1 //---------------------------------------------------------------------- 2 // File: ANN.h 3 // Programmer: Sunil Arya and David Mount 4 // Description: Basic include file for approximate nearest 5 // neighbor searching. 6 // Last modified: 01/27/10 (Version 1.1.2) 7 //---------------------------------------------------------------------- 8 // Copyright (c) 1997-2010 University of Maryland and Sunil Arya and 9 // David Mount. All Rights Reserved. 10 // 11 // This software and related documentation is part of the Approximate 12 // Nearest Neighbor Library (ANN). This software is provided under 13 // the provisions of the Lesser GNU Public License (LGPL). See the 14 // file ../ReadMe.txt for further information. 15 // 16 // The University of Maryland (U.M.) and the authors make no 17 // representations about the suitability or fitness of this software for 18 // any purpose. It is provided "as is" without express or implied 19 // warranty. 20 //---------------------------------------------------------------------- 21 // History: 22 // Revision 0.1 03/04/98 23 // Initial release 24 // Revision 1.0 04/01/05 25 // Added copyright and revision information 26 // Added ANNcoordPrec for coordinate precision. 27 // Added methods theDim, nPoints, maxPoints, thePoints to ANNpointSet. 28 // Cleaned up C++ structure for modern compilers 29 // Revision 1.1 05/03/05 30 // Added fixed-radius k-NN searching 31 // Revision 1.1.2 01/27/10 32 // Fixed minor compilation bugs for new versions of gcc 33 //---------------------------------------------------------------------- 34 35 //---------------------------------------------------------------------- 36 // ANN - approximate nearest neighbor searching 37 // ANN is a library for approximate nearest neighbor searching, 38 // based on the use of standard and priority search in kd-trees 39 // and balanced box-decomposition (bbd) trees. Here are some 40 // references to the main algorithmic techniques used here: 41 // 42 // kd-trees: 43 // Friedman, Bentley, and Finkel, ``An algorithm for finding 44 // best matches in logarithmic expected time,'' ACM 45 // Transactions on Mathematical Software, 3(3):209-226, 1977. 46 // 47 // Priority search in kd-trees: 48 // Arya and Mount, ``Algorithms for fast vector quantization,'' 49 // Proc. of DCC '93: Data Compression Conference, eds. J. A. 50 // Storer and M. Cohn, IEEE Press, 1993, 381-390. 51 // 52 // Approximate nearest neighbor search and bbd-trees: 53 // Arya, Mount, Netanyahu, Silverman, and Wu, ``An optimal 54 // algorithm for approximate nearest neighbor searching,'' 55 // 5th Ann. ACM-SIAM Symposium on Discrete Algorithms, 56 // 1994, 573-582. 57 //---------------------------------------------------------------------- 58 59 #ifndef ANN_H 60 #define ANN_H 61 62 #ifdef WIN32 63 //---------------------------------------------------------------------- 64 // For Microsoft Visual C++, externally accessible symbols must be 65 // explicitly indicated with DLL_API, which is somewhat like "extern." 66 // 67 // The following ifdef block is the standard way of creating macros 68 // which make exporting from a DLL simpler. All files within this DLL 69 // are compiled with the DLL_EXPORTS preprocessor symbol defined on the 70 // command line. In contrast, projects that use (or import) the DLL 71 // objects do not define the DLL_EXPORTS symbol. This way any other 72 // project whose source files include this file see DLL_API functions as 73 // being imported from a DLL, wheras this DLL sees symbols defined with 74 // this macro as being exported. 75 //---------------------------------------------------------------------- 76 #ifdef DLL_EXPORTS 77 #define DLL_API __declspec(dllexport) 78 #else 79 // BMA: This results in link warnings about local Dakota symbols 80 // hiding those from the library (when building static libs) 81 // #define DLL_API __declspec(dllimport) 82 // BMA: This doesn't help at all: 83 // #define DLL_API extern 84 // BMA TODO: Dakota builds static libraries, so this works for our use 85 // case, but may need to make this conditional if migrating to DLL: 86 #define DLL_API 87 #endif 88 //---------------------------------------------------------------------- 89 // DLL_API is ignored for all other systems 90 //---------------------------------------------------------------------- 91 #else 92 #define DLL_API 93 #endif 94 95 //---------------------------------------------------------------------- 96 // basic includes 97 //---------------------------------------------------------------------- 98 99 #include <cstdlib> // standard lib includes 100 #include <cmath> // math includes 101 #include <iostream> // I/O streams 102 #include <cstring> // C-style strings 103 104 //---------------------------------------------------------------------- 105 // Limits 106 // There are a number of places where we use the maximum double value as 107 // default initializers (and others may be used, depending on the 108 // data/distance representation). These can usually be found in limits.h 109 // (as LONG_MAX, INT_MAX) or in float.h (as DBL_MAX, FLT_MAX). 