[37] | 1 | //---------------------------------------------------------------------- |
---|
| 2 | // File: kd_split.cpp |
---|
| 3 | // Programmer: Sunil Arya and David Mount |
---|
| 4 | // Description: Methods for splitting kd-trees |
---|
| 5 | // Last modified: 01/04/05 (Version 1.0) |
---|
| 6 | //---------------------------------------------------------------------- |
---|
| 7 | // Copyright (c) 1997-2005 University of Maryland and Sunil Arya and |
---|
| 8 | // David Mount. All Rights Reserved. |
---|
| 9 | // |
---|
| 10 | // This software and related documentation is part of the Approximate |
---|
| 11 | // Nearest Neighbor Library (ANN). This software is provided under |
---|
| 12 | // the provisions of the Lesser GNU Public License (LGPL). See the |
---|
| 13 | // file ../ReadMe.txt for further information. |
---|
| 14 | // |
---|
| 15 | // The University of Maryland (U.M.) and the authors make no |
---|
| 16 | // representations about the suitability or fitness of this software for |
---|
| 17 | // any purpose. It is provided "as is" without express or implied |
---|
| 18 | // warranty. |
---|
| 19 | //---------------------------------------------------------------------- |
---|
| 20 | // History: |
---|
| 21 | // Revision 0.1 03/04/98 |
---|
| 22 | // Initial release |
---|
| 23 | // Revision 1.0 04/01/05 |
---|
| 24 | //---------------------------------------------------------------------- |
---|
| 25 | |
---|
| 26 | #include "kd_tree.h" // kd-tree definitions |
---|
| 27 | #include "kd_util.h" // kd-tree utilities |
---|
| 28 | #include "kd_split.h" // splitting functions |
---|
| 29 | |
---|
| 30 | //---------------------------------------------------------------------- |
---|
| 31 | // Constants |
---|
| 32 | //---------------------------------------------------------------------- |
---|
| 33 | |
---|
| 34 | const double ERR = 0.001; // a small value |
---|
| 35 | const double FS_ASPECT_RATIO = 3.0; // maximum allowed aspect ratio |
---|
| 36 | // in fair split. Must be >= 2. |
---|
| 37 | |
---|
| 38 | //---------------------------------------------------------------------- |
---|
| 39 | // kd_split - Bentley's standard splitting routine for kd-trees |
---|
| 40 | // Find the dimension of the greatest spread, and split |
---|
| 41 | // just before the median point along this dimension. |
---|
| 42 | //---------------------------------------------------------------------- |
---|
| 43 | |
---|
| 44 | void kd_split( |
---|
| 45 | ANNpointArray pa, // point array (permuted on return) |
---|
| 46 | ANNidxArray pidx, // point indices |
---|
| 47 | const ANNorthRect &bnds, // bounding rectangle for cell |
---|
| 48 | int n, // number of points |
---|
| 49 | int dim, // dimension of space |
---|
| 50 | int &cut_dim, // cutting dimension (returned) |
---|
| 51 | ANNcoord &cut_val, // cutting value (returned) |
---|
| 52 | int &n_lo) // num of points on low side (returned) |
---|
| 53 | { |
---|
| 54 | // find dimension of maximum spread |
---|
| 55 | cut_dim = annMaxSpread(pa, pidx, n, dim); |
---|
| 56 | n_lo = n/2; // median rank |
---|
| 57 | // split about median |
---|
| 58 | annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); |
---|
| 59 | } |
---|
| 60 | |
---|
| 61 | //---------------------------------------------------------------------- |
---|
| 62 | // midpt_split - midpoint splitting rule for box-decomposition trees |
---|
| 63 | // |
---|
| 64 | // This is the simplest splitting rule that guarantees boxes |
---|
| 65 | // of bounded aspect ratio. It simply cuts the box with the |
---|
| 66 | // longest side through its midpoint. If there are ties, it |
---|
