NearTree -- function library efficiently solving the Nearest Neighbor Problem

CVector |

## NearTree

Release 5.1.1
24 April 2016
© Copyright 2001, 2008, 2009, 2010, 2011, 2014, 2016 Larry Andrews.
All rights reserved
based on
Lawrence C. Andrews, Herbert J. Bernstein, "NearTree, a data structure
and a software toolkit for the nearest-neighbor problem",
J. Appl. Crystallogr., Volume 49, Part 3 (June 2016),
doi: 10.1107/S1600576716004350, ISSN:1600-5767,

Larry Andrews, "A template for the nearest neighbor problem",
C/C++ Users Journal, Volume 19, Issue 11 (November 2001), 40 - 49 (2001),
ISSN:1075-2838,
www.ddj.com/architect/184401449

Revised 12 Dec 2008, for sourceforge release, Larry Andrews and Herbert J. Bernstein
8 Jan 2009 Release 1.0 LCA and HJB
11 Jan 2009 Release 1.0.1 LCA and HJB
21 March 2009 Release 2.0 LCA and HJB
30 May 2009 Release 2.1 LCA and HJB
4 June 2009 Release 2.1.1 LCA and HJB
7 June 2009 Release 2.1.2 LCA and HJB
7 July 2009 Release 2.1.3 LCA and HJB
29 November 2009 Release 2.1.4 LCA
23 April 2010 Release 2.1.5 LCA and HJB
18 July 2010 Release 2.2 HJB
25 July 2010 Release 2.2.1 HJB
31 August 2010 Release 2.3 LCA
7 September 2010 Release 2.3.1 LCA
30 October 2010 Release 2.3.2 LCA
22 March 2011 Release 3.0 LCA and HJB
5 April 2011 Release 3.0.1 LCA and HJB
19 April 2011 Release 3.0.2 HJB
23 April 2011 Release 3.1 HJB
27 September 2011 Release 3.1.1 HJB
18 April 2014 Release 4.0 HJB
23 April 2016 Release 5.0 HJB
25 April 2016 Release 5.1 LCA
30 April 2016 Release 5.1.1 LCA and HJB

#### YOU MAY REDISTRIBUTE NearTree UNDER THE TERMS OF THE LGPL

#### LGPL NOTICES This library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2.1 of the License, or (at your option) any later version. This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU* Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this library; if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

This is a release of an API for finding nearest neighbors among points in spaces of arbitrary dimensions. This release provides a C++ template, TNear.h, and a C library, CNearTree.c, with example/test programs.

Release 5.1.1 added a pdf of the 2001 Dr. Dobbs article, added with permission of the editor.

Release 5.1 augmented the Lloyd alogorithm code to allow for an arbitrary number of cluster points. The Makefile and README have been updated.

Release 5.0 has cummulative changes from 2014, 2015, 2016 (svn revisions 153 - 159) including fixing a bug in the Lloyd cluster test and revising the KNN code to do an annular search. A checkpoint capability and a recovery constructor have been added to TNear.h.

Release 4.0 cummulative changes from 2011, 2013, 2014, including flattening the tree for the C++ template by moving collisions into a separate vector, optional support for armadillo, and new code to facilitate dumping and neartree from the C++ template. Miscellaneous bug fixes were also applied. Thanks to Michael Tautschnig for a duplicate library load fix.

Release 3.1.1 adjusted the libtool version from 5:0:1 to 6:0:1 to avoid confusion on the SONAME of the library as requested by Teemu Ikonen for use as a Debian package.

Release 3.1 adjusted the randomization to be based on the depth rather than the population and added an optional detailed height calculation.

Release 3.0.2 added to randomization on insertion when the tree is not well balanced.

Release 3.0.1 updated the diameter calculation and fixed some documentation errors.

Release 3.0 (formerly named Release 2.4) is a major change to NearTree, restructuring the default search from left-first to balanced and adding hooks to collect information about the tree.

Release 2.3.2 adds optional returns of vectors of ordinals of found objects

Release 2.3.1 adds Centroid method for Lloyd clustering.

Release 2.3 added methods for clustering.

Release 2.2.1 was a minor revision to Release 2.2 to add an include of limits.h to TNear.h, primarily for MINGW use.

Release 2.2 added support for C code for fixed length string searches using a hamming distance norm, and for spherical and hemispherical geodesic norm based searches. Because of the addition of new type and norm flags, the version 2.2 shared libraries cannot be used to support binaries compiled against earlier headers and vice-versa.