110 // 111 // Not all systems have these files. If you are using such a system, 112 // you should set the preprocessor symbol ANN_NO_LIMITS_H when 113 // compiling, and modify the statements below to generate the 114 // appropriate value. For practical purposes, this does not need to be 115 // the maximum double value. It is sufficient that it be at least as 116 // large than the maximum squared distance between between any two 117 // points. 118 //---------------------------------------------------------------------- 119 #ifdef ANN_NO_LIMITS_H // limits.h unavailable 120 #include <cvalues> // replacement for limits.h 121 const double ANN_DBL_MAX = MAXDOUBLE; // insert maximum double 122 #else 123 #include <climits> 124 #include <cfloat> 125 const double ANN_DBL_MAX = DBL_MAX; 126 #endif 127 128 129 // ----- 130 // Runtime norm selector; see included header 131 // ----- 132 #define ANN_NORM_SELECT 1 133 #include "ANNnormselect.h" 134 135 #define ANNversion "1.1.2" // ANN version and information 136 #define ANNversionCmt "" 137 #define ANNcopyright "David M. Mount and Sunil Arya" 138 #define ANNlatestRev "Jan 27, 2010" 139 140 //---------------------------------------------------------------------- 141 // ANNbool 142 // This is a simple boolean type. Although ANSI C++ is supposed 143 // to support the type bool, some compilers do not have it. 144 //---------------------------------------------------------------------- 145 146 enum ANNbool {ANNfalse = 0, ANNtrue = 1}; // ANN boolean type (non ANSI C++) 147 148 //---------------------------------------------------------------------- 149 // ANNcoord, ANNdist 150 // ANNcoord and ANNdist are the types used for representing 151 // point coordinates and distances. They can be modified by the 152 // user, with some care. It is assumed that they are both numeric 153 // types, and that ANNdist is generally of an equal or higher type 154 // from ANNcoord. A variable of type ANNdist should be large 155 // enough to store the sum of squared components of a variable 156 // of type ANNcoord for the number of dimensions needed in the 157 // application. For example, the following combinations are 158 // legal: 159 // 160 // ANNcoord ANNdist 161 // --------- ------------------------------- 162 // short short, int, long, float, double 163 // int int, long, float, double 164 // long long, float, double 165 // float float, double 166 // double double 167 // 168 // It is the user's responsibility to make sure that overflow does 169 // not occur in distance calculation. 170 //---------------------------------------------------------------------- 171 172 typedef double ANNcoord; // coordinate data type 173 typedef double ANNdist; // distance data type 174 175 //---------------------------------------------------------------------- 176 // ANNidx 177 // ANNidx is a point index. When the data structure is built, the 178 // points are given as an array. Nearest neighbor results are 179 // returned as an integer index into this array. To make it 180 // clearer when this is happening, we define the integer type 181 // ANNidx. Indexing starts from 0. 182 // 183 // For fixed-radius near neighbor searching, it is possible that 184 // there are not k nearest neighbors within the search radius. To 185 // indicate this, the algorithm returns ANN_NULL_IDX as its result. 186 // It should be distinguishable from any valid array index. 187 //---------------------------------------------------------------------- 188 189 typedef int ANNidx; // point index 190 const ANNidx ANN_NULL_IDX = -1; // a NULL point index 191 192 //---------------------------------------------------------------------- 193 // Infinite distance: 194 // The code assumes that there is an "infinite distance" which it 195 // uses to initialize distances before performing nearest neighbor 196 // searches. It should be as larger or larger than any legitimate 197 // nearest neighbor distance. 198 // 199 // On most systems, these should be found in the standard include 200 // file <limits.h> or possibly <float.h>. If you do not have these 201 // file, some suggested values are listed below, assuming 64-bit 202 // long, 32-bit int and 16-bit short. 