| 67 | // selects the dimension with the maximum point spread. |
---|
| 68 | // |
---|
| 69 | // WARNING: This routine (while simple) doesn't seem to work |
---|
| 70 | // well in practice in high dimensions, because it tends to |
---|
| 71 | // generate a large number of trivial and/or unbalanced splits. |
---|
| 72 | // Either kd_split(), sl_midpt_split(), or fair_split() are |
---|
| 73 | // recommended, instead. |
---|
| 74 | //---------------------------------------------------------------------- |
---|
| 75 | |
---|
| 76 | void midpt_split( |
---|
| 77 | ANNpointArray pa, // point array |
---|
| 78 | ANNidxArray pidx, // point indices (permuted on return) |
---|
| 79 | const ANNorthRect &bnds, // bounding rectangle for cell |
---|
| 80 | int n, // number of points |
---|
| 81 | int dim, // dimension of space |
---|
| 82 | int &cut_dim, // cutting dimension (returned) |
---|
| 83 | ANNcoord &cut_val, // cutting value (returned) |
---|
| 84 | int &n_lo) // num of points on low side (returned) |
---|
| 85 | { |
---|
| 86 | int d; |
---|
| 87 | |
---|
| 88 | ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; |
---|
| 89 | for (d = 1; d < dim; d++) { // find length of longest box side |
---|
| 90 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 91 | if (length > max_length) { |
---|
| 92 | max_length = length; |
---|
| 93 | } |
---|
| 94 | } |
---|
| 95 | ANNcoord max_spread = -1; // find long side with most spread |
---|
| 96 | for (d = 0; d < dim; d++) { |
---|
| 97 | // is it among longest? |
---|
| 98 | if (double(bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { |
---|
| 99 | // compute its spread |
---|
| 100 | ANNcoord spr = annSpread(pa, pidx, n, d); |
---|
| 101 | if (spr > max_spread) { // is it max so far? |
---|
| 102 | max_spread = spr; |
---|
| 103 | cut_dim = d; |
---|
| 104 | } |
---|
| 105 | } |
---|
| 106 | } |
---|
| 107 | // split along cut_dim at midpoint |
---|
| 108 | cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim]) / 2; |
---|
| 109 | // permute points accordingly |
---|
| 110 | int br1, br2; |
---|
| 111 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 112 | //------------------------------------------------------------------ |
---|
| 113 | // On return: pa[0..br1-1] < cut_val |
---|
| 114 | // pa[br1..br2-1] == cut_val |
---|
| 115 | // pa[br2..n-1] > cut_val |
---|
| 116 | // |
---|
| 117 | // We can set n_lo to any value in the range [br1..br2]. |
---|
| 118 | // We choose split so that points are most evenly divided. |
---|
| 119 | //------------------------------------------------------------------ |
---|
| 120 | if (br1 > n/2) n_lo = br1; |
---|
| 121 | else if (br2 < n/2) n_lo = br2; |
---|
| 122 | else n_lo = n/2; |
---|
| 123 | } |
---|
| 124 | |
---|
| 125 | //---------------------------------------------------------------------- |
---|
| 126 | // sl_midpt_split - sliding midpoint splitting rule |
---|
| 127 | // |
---|
| 128 | // This is a modification of midpt_split, which has the nonsensical |
---|
| 129 | // name "sliding midpoint". The idea is that we try to use the |
---|
| 130 | // midpoint rule, by bisecting the longest side. If there are |
---|
| 131 | // ties, the dimension with the maximum spread is selected. If, |
---|
| 132 | // however, the midpoint split produces a trivial split (no points |
---|
| 133 | // on one side of the splitting plane) then we slide the splitting |
---|
| 134 | // (maintaining its orientation) until it produces a nontrivial |
---|
| 135 | // split. For example, if the splitting plane is along the x-axis, |
---|
| 136 | // and all the data points have x-coordinate less than the x-bisector, |
---|
| 137 | // then the split is taken along the maximum x-coordinate of the |