Release 2.1.5 was a cleanup update to the 2.1 release of 30 May 2009 to increase portability, in five stages (2.1.1 on 4 June 2009, 2.1.2 on 7 June 2009, 2.1.3 on 7 July 2009, 2.1.4 on 29 November 2009 and 2.1.5 on 23 April 2010) dealing with the following issues:

- Convert to use of a self-contained portable random-number generator from Rob Harrison (2.1.1)
- Ensure wider use of const where appropriate (2.1.1)
- Correct typos and unclear wording in the README (2.1.2)
- Reorganize use of USE_LOCAL_HEADERS in CNearTreeTest.cpp (2.1.2)
- Change FAR macro to CNEARTREE_FAR (2.1.3)
- Add BelongsToPoints and SeparateByRadius (2.1.4)
- Fix dimensions for rhrand (2.1.5)

The 2.1 release was a minor update to the 2.0 release of 21 March 2009 to deal with the following issues:

- Make delayed insertion the default
- Complete the containerization of TNear.h
- Add code for K-nearest/farthest in TNear.h and in CNearTree.c
- Correct the InAnnulus search filter

Release 2.0 was a major update to the 1.0 release of 8 January 2009 to deal with the following issues:

- Replace use recursion with a stack, except in insertion logic
- Replace use of double with templated DistanceType (usually double)
- Provide constuctors to build NearTree from vectors, lists or sets
- Change "Insert" to "insert" for consistency with other containers
- Add access function "at" or array type references [], and provide contents of a neartree as a vector
- Add iterator support
- Provide delayed insertion logic
- Functions added for searches outside of a sphere or in an annular region

Our thanks to Nicolas Brodu for suggesting the more general handling of the distance type.

Note: As Nicolas Brodu has noted, CNearTree is particularly well-suited to multi-threaded applications. However, if the same CNearTree is to be searched in multiple threads, it is important to complete all insertions and/or delayed insertions before parallel execution of parallel searches.

#### Contents

- Installation
- The C++ template: TNear.h
- The C NearTree API: CNearTree.c
- A Portable pseudo-random number generator: rhrand.h

#### Installation

The NearTree package is available at www.sourceforge.net/projects/neartree. A source tarball is available at downloads.sourceforge.net/neartree/NearTree-5.1.1.tar.gz. Later tarballs may be available.

If you decide to simply use the TNear.h header to add nearest neighbor support to C++ code under Visual Studio, be sure to also use the rhrand.h and triple.h headers. It is no longer necessary to define USE_LOCAL_HEADERS, which is automatically defined if _MSC_VER is defined. For unix or MINGW, you will need to use the Makefile and to have libtool on your system. Be warned that the default libtool under Mac OS X will not work for this installation.

When the source tarball is downloaded and unpacked, you should have a directory NearTree-5.1.1. To see the current settings for a build execute

make

which should give the following information:

     PLEASE READ README_NearTree.txt and lgpl.txt

     Before making the NearTree libraries and example programs, check
     that the chosen settings are correct

     The current C++ and C compile commands are:

       libtool --mode=compile g++ -g -O2  -Wall -ansi -pedantic  \
          -DCNEARTREE_SAFE_TRIANG=1 -I.   -c
       libtool --mode=compile gcc -g -O2  -Wall -ansi -pedantic  \
          -DCNEARTREE_SAFE_TRIANG=1 -I.   -c

     The C API, CNearTree.c, depends on the sourceforge project CVector
     You are currently setup to use the system defaults for CVector
     If that is not correct, define the variable CVECTOR_INCLUDE

     The current library link command is:

       libtool --mode=link  gcc -version-info 7:0:0 \
         -no-undefined -rpath /usr/local/lib

     The current C++ and C library local, and C dynamic and static build commands are:

       libtool --mode=link g++ -no-undefined -g -O2  -Wall -ansi -pedantic \
          -DCNEARTREE_SAFE_TRIANG=1 -I.
       libtool --mode=link gcc -g -O2  -Wall -ansi -pedantic \
          -DCNEARTREE_SAFE_TRIANG=1 -I.
       libtool --mode=link gcc -no-undefined -g -O2  -Wall -ansi -pedantic \
          -DCNEARTREE_SAFE_TRIANG=1 -shared -I/usr/local/include
       libtool --mode=link gcc -g -O2  -Wall -ansi -pedantic  \
          -DCNEARTREE_SAFE_TRIANG=1 -static-libtool-libs -I/usr/local/include

     Before installing the NearTree library and example programs, check
     that the install directory and install commands are correct:

     The current values are :

       /usr/local
       libtool --mode=install cp

     To compile the NearTree library and example programs type:

       make clean
       make all

     To run a set of tests type:

       make tests

     To clean up the directories type:

       make clean

     To install the library and headers type:

       make install

If these settings need to be changed, edit Makefile. On some systems, e.g. Mac OS X, the default libtool is not appropriate. In that case you should install a recent version of libtool. The CVector kit has been tested with libtool versions 1.3.5 and 1.5.4. For MINGW, libtool version 2.2.6 and gcc version 4 are needed to work with shared libraries (DLLs). If the system libtool is not to be used, define the variable LIBTOOL to be the path to the libtool executable, e.g. in bash

export LIBTOOL=$HOME/bin/libtool

or in the Makefile

LIBTOOL = $(HOME)/bin/libtool

If you need to include local header files using #include "..." instead of #include <...>, define the variable USE_LOCAL_HEADERS. USE_LOCAL_HEADERS is the default for Visual Studio under Microsoft Windows.

