as possible within - // [br1..br2]. - //------------------------------------------------------------------ - if (ideal_cut_val < min) n_lo = 1; - else if (ideal_cut_val > max) n_lo = n-1; - else if (br1 > n/2) n_lo = br1; - else if (br2 < n/2) n_lo = br2; - else n_lo = n/2; -} -} |