---|
| 138 | // data points. |
---|
| 139 | // |
---|
| 140 | // Intuitively, this rule cannot generate trivial splits, and |
---|
| 141 | // hence avoids midpt_split's tendency to produce trees with |
---|
| 142 | // a very large number of nodes. |
---|
| 143 | // |
---|
| 144 | //---------------------------------------------------------------------- |
---|
| 145 | |
---|
| 146 | void sl_midpt_split( |
---|
| 147 | ANNpointArray pa, // point array |
---|
| 148 | ANNidxArray pidx, // point indices (permuted on return) |
---|
| 149 | const ANNorthRect &bnds, // bounding rectangle for cell |
---|
| 150 | int n, // number of points |
---|
| 151 | int dim, // dimension of space |
---|
| 152 | int &cut_dim, // cutting dimension (returned) |
---|
| 153 | ANNcoord &cut_val, // cutting value (returned) |
---|
| 154 | int &n_lo) // num of points on low side (returned) |
---|
| 155 | { |
---|
| 156 | int d; |
---|
| 157 | |
---|
| 158 | ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; |
---|
| 159 | for (d = 1; d < dim; d++) { // find length of longest box side |
---|
| 160 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 161 | if (length > max_length) { |
---|
| 162 | max_length = length; |
---|
| 163 | } |
---|
| 164 | } |
---|
| 165 | ANNcoord max_spread = -1; // find long side with most spread |
---|
| 166 | for (d = 0; d < dim; d++) { |
---|
| 167 | // is it among longest? |
---|
| 168 | if ((bnds.hi[d] - bnds.lo[d]) >= (1-ERR)*max_length) { |
---|
| 169 | // compute its spread |
---|
| 170 | ANNcoord spr = annSpread(pa, pidx, n, d); |
---|
| 171 | if (spr > max_spread) { // is it max so far? |
---|
| 172 | max_spread = spr; |
---|
| 173 | cut_dim = d; |
---|
| 174 | } |
---|
| 175 | } |
---|
| 176 | } |
---|
| 177 | // ideal split at midpoint |
---|
| 178 | ANNcoord ideal_cut_val = (bnds.lo[cut_dim] + bnds.hi[cut_dim])/2; |
---|
| 179 | |
---|
| 180 | ANNcoord min, max; |
---|
| 181 | annMinMax(pa, pidx, n, cut_dim, min, max); // find min/max coordinates |
---|
| 182 | |
---|
| 183 | if (ideal_cut_val < min) // slide to min or max as needed |
---|
| 184 | cut_val = min; |
---|
| 185 | else if (ideal_cut_val > max) |
---|
| 186 | cut_val = max; |
---|
| 187 | else |
---|
| 188 | cut_val = ideal_cut_val; |
---|
| 189 | |
---|
| 190 | // permute points accordingly |
---|
| 191 | int br1, br2; |
---|
| 192 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 193 | //------------------------------------------------------------------ |
---|
| 194 | // On return: pa[0..br1-1] < cut_val |
---|
| 195 | // pa[br1..br2-1] == cut_val |
---|
| 196 | // pa[br2..n-1] > cut_val |
---|
| 197 | // |
---|
| 198 | // We can set n_lo to any value in the range [br1..br2] to satisfy |
---|
| 199 | // the exit conditions of the procedure. |
---|
| 200 | // |
---|
| 201 | // if ideal_cut_val < min (implying br2 >= 1), |
---|
| 202 | // then we select n_lo = 1 (so there is one point on left) and |
---|
| 203 | // if ideal_cut_val > max (implying br1 <= n-1), |
---|
| 204 | // then we select n_lo = n-1 (so there is one point on right). |
---|
| 205 | // Otherwise, we select n_lo as close to n/2 as possible within |
---|
| 206 | // [br1..br2]. |
---|
| 207 | //------------------------------------------------------------------ |
---|
| 208 | if (ideal_cut_val < min) n_lo = 1; |
---|
| 209 | else if (ideal_cut_val > max) n_lo = n-1; |
---|
| 210 | else if (br1 > n/2) n_lo = br1; |
---|
| 211 | else if (br2 < n/2) n_lo = br2; |
---|
| 212 | else n_lo = n/2; |
---|
| 213 | } |
---|
| 214 | |
---|
| 215 | //---------------------------------------------------------------------- |
---|