203 // 204 // ANNdist ANN_DIST_INF Values (see <limits.h> or <float.h>) 205 // ------- ------------ ------------------------------------ 206 // double DBL_MAX 1.79769313486231570e+308 207 // float FLT_MAX 3.40282346638528860e+38 208 // long LONG_MAX 0x7fffffffffffffff 209 // int INT_MAX 0x7fffffff 210 // short SHRT_MAX 0x7fff 211 //---------------------------------------------------------------------- 212 213 const ANNdist ANN_DIST_INF = ANN_DBL_MAX; 214 215 //---------------------------------------------------------------------- 216 // Significant digits for tree dumps: 217 // When floating point coordinates are used, the routine that dumps 218 // a tree needs to know roughly how many significant digits there 219 // are in a ANNcoord, so it can output points to full precision. 220 // This is defined to be ANNcoordPrec. On most systems these 221 // values can be found in the standard include files <limits.h> or 222 // <float.h>. For integer types, the value is essentially ignored. 223 // 224 // ANNcoord ANNcoordPrec Values (see <limits.h> or <float.h>) 225 // -------- ------------ ------------------------------------ 226 // double DBL_DIG 15 227 // float FLT_DIG 6 228 // long doesn't matter 19 229 // int doesn't matter 10 230 // short doesn't matter 5 231 //---------------------------------------------------------------------- 232 233 #ifdef DBL_DIG // number of sig. bits in ANNcoord 234 const int ANNcoordPrec = DBL_DIG; 235 #else 236 const int ANNcoordPrec = 15; // default precision 237 #endif 238 239 //---------------------------------------------------------------------- 240 // Self match? 241 // In some applications, the nearest neighbor of a point is not 242 // allowed to be the point itself. This occurs, for example, when 243 // computing all nearest neighbors in a set. By setting the 244 // parameter ANN_ALLOW_SELF_MATCH to ANNfalse, the nearest neighbor 245 // is the closest point whose distance from the query point is 246 // strictly positive. 247 //---------------------------------------------------------------------- 248 249 const ANNbool ANN_ALLOW_SELF_MATCH = ANNtrue; 250 251 //---------------------------------------------------------------------- 252 // Norms and metrics: 253 // ANN supports any Minkowski norm for defining distance. In 254 // particular, for any p >= 1, the L_p Minkowski norm defines the 255 // length of a d-vector (v0, v1, ..., v(d-1)) to be 256 // 257 // (|v0|^p + |v1|^p + ... + |v(d-1)|^p)^(1/p), 258 // 259 // (where ^ denotes exponentiation, and |.| denotes absolute 260 // value). The distance between two points is defined to be the 261 // norm of the vector joining them. Some common distance metrics 262 // include 263 // 264 // Euclidean metric p = 2 265 // Manhattan metric p = 1 266 // Max metric p = infinity 267 // 268 // In the case of the max metric, the norm is computed by taking 269 // the maxima of the absolute values of the components. ANN is 270 // highly "coordinate-based" and does not support general distances 271 // functions (e.g. those obeying just the triangle inequality). It 272 // also does not support distance functions based on 273 // inner-products. 274 // 275 // For the purpose of computing nearest neighbors, it is not 276 // necessary to compute the final power (1/p). Thus the only 277 // component that is used by the program is |v(i)|^p. 278 // 279 // ANN parameterizes the distance computation through the following 280 // macros. (Macros are used rather than procedures for 281 // efficiency.) Recall that the distance between two points is 282 // given by the length of the vector joining them, and the length 283 // or norm of a vector v is given by formula: 284 // 285 // |v| = ROOT(POW(v0) # POW(v1) # ... # POW(v(d-1))) 286 // 287 // where ROOT, POW are unary functions and # is an associative and 288 // commutative binary operator mapping the following types: 289 // 290 // ** POW: ANNcoord --> ANNdist 291 // ** #: ANNdist x ANNdist --> ANNdist 292 // ** ROOT: ANNdist (>0) --> double 293 // 294 // For early termination in distance calculation (partial distance 295 // calculation) we assume that POW and # together are monotonically 296 // increasing on sequences of arguments, meaning that for all 297 // v0..vk and y: 298 // 299 // POW(v0) #...# POW(vk) <= (POW(v0) #...# POW(vk)) # POW(y). 300 // 301 // Incremental Distance Calculation: 302 // The program uses an optimized method of computing distances for 303 // kd-trees and bd-trees, called incremental distance calculation. 