ANN.h

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//----------------------------------------------------------------------
// File:                        ANN.h
// Programmer:          Sunil Arya and David Mount
// Description:         Basic include file for approximate nearest
//                                      neighbor searching.
// Last modified:       01/27/10 (Version 1.1.2)
//----------------------------------------------------------------------
// Copyright (c) 1997-2010 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
//              Added copyright and revision information
//              Added ANNcoordPrec for coordinate precision.
//              Added methods theDim, nPoints, maxPoints, thePoints to ANNpointSet.
//              Cleaned up C++ structure for modern compilers
//      Revision 1.1  05/03/05
//              Added fixed-radius k-NN searching
//      Revision 1.1.2  01/27/10
//              Fixed minor compilation bugs for new versions of gcc
//----------------------------------------------------------------------

//----------------------------------------------------------------------
// ANN - approximate nearest neighbor searching
//      ANN is a library for approximate nearest neighbor searching,
//      based on the use of standard and priority search in kd-trees
//      and balanced box-decomposition (bbd) trees. Here are some
//      references to the main algorithmic techniques used here:
//
//              kd-trees:
//                      Friedman, Bentley, and Finkel, ``An algorithm for finding
//                              best matches in logarithmic expected time,'' ACM
//                              Transactions on Mathematical Software, 3(3):209-226, 1977.
//
//              Priority search in kd-trees:
//                      Arya and Mount, ``Algorithms for fast vector quantization,''
//                              Proc. of DCC '93: Data Compression Conference, eds. J. A.
//                              Storer and M. Cohn, IEEE Press, 1993, 381-390.
//
//              Approximate nearest neighbor search and bbd-trees:
//                      Arya, Mount, Netanyahu, Silverman, and Wu, ``An optimal
//                              algorithm for approximate nearest neighbor searching,''
//                              5th Ann. ACM-SIAM Symposium on Discrete Algorithms,
//                              1994, 573-582.
//----------------------------------------------------------------------

#ifndef ANN_H
#define ANN_H

#ifdef WIN32
  //----------------------------------------------------------------------
  // For Microsoft Visual C++, externally accessible symbols must be
  // explicitly indicated with DLL_API, which is somewhat like "extern."
  //
  // The following ifdef block is the standard way of creating macros
  // which make exporting from a DLL simpler. All files within this DLL
  // are compiled with the DLL_EXPORTS preprocessor symbol defined on the
  // command line. In contrast, projects that use (or import) the DLL
  // objects do not define the DLL_EXPORTS symbol. This way any other
  // project whose source files include this file see DLL_API functions as
  // being imported from a DLL, wheras this DLL sees symbols defined with
  // this macro as being exported.
  //----------------------------------------------------------------------
  #ifdef DLL_EXPORTS
         #define DLL_API __declspec(dllexport)
  #else
        #define DLL_API __declspec(dllimport)
  #endif
  //----------------------------------------------------------------------
  // DLL_API is ignored for all other systems
  //----------------------------------------------------------------------
#else
  #define DLL_API
#endif

//----------------------------------------------------------------------
//  basic includes
//----------------------------------------------------------------------

#include <cstdlib>                      // standard lib includes
#include <cmath>                        // math includes
#include <iostream>                     // I/O streams
#include <cstring>                      // C-style strings

//----------------------------------------------------------------------
// Limits
// There are a number of places where we use the maximum double value as
// default initializers (and others may be used, depending on the
// data/distance representation). These can usually be found in limits.h
// (as LONG_MAX, INT_MAX) or in float.h (as DBL_MAX, FLT_MAX).
//
// Not all systems have these files.  If you are using such a system,
// you should set the preprocessor symbol ANN_NO_LIMITS_H when
// compiling, and modify the statements below to generate the
// appropriate value. For practical purposes, this does not need to be
// the maximum double value. It is sufficient that it be at least as
// large than the maximum squared distance between between any two
// points.
//----------------------------------------------------------------------
#ifdef ANN_NO_LIMITS_H                                  // limits.h unavailable
  #include <cvalues>                                    // replacement for limits.h
  const double ANN_DBL_MAX = MAXDOUBLE; // insert maximum double
#else
  #include <climits>
  #include <cfloat>
  const double ANN_DBL_MAX = DBL_MAX;
#endif