Optionally, you may also define CNEARTREE_FORCEFLIP to maximize tree reorganization on insertion, CNEARTREE_NOFLIP to suppress tree reorganization on insertion, CNEARTREE_NODEFER to make all insertions immediate, CNEARTREE_FORCEPREPUNE to do searches first with a tighter estimate on the search radius, and CNEARTREE_NOPREPRUNE to suppress that behavior. The defaults are to do tree reorganization on insertion, to defer insertions, but not to preprune the search radius.

If you define CNEARTREE_INSTRUMENTED, code will be enabled to track node visits in searching the tree.

If you define USE_ARMADILLO_LIBRARY, armadillo will be included without BLAS and without LAPACK, and a DistanceBetween for arma::vec6 vectors will be defined.

The triangle inequality that must be evaluated in building trees and retrieving data may not be evaluated correctly if the range of the three values is extremely large (>10**15 or so for doubles) or may be evaluated differently by some compilers in different parts of a program (due to differing usage of registers). The default in this API is to do the triangle inequality three different ways under the control of CNEARTREE_SAFE_TRIANG

    #ifdef CNEARTREE_SAFE_TRIANG
    #define TRIANG(a,b,c) (  (((b)+(c))-(a) >= 0) \
                          || ((b)-((a)-(c)) >= 0) \
                          || ((c)-((a)-(b)) >= 0))
    #else
    #define TRIANG(a,b,c) (  (((b)+(c))-(a) >= 0))
    #endif

Problems with the unsafe definition of TRIANG have been seen in Linux under gcc version 4 and in MS Window under VS 2003. There is a slight performance hit from the triple test. If maximal speed is critical and misidentification of nearest points by relative distance errors of about 1 part in 10**15 is not a serious problem, the definition of -DCNEARTREE_SAFE_TRIANG=1 can be removed from the definition of CFLAGS in the Makefile.

NOTE: A range of 10**15 is comparable to the diameter of the earth vs. the separation of two bonded atoms.

As of version 5.0, the default for processing K-nearest-neighbor request is to search in nested annuli. For KNN searches on high dimension spaces or spaces with expensive distance calculations, this is the best choice. However, flags are provided to revert to the version 4.0 spherical KNN search if desired. See NTF_SphericalKNN in TNear.h and CNTF_SKNN in CNearTree.h.

If you define CNEARTREE_DIMSAMPLES with a integer value, that value will be used as the count of the number of radii to try to estimate the Hausdorff dimension in doing K-nearest-neighbor processinf. Values as low as 2 can be used. The default is 4. The higher the value, the more accurate the dimension estimate. The Makefile includes tests of 2, 4, 6 and 8 samples.

#### The C++ template: TNear.h

This is a revised release of

> template <typename T, typename DistanceType=double, int distMinValue=-1 > class CNearTree;

implementing the Nearest Neighbor algorithm after Kalantari and McDonald, (IEEE Transactions on Software Engineering, v. SE-9, pp. 631-634,1983) modified to use recursion for insertions and recursion (original version) or a stack (current version) for searches instead of a double-linked tree and simplified. The default search algorithm no longer favors the left branch first, but follows the more balanced Kalantari and McDonald approach. The prior search algorithm is available in "Left" versions of the search routines doing a bit less checking for things like is the distance to the right less than the distance to the left.

This template is used to contain a collection of objects. After the collection has been loaded into this structure, it can be quickly queried for which object is "closest" to some probe object of the same type. The major restriction on applicability of the near-tree is that the algorithm only works if the objects obey the triangle inequality. The triangle rule states that the length of any side of a triangle cannot exceed the sum of the lengths of the other two sides.

CNearTree is the root class for the neartree. The actual data of the tree is stored in NearTreeNode objects descending from a CNearTree.

The types of objects that can be stored in the tree is quite broad. The biggest limitation is that the objects must reside in some sort of metric space and must obey the triangle rule. They must also be all of the same size because they are stored in an std::vector. If your application requires objects of varying storage, then your best way to use this code is to store pointers or handles and to write your own distance functions. Note that std::string is a pointer type variable and so can be stored directly.

The type of the objects to be stored is the only required template argument. The type of the distance measure (DistanceType) defaults to double. If your application is for an integer type, then the type for DistanceType can be your integer type. This has the potential for speeding the calculations by avoiding FP computation. Other general types can be used if desired, but you may need to also input a value of distMinValue.