304 // It is used when distances are to be updated when only a single 305 // coordinate of a point has been changed. In order to use this, 306 // we assume that there is an incremental update function DIFF(x,y) 307 // for #, such that if: 308 // 309 // s = x0 # ... # xi # ... # xk 310 // 311 // then if s' is equal to s but with xi replaced by y, that is, 312 // 313 // s' = x0 # ... # y # ... # xk 314 // 315 // then the length of s' can be computed by: 316 // 317 // |s'| = |s| # DIFF(xi,y). 318 // 319 // Thus, if # is + then DIFF(xi,y) is (yi-x). For the L_infinity 320 // norm we make use of the fact that in the program this function 321 // is only invoked when y > xi, and hence DIFF(xi,y)=y. 322 // 323 // Finally, for approximate nearest neighbor queries we assume 324 // that POW and ROOT are related such that 325 // 326 // v*ROOT(x) = ROOT(POW(v)*x) 327 // 328 // Here are the values for the various Minkowski norms: 329 // 330 // L_p: p even: p odd: 331 // ------------------------- ------------------------ 332 // POW(v) = v^p POW(v) = |v|^p 333 // ROOT(x) = x^(1/p) ROOT(x) = x^(1/p) 334 // # = + # = + 335 // DIFF(x,y) = y - x DIFF(x,y) = y - x 336 // 337 // L_inf: 338 // POW(v) = |v| 339 // ROOT(x) = x 340 // # = max 341 // DIFF(x,y) = y 342 // 343 // By default the Euclidean norm is assumed. To change the norm, 344 // uncomment the appropriate set of macros below. 345 //---------------------------------------------------------------------- 346 347 #ifdef ANN_NORM_SELECT 348 349 #define ANN_POW(v) (approxnn::normSelector::instance().pow((v))) 350 #define ANN_ROOT(x) approxnn::normSelector::instance().root((x)) 351 #define ANN_SUM(x,y) (approxnn::normSelector::instance().sum((x),(y))) 352 #define ANN_DIFF(x,y) (approxnn::normSelector::instance().diff((x),(y))) 353 354 #else 355 356 //---------------------------------------------------------------------- 357 // Use the following for the Euclidean norm 358 //---------------------------------------------------------------------- 359 #define ANN_POW(v) ((v)*(v)) 360 #define ANN_ROOT(x) sqrt(x) 361 #define ANN_SUM(x,y) ((x) + (y)) 362 #define ANN_DIFF(x,y) ((y) - (x)) 363 364 //---------------------------------------------------------------------- 365 // Use the following for the L_1 (Manhattan) norm 366 //---------------------------------------------------------------------- 367 // #define ANN_POW(v) fabs(v) 368 // #define ANN_ROOT(x) (x) 369 // #define ANN_SUM(x,y) ((x) + (y)) 370 // #define ANN_DIFF(x,y) ((y) - (x)) 371 372 //---------------------------------------------------------------------- 373 // Use the following for a general L_p norm 374 //---------------------------------------------------------------------- 375 // #define ANN_POW(v) pow(fabs(v),p) 376 // #define ANN_ROOT(x) pow(fabs(x),1/p) 377 // #define ANN_SUM(x,y) ((x) + (y)) 378 // #define ANN_DIFF(x,y) ((y) - (x)) 379 380 //---------------------------------------------------------------------- 381 // Use the following for the L_infinity (Max) norm 382 //---------------------------------------------------------------------- 383 // #define ANN_POW(v) fabs(v) 384 // #define ANN_ROOT(x) (x) 385 // #define ANN_SUM(x,y) ((x) > (y) ? (x) : (y)) 386 // #define ANN_DIFF(x,y) (y) 387 388 #endif // DAKOTA_ANN_NORM_SELECTOR 389 390 //---------------------------------------------------------------------- 391 // Array types 392 // The following array types are of basic interest. A point is 393 // just a dimensionless array of coordinates, a point array is a 394 // dimensionless array of points. A distance array is a 395 // dimensionless array of distances and an index array is a 396 // dimensionless array of point indices. The latter two are used 397 // when returning the results of k-nearest neighbor queries. 398 //---------------------------------------------------------------------- 399 400 typedef ANNcoord* ANNpoint; // a point 401 typedef ANNpoint* ANNpointArray; // an array of points 402 typedef ANNdist* ANNdistArray; // an array of distances 403 typedef ANNidx* ANNidxArray; // an array of point indices 404 405 //---------------------------------------------------------------------- 406 // Basic point and array utilities: 407 // The following procedures are useful supplements to ANN's nearest 408 // neighbor capabilities. 409 // 410 // annDist(): 411 // Computes the (squared) distance between a pair of points. 412 // Note that this routine is not used internally by ANN for 413 // computing distance calculations. For reasons of efficiency 414 // this is done using incremental distance calculation. Thus, 415 // this routine cannot be modified as a method of changing the 416 // metric. 