#define ANNversion              "1.1.2"                 // ANN version and information
#define ANNversionCmt   ""
#define ANNcopyright    "David M. Mount and Sunil Arya"
#define ANNlatestRev    "Jan 27, 2010"

//----------------------------------------------------------------------
//      ANNbool
//      This is a simple boolean type. Although ANSI C++ is supposed
//      to support the type bool, some compilers do not have it.
//----------------------------------------------------------------------

enum ANNbool {ANNfalse = 0, ANNtrue = 1}; // ANN boolean type (non ANSI C++)

//----------------------------------------------------------------------
//      ANNcoord, ANNdist
//              ANNcoord and ANNdist are the types used for representing
//              point coordinates and distances.  They can be modified by the
//              user, with some care.  It is assumed that they are both numeric
//              types, and that ANNdist is generally of an equal or higher type
//              from ANNcoord.  A variable of type ANNdist should be large
//              enough to store the sum of squared components of a variable
//              of type ANNcoord for the number of dimensions needed in the
//              application.  For example, the following combinations are
//              legal:
//
//              ANNcoord                ANNdist
//              ---------               -------------------------------
//              short                   short, int, long, float, double
//              int                             int, long, float, double
//              long                    long, float, double
//              float                   float, double
//              double                  double
//
//              It is the user's responsibility to make sure that overflow does
//              not occur in distance calculation.
//----------------------------------------------------------------------

typedef double  ANNcoord;                               // coordinate data type
typedef double  ANNdist;                                // distance data type

//----------------------------------------------------------------------
//      ANNidx
//              ANNidx is a point index.  When the data structure is built, the
//              points are given as an array.  Nearest neighbor results are
//              returned as an integer index into this array.  To make it
//              clearer when this is happening, we define the integer type
//              ANNidx.  Indexing starts from 0.
//
//              For fixed-radius near neighbor searching, it is possible that
//              there are not k nearest neighbors within the search radius.  To
//              indicate this, the algorithm returns ANN_NULL_IDX as its result.
//              It should be distinguishable from any valid array index.
//----------------------------------------------------------------------

typedef int             ANNidx;                                 // point index
const ANNidx    ANN_NULL_IDX = -1;              // a NULL point index

//----------------------------------------------------------------------
//      Infinite distance:
//              The code assumes that there is an "infinite distance" which it
//              uses to initialize distances before performing nearest neighbor
//              searches.  It should be as larger or larger than any legitimate
//              nearest neighbor distance.
//
//              On most systems, these should be found in the standard include
//              file <limits.h> or possibly <float.h>.  If you do not have these
//              file, some suggested values are listed below, assuming 64-bit
//              long, 32-bit int and 16-bit short.
//
//              ANNdist ANN_DIST_INF    Values (see <limits.h> or <float.h>)
//              ------- ------------    ------------------------------------
//              double  DBL_MAX                 1.79769313486231570e+308
//              float   FLT_MAX                 3.40282346638528860e+38
//              long    LONG_MAX                0x7fffffffffffffff
//              int             INT_MAX                 0x7fffffff
//              short   SHRT_MAX                0x7fff
//----------------------------------------------------------------------

const ANNdist   ANN_DIST_INF = ANN_DBL_MAX;

//----------------------------------------------------------------------
//      Significant digits for tree dumps:
//              When floating point coordinates are used, the routine that dumps
//              a tree needs to know roughly how many significant digits there
//              are in a ANNcoord, so it can output points to full precision.
//              This is defined to be ANNcoordPrec.  On most systems these
//              values can be found in the standard include files <limits.h> or
//              <float.h>.  For integer types, the value is essentially ignored.
//
//              ANNcoord ANNcoordPrec   Values (see <limits.h> or <float.h>)
//              -------- ------------   ------------------------------------
//              double   DBL_DIG                15
//              float    FLT_DIG                6
//              long     doesn't matter 19
//              int              doesn't matter 10
//              short    doesn't matter 5
//----------------------------------------------------------------------