| 216 | // fair_split - fair-split splitting rule |
---|
| 217 | // |
---|
| 218 | // This is a compromise between the kd-tree splitting rule (which |
---|
| 219 | // always splits data points at their median) and the midpoint |
---|
| 220 | // splitting rule (which always splits a box through its center. |
---|
| 221 | // The goal of this procedure is to achieve both nicely balanced |
---|
| 222 | // splits, and boxes of bounded aspect ratio. |
---|
| 223 | // |
---|
| 224 | // A constant FS_ASPECT_RATIO is defined. Given a box, those sides |
---|
| 225 | // which can be split so that the ratio of the longest to shortest |
---|
| 226 | // side does not exceed ASPECT_RATIO are identified. Among these |
---|
| 227 | // sides, we select the one in which the points have the largest |
---|
| 228 | // spread. We then split the points in a manner which most evenly |
---|
| 229 | // distributes the points on either side of the splitting plane, |
---|
| 230 | // subject to maintaining the bound on the ratio of long to short |
---|
| 231 | // sides. To determine that the aspect ratio will be preserved, |
---|
| 232 | // we determine the longest side (other than this side), and |
---|
| 233 | // determine how narrowly we can cut this side, without causing the |
---|
| 234 | // aspect ratio bound to be exceeded (small_piece). |
---|
| 235 | // |
---|
| 236 | // This procedure is more robust than either kd_split or midpt_split, |
---|
| 237 | // but is more complicated as well. When point distribution is |
---|
| 238 | // extremely skewed, this degenerates to midpt_split (actually |
---|
| 239 | // 1/3 point split), and when the points are most evenly distributed, |
---|
| 240 | // this degenerates to kd-split. |
---|
| 241 | //---------------------------------------------------------------------- |
---|
| 242 | |
---|
| 243 | void fair_split( |
---|
| 244 | ANNpointArray pa, // point array |
---|
| 245 | ANNidxArray pidx, // point indices (permuted on return) |
---|
| 246 | const ANNorthRect &bnds, // bounding rectangle for cell |
---|
| 247 | int n, // number of points |
---|
| 248 | int dim, // dimension of space |
---|
| 249 | int &cut_dim, // cutting dimension (returned) |
---|
| 250 | ANNcoord &cut_val, // cutting value (returned) |
---|
| 251 | int &n_lo) // num of points on low side (returned) |
---|
| 252 | { |
---|
| 253 | int d; |
---|
| 254 | ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; |
---|
| 255 | cut_dim = 0; |
---|
| 256 | for (d = 1; d < dim; d++) { // find length of longest box side |
---|
| 257 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 258 | if (length > max_length) { |
---|
| 259 | max_length = length; |
---|
| 260 | cut_dim = d; |
---|
| 261 | } |
---|
| 262 | } |
---|
| 263 | |
---|
| 264 | ANNcoord max_spread = 0; // find legal cut with max spread |
---|
| 265 | cut_dim = 0; |
---|
| 266 | for (d = 0; d < dim; d++) { |
---|
| 267 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 268 | // is this side midpoint splitable |
---|
| 269 | // without violating aspect ratio? |
---|
| 270 | if (((double) max_length)*2.0/((double) length) <= FS_ASPECT_RATIO) { |
---|
| 271 | // compute spread along this dim |
---|
| 272 | ANNcoord spr = annSpread(pa, pidx, n, d); |
---|
| 273 | if (spr > max_spread) { // best spread so far |
---|
| 274 | max_spread = spr; |
---|
| 275 | cut_dim = d; // this is dimension to cut |
---|
| 276 | } |
---|
| 277 | } |
---|
| 278 | } |
---|
| 279 | |
---|
| 280 | max_length = 0; // find longest side other than cut_dim |
---|
| 281 | for (d = 0; d < dim; d++) { |
---|
| 282 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 283 | if (d != cut_dim && length > max_length) |
---|