417 // 418 // Because points (somewhat like strings in C) are stored as 419 // pointers. Consequently, creating and destroying copies of 420 // points may require storage allocation. These procedures do 421 // this. 422 // 423 // annAllocPt() and annDeallocPt(): 424 // Allocate a deallocate storage for a single point, and 425 // return a pointer to it. The argument to AllocPt() is 426 // used to initialize all components. 427 // 428 // annAllocPts() and annDeallocPts(): 429 // Allocate and deallocate an array of points as well a 430 // place to store their coordinates, and initializes the 431 // points to point to their respective coordinates. It 432 // allocates point storage in a contiguous block large 433 // enough to store all the points. It performs no 434 // initialization. 435 // 436 // annCopyPt(): 437 // Creates a copy of a given point, allocating space for 438 // the new point. It returns a pointer to the newly 439 // allocated copy. 440 //---------------------------------------------------------------------- 441 442 DLL_API ANNdist annDist( 443 int dim, // dimension of space 444 ANNpoint p, // points 445 ANNpoint q); 446 447 DLL_API ANNpoint annAllocPt( 448 int dim, // dimension 449 ANNcoord c = 0); // coordinate value (all equal) 450 451 DLL_API ANNpointArray annAllocPts( 452 int n, // number of points 453 int dim); // dimension 454 455 DLL_API void annDeallocPt( 456 ANNpoint &p); // deallocate 1 point 457 458 DLL_API void annDeallocPts( 459 ANNpointArray &pa); // point array 460 461 DLL_API ANNpoint annCopyPt( 462 int dim, // dimension 463 ANNpoint source); // point to copy 464 465 //---------------------------------------------------------------------- 466 //Overall structure: ANN supports a number of different data structures 467 //for approximate and exact nearest neighbor searching. These are: 468 // 469 // ANNbruteForce A simple brute-force search structure. 470 // ANNkd_tree A kd-tree tree search structure. ANNbd_tree 471 // A bd-tree tree search structure (a kd-tree with shrink 472 // capabilities). 473 // 474 // At a minimum, each of these data structures support k-nearest 475 // neighbor queries. The nearest neighbor query, annkSearch, 476 // returns an integer identifier and the distance to the nearest 477 // neighbor(s) and annRangeSearch returns the nearest points that 478 // lie within a given query ball. 479 // 480 // Each structure is built by invoking the appropriate constructor 481 // and passing it (at a minimum) the array of points, the total 482 // number of points and the dimension of the space. Each structure 483 // is also assumed to support a destructor and member functions 484 // that return basic information about the point set. 485 // 486 // Note that the array of points is not copied by the data 487 // structure (for reasons of space efficiency), and it is assumed 488 // to be constant throughout the lifetime of the search structure. 489 // 490 // The search algorithm, annkSearch, is given the query point (q), 491 // and the desired number of nearest neighbors to report (k), and 492 // the error bound (eps) (whose default value is 0, implying exact 493 // nearest neighbors). It returns two arrays which are assumed to 494 // contain at least k elements: one (nn_idx) contains the indices 495 // (within the point array) of the nearest neighbors and the other 496 // (dd) contains the squared distances to these nearest neighbors. 497 // 498 // The search algorithm, annkFRSearch, is a fixed-radius kNN 499 // search. In addition to a query point, it is given a (squared) 500 // radius bound. (This is done for consistency, because the search 501 // returns distances as squared quantities.) It does two things. 502 // First, it computes the k nearest neighbors within the radius 503 // bound, and second, it returns the total number of points lying 504 // within the radius bound. It is permitted to set k = 0, in which 505 // case it effectively answers a range counting query. If the 506 // error bound epsilon is positive, then the search is approximate 507 // in the sense that it is free to ignore any point that lies 508 // outside a ball of radius r/(1+epsilon), where r is the given 509 // (unsquared) radius bound. 510 // 511 // The generic object from which all the search structures are 512 // dervied is given below. It is a virtual object, and is useless 513 // by itself. 