#ifdef DBL_DIG                                                  // number of sig. bits in ANNcoord
        const int        ANNcoordPrec   = DBL_DIG;
#else
        const int        ANNcoordPrec   = 15;   // default precision
#endif

//----------------------------------------------------------------------
// Self match?
//      In some applications, the nearest neighbor of a point is not
//      allowed to be the point itself. This occurs, for example, when
//      computing all nearest neighbors in a set.  By setting the
//      parameter ANN_ALLOW_SELF_MATCH to ANNfalse, the nearest neighbor
//      is the closest point whose distance from the query point is
//      strictly positive.
//----------------------------------------------------------------------

const ANNbool   ANN_ALLOW_SELF_MATCH    = ANNtrue;

//----------------------------------------------------------------------
//      Norms and metrics:
//              ANN supports any Minkowski norm for defining distance.  In
//              particular, for any p >= 1, the L_p Minkowski norm defines the
//              length of a d-vector (v0, v1, ..., v(d-1)) to be
//
//                              (|v0|^p + |v1|^p + ... + |v(d-1)|^p)^(1/p),
//
//              (where ^ denotes exponentiation, and |.| denotes absolute
//              value).  The distance between two points is defined to be the
//              norm of the vector joining them.  Some common distance metrics
//              include
//
//                              Euclidean metric                p = 2
//                              Manhattan metric                p = 1
//                              Max metric                              p = infinity
//
//              In the case of the max metric, the norm is computed by taking
//              the maxima of the absolute values of the components.  ANN is
//              highly "coordinate-based" and does not support general distances
//              functions (e.g. those obeying just the triangle inequality).  It
//              also does not support distance functions based on
//              inner-products.
//
//              For the purpose of computing nearest neighbors, it is not
//              necessary to compute the final power (1/p).  Thus the only
//              component that is used by the program is |v(i)|^p.
//
//              ANN parameterizes the distance computation through the following
//              macros.  (Macros are used rather than procedures for
//              efficiency.) Recall that the distance between two points is
//              given by the length of the vector joining them, and the length
//              or norm of a vector v is given by formula:
//
//                              |v| = ROOT(POW(v0) # POW(v1) # ... # POW(v(d-1)))
//
//              where ROOT, POW are unary functions and # is an associative and
//              commutative binary operator mapping the following types:
//
//                      **      POW:    ANNcoord                                --> ANNdist
//                      **      #:              ANNdist x ANNdist               --> ANNdist
//                      **      ROOT:   ANNdist (>0)                    --> double
//
//              For early termination in distance calculation (partial distance
//              calculation) we assume that POW and # together are monotonically
//              increasing on sequences of arguments, meaning that for all
//              v0..vk and y:
//
//              POW(v0) #...# POW(vk) <= (POW(v0) #...# POW(vk)) # POW(y).
//
//      Incremental Distance Calculation:
//              The program uses an optimized method of computing distances for
//              kd-trees and bd-trees, called incremental distance calculation.
//              It is used when distances are to be updated when only a single
//              coordinate of a point has been changed.  In order to use this,
//              we assume that there is an incremental update function DIFF(x,y)
//              for #, such that if:
//
//                                      s = x0 # ... # xi # ... # xk
//
//              then if s' is equal to s but with xi replaced by y, that is,
//
//                                      s' = x0 # ... # y # ... # xk
//
//              then the length of s' can be computed by:
//
//                                      |s'| = |s| # DIFF(xi,y).
//
//              Thus, if # is + then DIFF(xi,y) is (yi-x).  For the L_infinity
//              norm we make use of the fact that in the program this function
//              is only invoked when y > xi, and hence DIFF(xi,y)=y.
//
//              Finally, for approximate nearest neighbor queries we assume
//              that POW and ROOT are related such that
//
//                                      v*ROOT(x) = ROOT(POW(v)*x)
//
//              Here are the values for the various Minkowski norms:
//
//              L_p:    p even:                                                 p odd:
//                              -------------------------               ------------------------
//                              POW(v)                  = v^p                   POW(v)                  = |v|^p
//                              ROOT(x)                 = x^(1/p)               ROOT(x)                 = x^(1/p)
//                              #                               = +                             #                               = +
//                              DIFF(x,y)               = y - x                 DIFF(x,y)               = y - x
//
//              L_inf:
//                              POW(v)                  = |v|
//                              ROOT(x)                 = x
//                              #                               = max
//                              DIFF(x,y)               = y
//
//              By default the Euclidean norm is assumed.  To change the norm,
//              uncomment the appropriate set of macros below.
//----------------------------------------------------------------------