| 284 | max_length = length; |
---|
| 285 | } |
---|
| 286 | // consider most extreme splits |
---|
| 287 | ANNcoord small_piece = max_length / FS_ASPECT_RATIO; |
---|
| 288 | ANNcoord lo_cut = bnds.lo[cut_dim] + small_piece;// lowest legal cut |
---|
| 289 | ANNcoord hi_cut = bnds.hi[cut_dim] - small_piece;// highest legal cut |
---|
| 290 | |
---|
| 291 | int br1, br2; |
---|
| 292 | // is median below lo_cut ? |
---|
| 293 | if (annSplitBalance(pa, pidx, n, cut_dim, lo_cut) >= 0) { |
---|
| 294 | cut_val = lo_cut; // cut at lo_cut |
---|
| 295 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 296 | n_lo = br1; |
---|
| 297 | } |
---|
| 298 | // is median above hi_cut? |
---|
| 299 | else if (annSplitBalance(pa, pidx, n, cut_dim, hi_cut) <= 0) { |
---|
| 300 | cut_val = hi_cut; // cut at hi_cut |
---|
| 301 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 302 | n_lo = br2; |
---|
| 303 | } |
---|
| 304 | else { // median cut preserves asp ratio |
---|
| 305 | n_lo = n/2; // split about median |
---|
| 306 | annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); |
---|
| 307 | } |
---|
| 308 | } |
---|
| 309 | |
---|
| 310 | //---------------------------------------------------------------------- |
---|
| 311 | // sl_fair_split - sliding fair split splitting rule |
---|
| 312 | // |
---|
| 313 | // Sliding fair split is a splitting rule that combines the |
---|
| 314 | // strengths of both fair split with sliding midpoint split. |
---|
| 315 | // Fair split tends to produce balanced splits when the points |
---|
| 316 | // are roughly uniformly distributed, but it can produce many |
---|
| 317 | // trivial splits when points are highly clustered. Sliding |
---|
| 318 | // midpoint never produces trivial splits, and shrinks boxes |
---|
| 319 | // nicely if points are highly clustered, but it may produce |
---|
| 320 | // rather unbalanced splits when points are unclustered but not |
---|
| 321 | // quite uniform. |
---|
| 322 | // |
---|
| 323 | // Sliding fair split is based on the theory that there are two |
---|
| 324 | // types of splits that are "good": balanced splits that produce |
---|
| 325 | // fat boxes, and unbalanced splits provided the cell with fewer |
---|
| 326 | // points is fat. |
---|
| 327 | // |
---|
| 328 | // This splitting rule operates by first computing the longest |
---|
| 329 | // side of the current bounding box. Then it asks which sides |
---|
| 330 | // could be split (at the midpoint) and still satisfy the aspect |
---|
| 331 | // ratio bound with respect to this side. Among these, it selects |
---|
| 332 | // the side with the largest spread (as fair split would). It |
---|
| 333 | // then considers the most extreme cuts that would be allowed by |
---|
| 334 | // the aspect ratio bound. This is done by dividing the longest |
---|
| 335 | // side of the box by the aspect ratio bound. If the median cut |
---|
| 336 | // lies between these extreme cuts, then we use the median cut. |
---|
| 337 | // If not, then consider the extreme cut that is closer to the |
---|
| 338 | // median. If all the points lie to one side of this cut, then |
---|
| 339 | // we slide the cut until it hits the first point. This may |
---|
| 340 | // violate the aspect ratio bound, but will never generate empty |
---|
| 341 | // cells. However the sibling of every such skinny cell is fat, |
---|
| 342 | // and hence packing arguments still apply. |
---|
| 343 | // |
---|
| 344 | //---------------------------------------------------------------------- |
---|
| 345 | |
---|
| 346 | void sl_fair_split( |
---|
| 347 | ANNpointArray pa, // point array |
---|
| 348 | ANNidxArray pidx, // point indices (permuted on return) |