514 //---------------------------------------------------------------------- 515 516 class DLL_API ANNpointSet { 517 public: ~ANNpointSet()518 virtual ~ANNpointSet() {} // virtual distructor 519 520 virtual void annkSearch( // approx k near neighbor search 521 ANNpoint q, // query point 522 int k, // number of near neighbors to return 523 ANNidxArray nn_idx, // nearest neighbor array (modified) 524 ANNdistArray dd, // dist to near neighbors (modified) 525 double eps=0.0 // error bound 526 ) = 0; // pure virtual (defined elsewhere) 527 528 virtual int annkFRSearch( // approx fixed-radius kNN search 529 ANNpoint q, // query point 530 ANNdist sqRad, // squared radius 531 int k = 0, // number of near neighbors to return 532 ANNidxArray nn_idx = NULL, // nearest neighbor array (modified) 533 ANNdistArray dd = NULL, // dist to near neighbors (modified) 534 double eps=0.0 // error bound 535 ) = 0; // pure virtual (defined elsewhere) 536 537 virtual int theDim() = 0; // return dimension of space 538 virtual int nPoints() = 0; // return number of points 539 // return pointer to points 540 virtual ANNpointArray thePoints() = 0; 541 }; 542 543 //---------------------------------------------------------------------- 544 // Brute-force nearest neighbor search: 545 // The brute-force search structure is very simple but inefficient. 546 // It has been provided primarily for the sake of comparison with 547 // and validation of the more complex search structures. 548 // 549 // Query processing is the same as described above, but the value 550 // of epsilon is ignored, since all distance calculations are 551 // performed exactly. 552 // 553 // WARNING: This data structure is very slow, and should not be 554 // used unless the number of points is very small. 555 // 556 // Internal information: 557 // --------------------- 558 // This data structure bascially consists of the array of points 559 // (each a pointer to an array of coordinates). The search is 560 // performed by a simple linear scan of all the points. 561 //---------------------------------------------------------------------- 562 563 class DLL_API ANNbruteForce: public ANNpointSet { 564 int dim; // dimension 565 int n_pts; // number of points 566 ANNpointArray pts; // point array 567 public: 568 ANNbruteForce( // constructor from point array 569 ANNpointArray pa, // point array 570 int n, // number of points 571 int dd); // dimension 572 573 ~ANNbruteForce(); // destructor 574 575 void annkSearch( // approx k near neighbor search 576 ANNpoint q, // query point 577 int k, // number of near neighbors to return 578 ANNidxArray nn_idx, // nearest neighbor array (modified) 579 ANNdistArray dd, // dist to near neighbors (modified) 580 double eps=0.0); // error bound 581 582 int annkFRSearch( // approx fixed-radius kNN search 583 ANNpoint q, // query point 584 ANNdist sqRad, // squared radius 585 int k = 0, // number of near neighbors to return 586 ANNidxArray nn_idx = NULL, // nearest neighbor array (modified) 587 ANNdistArray dd = NULL, // dist to near neighbors (modified) 588 double eps=0.0); // error bound 589 theDim()590 int theDim() // return dimension of space 591 { return dim; } 592 nPoints()593 int nPoints() // return number of points 594 { return n_pts; } 595 thePoints()596 ANNpointArray thePoints() // return pointer to points 597 { return pts; } 598 }; 599 600 //---------------------------------------------------------------------- 601 // kd- and bd-tree splitting and shrinking rules 602 // kd-trees supports a collection of different splitting rules. 603 // In addition to the standard kd-tree splitting rule proposed 604 // by Friedman, Bentley, and Finkel, we have introduced a 605 // number of other splitting rules, which seem to perform 606 // as well or better (for the distributions we have tested). 607 // 608 // The splitting methods given below allow the user to tailor 609 // the data structure to the particular data set. They are 610 // are described in greater details in the kd_split.cc source 611 // file. The method ANN_KD_SUGGEST is the method chosen (rather 612 // subjectively) by the implementors as the one giving the 613 // fastest performance, and is the default splitting method. 614 // 615 // As with splitting rules, there are a number of different 616 // shrinking rules. The shrinking rule ANN_BD_NONE does no 617 // shrinking (and hence produces a kd-tree tree). The rule 618 // ANN_BD_SUGGEST uses the implementors favorite rule. 619 //---------------------------------------------------------------------- 620 621 enum ANNsplitRule { 622 ANN_KD_STD = 0, // the optimized kd-splitting rule 623 ANN_KD_MIDPT = 1, // midpoint split 624 ANN_KD_FAIR = 2, // fair split 625 ANN_KD_SL_MIDPT = 3, // sliding midpoint splitting method 626 ANN_KD_SL_FAIR = 4, // sliding fair split method 627 ANN_KD_SUGGEST = 5}; // the authors' suggestion for best 628 const int ANN_N_SPLIT_RULES = 6; // number of split rules 629 630 enum ANNshrinkRule { 631 ANN_BD_NONE = 0, // no shrinking at all (just kd-tree) 632 ANN_BD_SIMPLE = 1, // simple splitting 633 ANN_BD_CENTROID = 2, // centroid splitting 634 ANN_BD_SUGGEST = 3}; // the