//----------------------------------------------------------------------
//      Use the following for the Euclidean norm
//----------------------------------------------------------------------
// #define ANN_POW(v)                   ((v)*(v))
// #define ANN_ROOT(x)                  sqrt(x)
// #define ANN_SUM(x,y)         ((x) + (y))
// #define ANN_DIFF(x,y)                ((y) - (x))

//----------------------------------------------------------------------
//      Use the following for the L_1 (Manhattan) norm
//----------------------------------------------------------------------
// #define ANN_POW(v)           fabs(v)
// #define ANN_ROOT(x)          (x)
// #define ANN_SUM(x,y)         ((x) + (y))
// #define ANN_DIFF(x,y)        ((y) - (x))

//----------------------------------------------------------------------
//      Use the following for a general L_p norm
//----------------------------------------------------------------------
// #define ANN_POW(v)           pow(fabs(v),p)
// #define ANN_ROOT(x)          pow(fabs(x),1/p)
// #define ANN_SUM(x,y)         ((x) + (y))
// #define ANN_DIFF(x,y)        ((y) - (x))

//----------------------------------------------------------------------
//      Use the following for the L_infinity (Max) norm
//----------------------------------------------------------------------
#define ANN_POW(v)              fabs(v)
#define ANN_ROOT(x)             (x)
#define ANN_SUM(x,y)            ((x) > (y) ? (x) : (y))
#define ANN_DIFF(x,y)   (y)

//----------------------------------------------------------------------
//      Array types
//              The following array types are of basic interest.  A point is
//              just a dimensionless array of coordinates, a point array is a
//              dimensionless array of points.  A distance array is a
//              dimensionless array of distances and an index array is a
//              dimensionless array of point indices.  The latter two are used
//              when returning the results of k-nearest neighbor queries.
//----------------------------------------------------------------------

typedef ANNcoord* ANNpoint;                     // a point
typedef ANNpoint* ANNpointArray;        // an array of points
typedef ANNdist*  ANNdistArray;         // an array of distances
typedef ANNidx*   ANNidxArray;          // an array of point indices

//----------------------------------------------------------------------
//      Basic point and array utilities:
//              The following procedures are useful supplements to ANN's nearest
//              neighbor capabilities.
//
//              annDist():
//                      Computes the (squared) distance between a pair of points.
//                      Note that this routine is not used internally by ANN for
//                      computing distance calculations.  For reasons of efficiency
//                      this is done using incremental distance calculation.  Thus,
//                      this routine cannot be modified as a method of changing the
//                      metric.
//
//              Because points (somewhat like strings in C) are stored as
//              pointers.  Consequently, creating and destroying copies of
//              points may require storage allocation.  These procedures do
//              this.
//
//              annAllocPt() and annDeallocPt():
//                              Allocate a deallocate storage for a single point, and
//                              return a pointer to it.  The argument to AllocPt() is
//                              used to initialize all components.
//
//              annAllocPts() and annDeallocPts():
//                              Allocate and deallocate an array of points as well a
//                              place to store their coordinates, and initializes the
//                              points to point to their respective coordinates.  It
//                              allocates point storage in a contiguous block large
//                              enough to store all the points.  It performs no
//                              initialization.
//
//              annCopyPt():
//                              Creates a copy of a given point, allocating space for
//                              the new point.  It returns a pointer to the newly
//                              allocated copy.
//----------------------------------------------------------------------

DLL_API ANNdist annDist(
        int                             dim,            // dimension of space
        ANNpoint                p,                      // points
        ANNpoint                q);

DLL_API ANNpoint annAllocPt(
        int                             dim,            // dimension
        ANNcoord                c = 0);         // coordinate value (all equal)