---|
| 349 | const ANNorthRect &bnds, // bounding rectangle for cell |
---|
| 350 | int n, // number of points |
---|
| 351 | int dim, // dimension of space |
---|
| 352 | int &cut_dim, // cutting dimension (returned) |
---|
| 353 | ANNcoord &cut_val, // cutting value (returned) |
---|
| 354 | int &n_lo) // num of points on low side (returned) |
---|
| 355 | { |
---|
| 356 | int d; |
---|
| 357 | ANNcoord min, max; // min/max coordinates |
---|
| 358 | int br1, br2; // split break points |
---|
| 359 | |
---|
| 360 | ANNcoord max_length = bnds.hi[0] - bnds.lo[0]; |
---|
| 361 | cut_dim = 0; |
---|
| 362 | for (d = 1; d < dim; d++) { // find length of longest box side |
---|
| 363 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 364 | if (length > max_length) { |
---|
| 365 | max_length = length; |
---|
| 366 | cut_dim = d; |
---|
| 367 | } |
---|
| 368 | } |
---|
| 369 | |
---|
| 370 | ANNcoord max_spread = 0; // find legal cut with max spread |
---|
| 371 | cut_dim = 0; |
---|
| 372 | for (d = 0; d < dim; d++) { |
---|
| 373 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 374 | // is this side midpoint splitable |
---|
| 375 | // without violating aspect ratio? |
---|
| 376 | if (((double) max_length)*2.0/((double) length) <= FS_ASPECT_RATIO) { |
---|
| 377 | // compute spread along this dim |
---|
| 378 | ANNcoord spr = annSpread(pa, pidx, n, d); |
---|
| 379 | if (spr > max_spread) { // best spread so far |
---|
| 380 | max_spread = spr; |
---|
| 381 | cut_dim = d; // this is dimension to cut |
---|
| 382 | } |
---|
| 383 | } |
---|
| 384 | } |
---|
| 385 | |
---|
| 386 | max_length = 0; // find longest side other than cut_dim |
---|
| 387 | for (d = 0; d < dim; d++) { |
---|
| 388 | ANNcoord length = bnds.hi[d] - bnds.lo[d]; |
---|
| 389 | if (d != cut_dim && length > max_length) |
---|
| 390 | max_length = length; |
---|
| 391 | } |
---|
| 392 | // consider most extreme splits |
---|
| 393 | ANNcoord small_piece = max_length / FS_ASPECT_RATIO; |
---|
| 394 | ANNcoord lo_cut = bnds.lo[cut_dim] + small_piece;// lowest legal cut |
---|
| 395 | ANNcoord hi_cut = bnds.hi[cut_dim] - small_piece;// highest legal cut |
---|
| 396 | // find min and max along cut_dim |
---|
| 397 | annMinMax(pa, pidx, n, cut_dim, min, max); |
---|
| 398 | // is median below lo_cut? |
---|
| 399 | if (annSplitBalance(pa, pidx, n, cut_dim, lo_cut) >= 0) { |
---|
| 400 | if (max > lo_cut) { // are any points above lo_cut? |
---|
| 401 | cut_val = lo_cut; // cut at lo_cut |
---|
| 402 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 403 | n_lo = br1; // balance if there are ties |
---|
| 404 | } |
---|
| 405 | else { // all points below lo_cut |
---|
| 406 | cut_val = max; // cut at max value |
---|
| 407 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 408 | n_lo = n-1; |
---|
| 409 | } |
---|
| 410 | } |
---|
| 411 | // is median above hi_cut? |
---|
| 412 | else if (annSplitBalance(pa, pidx, n, cut_dim, hi_cut) <= 0) { |
---|
| 413 | if (min < hi_cut) { // are any points below hi_cut? |
---|
| 414 | cut_val = hi_cut; // cut at hi_cut |
---|
| 415 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 416 | n_lo = br2; // balance if there are ties |
---|
| 417 | } |
---|
| 418 | else { // all points above hi_cut |
---|
| 419 | cut_val = min; // cut at min value |
---|
| 420 | annPlaneSplit(pa, pidx, n, cut_dim, cut_val, br1, br2); |
---|
| 421 | n_lo = 1; |
---|
| 422 | } |
---|
| 423 | } |
---|
| 424 | else { // median cut is good enough |
---|
| 425 | n_lo = n/2; // split about median |
---|
| 426 | annMedianSplit(pa, pidx, n, cut_dim, cut_val, n_lo); |
---|
| 427 | } |
---|
| 428 | } |
---|