authors' suggested choice 635 const int ANN_N_SHRINK_RULES = 4; // number of shrink rules 636 637 //---------------------------------------------------------------------- 638 // kd-tree: 639 // The main search data structure supported by ANN is a kd-tree. 640 // The main constructor is given a set of points and a choice of 641 // splitting method to use in building the tree. 642 // 643 // Construction: 644 // ------------- 645 // The constructor is given the point array, number of points, 646 // dimension, bucket size (default = 1), and the splitting rule 647 // (default = ANN_KD_SUGGEST). The point array is not copied, and 648 // is assumed to be kept constant throughout the lifetime of the 649 // search structure. There is also a "load" constructor that 650 // builds a tree from a file description that was created by the 651 // Dump operation. 652 // 653 // Search: 654 // ------- 655 // There are two search methods: 656 // 657 // Standard search (annkSearch()): 658 // Searches nodes in tree-traversal order, always visiting 659 // the closer child first. 660 // Priority search (annkPriSearch()): 661 // Searches nodes in order of increasing distance of the 662 // associated cell from the query point. For many 663 // distributions the standard search seems to work just 664 // fine, but priority search is safer for worst-case 665 // performance. 666 // 667 // Printing: 668 // --------- 669 // There are two methods provided for printing the tree. Print() 670 // is used to produce a "human-readable" display of the tree, with 671 // indenation, which is handy for debugging. Dump() produces a 672 // format that is suitable reading by another program. There is a 673 // "load" constructor, which constructs a tree which is assumed to 674 // have been saved by the Dump() procedure. 675 // 676 // Performance and Structure Statistics: 677 // ------------------------------------- 678 // The procedure getStats() collects statistics information on the 679 // tree (its size, height, etc.) See ANNperf.h for information on 680 // the stats structure it returns. 681 // 682 // Internal information: 683 // --------------------- 684 // The data structure consists of three major chunks of storage. 685 // The first (implicit) storage are the points themselves (pts), 686 // which have been provided by the users as an argument to the 687 // constructor, or are allocated dynamically if the tree is built 688 // using the load constructor). These should not be changed during 689 // the lifetime of the search structure. It is the user's 690 // responsibility to delete these after the tree is destroyed. 691 // 692 // The second is the tree itself (which is dynamically allocated in 693 // the constructor) and is given as a pointer to its root node 694 // (root). These nodes are automatically deallocated when the tree 695 // is deleted. See the file src/kd_tree.h for further information 696 // on the structure of the tree nodes. 697 // 698 // Each leaf of the tree does not contain a pointer directly to a 699 // point, but rather contains a pointer to a "bucket", which is an 700 // array consisting of point indices. The third major chunk of 701 // storage is an array (pidx), which is a large array in which all 702 // these bucket subarrays reside. (The reason for storing them 703 // separately is the buckets are typically small, but of varying 704 // sizes. This was done to avoid fragmentation.) This array is 705 // also deallocated when the tree is deleted. 706 // 707 // In addition to this, the tree consists of a number of other 708 // pieces of information which are used in searching and for 709 // subsequent tree operations. These consist of the following: 710 // 711 // dim Dimension of space 712 // n_pts Number of points currently in the tree 713 // n_max Maximum number of points that are allowed 714 // in the tree 715 // bkt_size Maximum bucket size (no. of points per leaf) 716 // bnd_box_lo Bounding box low point 717 // bnd_box_hi Bounding box high point 718 // splitRule Splitting method used 719 // 720 //---------------------------------------------------------------------- 721 722 //---------------------------------------------------------------------- 723 // Some types and objects used by kd-tree functions 724 // See src/kd_tree.h and src/kd_tree.cpp for definitions 725 //---------------------------------------------------------------------- 726 class ANNkdStats; // stats on kd-tree 727 class ANNkd_node; // generic node in a kd-tree 728 typedef ANNkd_node* ANNkd_ptr; // pointer to a kd-tree node 729 730 class DLL_API ANNkd_tree: public ANNpointSet { 731 protected: 732 int dim; // dimension of space 733 int n_pts; // number