DLL_API ANNpointArray annAllocPts(
        int                             n,                      // number of points
        int                             dim);           // dimension

DLL_API void annDeallocPt(
        ANNpoint                &p);            // deallocate 1 point

DLL_API void annDeallocPts(
        ANNpointArray   &pa);           // point array

DLL_API ANNpoint annCopyPt(
        int                             dim,            // dimension
        ANNpoint                source);        // point to copy

//----------------------------------------------------------------------
//Overall structure: ANN supports a number of different data structures
//for approximate and exact nearest neighbor searching.  These are:
//
//              ANNbruteForce   A simple brute-force search structure.
//              ANNkd_tree              A kd-tree tree search structure.  ANNbd_tree
//              A bd-tree tree search structure (a kd-tree with shrink
//              capabilities).
//
//              At a minimum, each of these data structures support k-nearest
//              neighbor queries.  The nearest neighbor query, annkSearch,
//              returns an integer identifier and the distance to the nearest
//              neighbor(s) and annRangeSearch returns the nearest points that
//              lie within a given query ball.
//
//              Each structure is built by invoking the appropriate constructor
//              and passing it (at a minimum) the array of points, the total
//              number of points and the dimension of the space.  Each structure
//              is also assumed to support a destructor and member functions
//              that return basic information about the point set.
//
//              Note that the array of points is not copied by the data
//              structure (for reasons of space efficiency), and it is assumed
//              to be constant throughout the lifetime of the search structure.
//
//              The search algorithm, annkSearch, is given the query point (q),
//              and the desired number of nearest neighbors to report (k), and
//              the error bound (eps) (whose default value is 0, implying exact
//              nearest neighbors).  It returns two arrays which are assumed to
//              contain at least k elements: one (nn_idx) contains the indices
//              (within the point array) of the nearest neighbors and the other
//              (dd) contains the squared distances to these nearest neighbors.
//
//              The search algorithm, annkFRSearch, is a fixed-radius kNN
//              search.  In addition to a query point, it is given a (squared)
//              radius bound.  (This is done for consistency, because the search
//              returns distances as squared quantities.) It does two things.
//              First, it computes the k nearest neighbors within the radius
//              bound, and second, it returns the total number of points lying
//              within the radius bound. It is permitted to set k = 0, in which
//              case it effectively answers a range counting query.  If the
//              error bound epsilon is positive, then the search is approximate
//              in the sense that it is free to ignore any point that lies
//              outside a ball of radius r/(1+epsilon), where r is the given
//              (unsquared) radius bound.
//
//              The generic object from which all the search structures are
//              dervied is given below.  It is a virtual object, and is useless
//              by itself.
//----------------------------------------------------------------------

class DLL_API ANNpointSet {
public:
        virtual ~ANNpointSet() {}                       // virtual distructor

        virtual void annkSearch(                        // approx k near neighbor search
                ANNpoint                q,                              // query point
                int                             k,                              // number of near neighbors to return
                ANNidxArray             nn_idx,                 // nearest neighbor array (modified)
                ANNdistArray    dd,                             // dist to near neighbors (modified)
                double                  eps=0.0                 // error bound
                ) = 0;                                                  // pure virtual (defined elsewhere)

        virtual int annkFRSearch(                       // approx fixed-radius kNN search
                ANNpoint                q,                              // query point
                ANNdist                 sqRad,                  // squared radius
                int                             k = 0,                  // number of near neighbors to return
                ANNidxArray             nn_idx = NULL,  // nearest neighbor array (modified)
                ANNdistArray    dd = NULL,              // dist to near neighbors (modified)
                double                  eps=0.0                 // error bound
                ) = 0;                                                  // pure virtual (defined elsewhere)

        virtual int theDim() = 0;                       // return dimension of space
        virtual int nPoints() = 0;                      // return number of points
                                                                                // return pointer to points
        virtual ANNpointArray thePoints() = 0;
};

//----------------------------------------------------------------------
//      Brute-force nearest neighbor search:
//              The brute-force search structure is very simple but inefficient.
//              It has been provided primarily for the sake of comparison with
//              and validation of the more complex search structures.
//
//              Query processing is the same as described above, but the value
//              of epsilon is ignored, since all distance calculations are
//              performed exactly.
//
//              WARNING: This data structure is very slow, and should not be
//              used unless the number of points is very small.
//
//              Internal information:
//              ---------------------
//              This data structure bascially consists of the array of points
//              (each a pointer to an array of coordinates).  The search is
//              performed by a simple linear scan of all the points.
//----------------------------------------------------------------------

class DLL_API ANNbruteForce: public ANNpointSet {
        int                             dim;                            // dimension
        int                             n_pts;                          // number of points
        ANNpointArray   pts;                            // point array
public:
        ANNbruteForce(                                          // constructor from point array
                ANNpointArray   pa,                             // point array
                int                             n,                              // number of points
                int                             dd);                    // dimension

        ~ANNbruteForce();                                       // destructor

        void annkSearch(                                        // approx k near neighbor search
                ANNpoint                q,                              // query point
                int                             k,                              // number of near neighbors to return
                ANNidxArray             nn_idx,                 // nearest neighbor array (modified)
                ANNdistArray    dd,                             // dist to near neighbors (modified)
                double                  eps=0.0);               // error bound

        int annkFRSearch(                                       // approx fixed-radius kNN search
                ANNpoint                q,                              // query point
                ANNdist                 sqRad,                  // squared radius
                int                             k = 0,                  // number of near neighbors to return
                ANNidxArray             nn_idx = NULL,  // nearest neighbor array (modified)
                ANNdistArray    dd = NULL,              // dist to near neighbors (modified)
                double                  eps=0.0);               // error bound

        int theDim()                                            // return dimension of space
                { return dim; }

        int nPoints()                                           // return number of points
                { return n_pts; }

        ANNpointArray thePoints()                       // return pointer to points
                {  return pts;  }
};

//----------------------------------------------------------------------
// kd- and bd-tree splitting and shrinking rules
//              kd-trees supports a collection of different splitting rules.
//              In addition to the standard kd-tree splitting rule proposed
//              by Friedman, Bentley, and Finkel, we have introduced a
//              number of other splitting rules, which seem to perform
//              as well or better (for the distributions we have tested).
//
//              The splitting methods given below allow the user to tailor
//              the data structure to the particular data set.  They are
//              are described in greater details in the kd_split.cc source
//              file.  The method ANN_KD_SUGGEST is the method chosen (rather
//              subjectively) by the implementors as the one giving the
//              fastest performance, and is the default splitting method.
//
//              As with splitting rules, there are a number of different
//              shrinking rules.  The shrinking rule ANN_BD_NONE does no
//              shrinking (and hence produces a kd-tree tree).  The rule
//              ANN_BD_SUGGEST uses the implementors favorite rule.
//----------------------------------------------------------------------

enum ANNsplitRule {
                ANN_KD_STD                              = 0,    // the optimized kd-splitting rule
                ANN_KD_MIDPT                    = 1,    // midpoint split
                ANN_KD_FAIR                             = 2,    // fair split
                ANN_KD_SL_MIDPT                 = 3,    // sliding midpoint splitting method
                ANN_KD_SL_FAIR                  = 4,    // sliding fair split method
                ANN_KD_SUGGEST                  = 5};   // the authors' suggestion for best
const int ANN_N_SPLIT_RULES             = 6;    // number of split rules

enum ANNshrinkRule {
                ANN_BD_NONE                             = 0,    // no shrinking at all (just kd-tree)
                ANN_BD_SIMPLE                   = 1,    // simple splitting
                ANN_BD_CENTROID                 = 2,    // centroid splitting
                ANN_BD_SUGGEST                  = 3};   // the authors' suggested choice
const int ANN_N_SHRINK_RULES    = 4;    // number of shrink rules