of points in tree 734 int bkt_size; // bucket size 735 ANNpointArray pts; // the points 736 ANNidxArray pidx; // point indices (to pts array) 737 ANNkd_ptr root; // root of kd-tree 738 ANNpoint bnd_box_lo; // bounding box low point 739 ANNpoint bnd_box_hi; // bounding box high point 740 741 void SkeletonTree( // construct skeleton tree 742 int n, // number of points 743 int dd, // dimension 744 int bs, // bucket size 745 ANNpointArray pa = NULL, // point array (optional) 746 ANNidxArray pi = NULL); // point indices (optional) 747 748 public: 749 ANNkd_tree( // build skeleton tree 750 int n = 0, // number of points 751 int dd = 0, // dimension 752 int bs = 1); // bucket size 753 754 ANNkd_tree( // build from point array 755 ANNpointArray pa, // point array 756 int n, // number of points 757 int dd, // dimension 758 int bs = 1, // bucket size 759 ANNsplitRule split = ANN_KD_SUGGEST); // splitting method 760 761 ANNkd_tree( // build from dump file 762 std::istream& in); // input stream for dump file 763 764 ~ANNkd_tree(); // tree destructor 765 766 void annkSearch( // approx k near neighbor search 767 ANNpoint q, // query point 768 int k, // number of near neighbors to return 769 ANNidxArray nn_idx, // nearest neighbor array (modified) 770 ANNdistArray dd, // dist to near neighbors (modified) 771 double eps=0.0); // error bound 772 773 void annkPriSearch( // priority k near neighbor search 774 ANNpoint q, // query point 775 int k, // number of near neighbors to return 776 ANNidxArray nn_idx, // nearest neighbor array (modified) 777 ANNdistArray dd, // dist to near neighbors (modified) 778 double eps=0.0); // error bound 779 780 int annkFRSearch( // approx fixed-radius kNN search 781 ANNpoint q, // the query point 782 ANNdist sqRad, // squared radius of query ball 783 int k, // number of neighbors to return 784 ANNidxArray nn_idx = NULL, // nearest neighbor array (modified) 785 ANNdistArray dd = NULL, // dist to near neighbors (modified) 786 double eps=0.0); // error bound 787 theDim()788 int theDim() // return dimension of space 789 { return dim; } 790 nPoints()791 int nPoints() // return number of points 792 { return n_pts; } 793 thePoints()794 ANNpointArray thePoints() // return pointer to points 795 { return pts; } 796 797 virtual void Print( // print the tree (for debugging) 798 ANNbool with_pts, // print points as well? 799 std::ostream& out); // output stream 800 801 virtual void Dump( // dump entire tree 802 ANNbool with_pts, // print points as well? 803 std::ostream& out); // output stream 804 805 virtual void getStats( // compute tree statistics 806 ANNkdStats& st); // the statistics (modified) 807 }; 808 809 //---------------------------------------------------------------------- 810 // Box decomposition tree (bd-tree) 811 // The bd-tree is inherited from a kd-tree. The main difference 812 // in the bd-tree and the kd-tree is a new type of internal node 813 // called a shrinking node (in the kd-tree there is only one type 814 // of internal node, a splitting node). The shrinking node 815 // makes it possible to generate balanced trees in which the 816 // cells have bounded aspect ratio, by allowing the decomposition 817 // to zoom in on regions of dense point concentration. Although 818 // this is a nice idea in theory, few point distributions are so 819 // densely clustered that this is really needed. 820 //---------------------------------------------------------------------- 821 822 class DLL_API ANNbd_tree: public ANNkd_tree { 823 public: 824 ANNbd_tree( // build skeleton tree 825 int n, // number of points 826 int dd, // dimension 827 int bs = 1) // bucket size ANNkd_tree(n,dd,bs)828 : ANNkd_tree(n, dd, bs) {} // build base kd-tree 829 830 ANNbd_tree( // build from point array 831 ANNpointArray pa, // point array 832 int n, // number of points 833 int dd, // dimension 834 int bs = 1, // bucket size 835 ANNsplitRule split = ANN_KD_SUGGEST, // splitting rule 836 ANNshrinkRule shrink = ANN_BD_SUGGEST); // shrinking rule 837 838 ANNbd_tree( // build from dump file 839 std::istream& in); // input stream for dump file 840 }; 841 842 //---------------------------------------------------------------------- 843 // Other functions 844 // annMaxPtsVisit Sets a limit on the maximum number of points 845 // to visit in the search. 846 // annClose Can be called when all use of ANN is finished. 847 // It clears up a minor memory leak. 848 //---------------------------------------------------------------------- 849 850 DLL_API void annMaxPtsVisit( // max. pts to visit in search 851 int maxPts); // the limit 852 853 DLL_API void annClose(); // called to end use of ANN 854 855 #endif 856