//----------------------------------------------------------------------
//      kd-tree:
//              The main search data structure supported by ANN is a kd-tree.
//              The main constructor is given a set of points and a choice of
//              splitting method to use in building the tree.
//
//              Construction:
//              -------------
//              The constructor is given the point array, number of points,
//              dimension, bucket size (default = 1), and the splitting rule
//              (default = ANN_KD_SUGGEST).  The point array is not copied, and
//              is assumed to be kept constant throughout the lifetime of the
//              search structure.  There is also a "load" constructor that
//              builds a tree from a file description that was created by the
//              Dump operation.
//
//              Search:
//              -------
//              There are two search methods:
//
//                      Standard search (annkSearch()):
//                              Searches nodes in tree-traversal order, always visiting
//                              the closer child first.
//                      Priority search (annkPriSearch()):
//                              Searches nodes in order of increasing distance of the
//                              associated cell from the query point.  For many
//                              distributions the standard search seems to work just
//                              fine, but priority search is safer for worst-case
//                              performance.
//
//              Printing:
//              ---------
//              There are two methods provided for printing the tree.  Print()
//              is used to produce a "human-readable" display of the tree, with
//              indenation, which is handy for debugging.  Dump() produces a
//              format that is suitable reading by another program.  There is a
//              "load" constructor, which constructs a tree which is assumed to
//              have been saved by the Dump() procedure.
//
//              Performance and Structure Statistics:
//              -------------------------------------
//              The procedure getStats() collects statistics information on the
//              tree (its size, height, etc.)  See ANNperf.h for information on
//              the stats structure it returns.
//
//              Internal information:
//              ---------------------
//              The data structure consists of three major chunks of storage.
//              The first (implicit) storage are the points themselves (pts),
//              which have been provided by the users as an argument to the
//              constructor, or are allocated dynamically if the tree is built
//              using the load constructor).  These should not be changed during
//              the lifetime of the search structure.  It is the user's
//              responsibility to delete these after the tree is destroyed.
//
//              The second is the tree itself (which is dynamically allocated in
//              the constructor) and is given as a pointer to its root node
//              (root).  These nodes are automatically deallocated when the tree
//              is deleted.  See the file src/kd_tree.h for further information
//              on the structure of the tree nodes.
//
//              Each leaf of the tree does not contain a pointer directly to a
//              point, but rather contains a pointer to a "bucket", which is an
//              array consisting of point indices.  The third major chunk of
//              storage is an array (pidx), which is a large array in which all
//              these bucket subarrays reside.  (The reason for storing them
//              separately is the buckets are typically small, but of varying
//              sizes.  This was done to avoid fragmentation.)  This array is
//              also deallocated when the tree is deleted.
//
//              In addition to this, the tree consists of a number of other
//              pieces of information which are used in searching and for
//              subsequent tree operations.  These consist of the following:
//
//              dim                                             Dimension of space
//              n_pts                                   Number of points currently in the tree
//              n_max                                   Maximum number of points that are allowed
//                                                              in the tree
//              bkt_size                                Maximum bucket size (no. of points per leaf)
//              bnd_box_lo                              Bounding box low point
//              bnd_box_hi                              Bounding box high point
//              splitRule                               Splitting method used
//
//----------------------------------------------------------------------

//----------------------------------------------------------------------
// Some types and objects used by kd-tree functions
// See src/kd_tree.h and src/kd_tree.cpp for definitions
//----------------------------------------------------------------------
class ANNkdStats;                               // stats on kd-tree
class ANNkd_node;                               // generic node in a kd-tree
typedef ANNkd_node*     ANNkd_ptr;      // pointer to a kd-tree node

class DLL_API ANNkd_tree: public ANNpointSet {
protected:
        int                             dim;                            // dimension of space
        int                             n_pts;                          // number of points in tree
        int                             bkt_size;                       // bucket size
        ANNpointArray   pts;                            // the points
        ANNidxArray             pidx;                           // point indices (to pts array)
        ANNkd_ptr               root;                           // root of kd-tree
        ANNpoint                bnd_box_lo;                     // bounding box low point
        ANNpoint                bnd_box_hi;                     // bounding box high point

        void SkeletonTree(                                      // construct skeleton tree
                int                             n,                              // number of points
                int                             dd,                             // dimension
                int                             bs,                             // bucket size
                ANNpointArray pa = NULL,                // point array (optional)
                ANNidxArray pi = NULL);                 // point indices (optional)

public:
        ANNkd_tree(                                                     // build skeleton tree
                int                             n = 0,                  // number of points
                int                             dd = 0,                 // dimension
                int                             bs = 1);                // bucket size

        ANNkd_tree(                                                     // build from point array
                ANNpointArray   pa,                             // point array
                int                             n,                              // number of points
                int                             dd,                             // dimension
                int                             bs = 1,                 // bucket size
                ANNsplitRule    split = ANN_KD_SUGGEST);        // splitting method

        ANNkd_tree(                                                     // build from dump file
                std::istream&   in);                    // input stream for dump file

        ~ANNkd_tree();                                          // tree destructor

        void annkSearch(                                        // approx k near neighbor search
                ANNpoint                q,                              // query point
                int                             k,                              // number of near neighbors to return
                ANNidxArray             nn_idx,                 // nearest neighbor array (modified)
                ANNdistArray    dd,                             // dist to near neighbors (modified)
                double                  eps=0.0);               // error bound

        void annkPriSearch(                             // priority k near neighbor search
                ANNpoint                q,                              // query point
                int                             k,                              // number of near neighbors to return
                ANNidxArray             nn_idx,                 // nearest neighbor array (modified)
                ANNdistArray    dd,                             // dist to near neighbors (modified)
                double                  eps=0.0);               // error bound

        int annkFRSearch(                                       // approx fixed-radius kNN search
                ANNpoint                q,                              // the query point
                ANNdist                 sqRad,                  // squared radius of query ball
                int                             k,                              // number of neighbors to return
                ANNidxArray             nn_idx = NULL,  // nearest neighbor array (modified)
                ANNdistArray    dd = NULL,              // dist to near neighbors (modified)
                double                  eps=0.0);               // error bound

        int theDim()                                            // return dimension of space
                { return dim; }

        int nPoints()                                           // return number of points
                { return n_pts; }

        ANNpointArray thePoints()                       // return pointer to points
                {  return pts;  }

        virtual void Print(                                     // print the tree (for debugging)
                ANNbool                 with_pts,               // print points as well?
                std::ostream&   out);                   // output stream

        virtual void Dump(                                      // dump entire tree
                ANNbool                 with_pts,               // print points as well?
                std::ostream&   out);                   // output stream

        virtual void getStats(                          // compute tree statistics
                ANNkdStats&             st);                    // the statistics (modified)
};

//----------------------------------------------------------------------
//      Box decomposition tree (bd-tree)
//              The bd-tree is inherited from a kd-tree.  The main difference
//              in the bd-tree and the kd-tree is a new type of internal node
//              called a shrinking node (in the kd-tree there is only one type
//              of internal node, a splitting node).  The shrinking node
//              makes it possible to generate balanced trees in which the
//              cells have bounded aspect ratio, by allowing the decomposition
//              to zoom in on regions of dense point concentration.  Although
//              this is a nice idea in theory, few point distributions are so
//              densely clustered that this is really needed.
//----------------------------------------------------------------------

class DLL_API ANNbd_tree: public ANNkd_tree {
public:
        ANNbd_tree(                                                     // build skeleton tree
                int                             n,                              // number of points
                int                             dd,                             // dimension
                int                             bs = 1)                 // bucket size
                : ANNkd_tree(n, dd, bs) {}              // build base kd-tree

        ANNbd_tree(                                                     // build from point array
                ANNpointArray   pa,                             // point array
                int                             n,                              // number of points
                int                             dd,                             // dimension
                int                             bs = 1,                 // bucket size
                ANNsplitRule    split  = ANN_KD_SUGGEST,        // splitting rule
                ANNshrinkRule   shrink = ANN_BD_SUGGEST);       // shrinking rule

        ANNbd_tree(                                                     // build from dump file
                std::istream&   in);                    // input stream for dump file
};

//----------------------------------------------------------------------
//      Other functions
//      annMaxPtsVisit          Sets a limit on the maximum number of points
//                                              to visit in the search.
//  annClose                    Can be called when all use of ANN is finished.
//                                              It clears up a minor memory leak.
//----------------------------------------------------------------------

DLL_API void annMaxPtsVisit(    // max. pts to visit in search
        int                             maxPts);        // the limit

DLL_API void annClose();                // called to end use of ANN

#endif