The template argument distMinValue must be something that your class will understand as a negative number. The default input is negative one. Internally, that is cast to DistanceType. Since most uses will be for DistanceType to be double, that is a simple conversion. Obviously, for integer types, there is no problem either. The need for this value is to have something internally that is recognizable as smaller than the smallest "distance" that can exist between any two objects in your type. For most users, there is no need to input anything other than the default, -1. -1 must be castable to DistanceType. It seems unlikely that anyone would actually need this optional parameter, but it is here for completeness.

It is a design decision that this class cannot work for unsigned types. Verifying the triangle rule for unsigned types is more complex. Sorry, unsigned types are left as an exercise for the reader.

The user of this class needs to provide at least the following functionality for the template to work. For the built-in numerics of C++, they are provided by the system.

DistanceType Norm( void );
| // a function "Norm( void )" of the templated class // to return DistanceType (usually will return a // "length" of type double)
operator- ( ); | // geometrical (vector) difference of two objects
| // a copy constructor would be nice
| // a constructor would be nice
| // a destructor would be nice

The provided interface is:

        #include <TNear.h>

        // Constructors

        CNearTree( void );   // constructor
           // nstantiated by something like:      CNearTree <T> vTree;
           // for some type T

        CNearTree( const ContainerType<T> & o);    // constructor from containers, e.g. ...

        CNearTree( const std::vector<T> & o );     // constructor

        CNearTree( const std::list<T> & o );       // constructor

        CNearTree( const std::set<T> & o );        // constructor

        CNearTree( const CNearTree<T> & o );       // constructor

        CNearTree( const ContainerType<T> & o1, const ContainerType<T> & o2 );
                                                    // constructor merging 2 containers, The
                                                    // containers can be standard library containers or CNearTrees.

        // *** The next constructor and the following Get_Checkpoint function are a matched
        //     pair.  The constructor will recreate a NearTree save by Get_Checkpoint, even
        //     if the objects have been saved to a file and restored. **

        CNearTree( const std::vector<long> & DelayedIndices,
                                                    // objects queued for insertion, possibly in random order
                   const std::vector<T> & ObjectStore,
                                                    // all inserted objects go here
                   const std::vector<size_t> & ObjectCollide,
                                                    // overflow chain of colliding objects
                   const size_t DeepestDepth,       // maximum depth of the tree
                   const std::vector< NearTreeNode<T, DistanceType, distMinValue> * > & NearTreeNodes,
                                                    // vector of pointers to nodes to build the tree
                   const NearTreeNode<T, DistanceType, distMinValue> BaseNode,
                                                    // the tree's data is stored down
                                                    // this node in m_NearTreeNodes
                   const long Flags,                // flags for operational control (mainly for testing)
                   const DistanceType DiamEstimate, // estimated diameter
                   const DistanceType SumSpacings,  // sum of spacings at time of insertion
                   const DistanceType SumSpacingsSq,// sum of squares of spacings at time of insertion
                   const double DimEstimate,        // estimated dimension
                   const double DimEstimateEsd      // estimated dimension estimated standard deviation
    #ifdef CNEARTREE_INSTRUMENTED
                   , const size_t NodeVisits        // number of node visits
    #endif
                                                  ) // constructor

        // Checkpoint Getter

        void Get_Checkpoint ( std::vector<long> * * DelayedIndices,
                                                    // objects queued for insertion, possibly in random order
                   std::vector<T> * * ObjectStore,  // all inserted objects go here
                   std::vector<size_t> * * ObjectCollide,
                                                    // overflow chain of colliding objects
                   size_t * DeepestDepth,           // maximum depth of the tree
                   std::vector< NearTreeNode<T, DistanceType, distMinValue> * > * * NearTreeNodes,
                                                    // vector of pointers to nodes to build the tree
                   NearTreeNode<T, DistanceType, distMinValue> * * BaseNode,
                                                    // the tree's data is stored down
                                                    // this node in m_NearTreeNodes
                   long * Flags,                    // flags for operational control (mainly for testing)
                   DistanceType * DiamEstimate,     // estimated diameter
                   DistanceType * SumSpacings,      // sum of spacings at time of insertion
                   DistanceType * SumSpacingsSq,    // sum of squares of spacings at time of insertion
                   double * DimEstimate,            // estimated dimension
                   double * DimEstimateEsd          // estimated dimension estimated standard deviation
    #ifdef CNEARTREE_INSTRUMENTED
                   , size_t * NodeVisits            // number of node visits
    #endif
                                                  ) // checkpoint getter

        // Destructor

        ~CNearTree( void );  // destructor

        void clear( void );  // clear the NearTree

        // Flag Management

        long GetFlags( void ) const;                       // Get all execution flags
        void SetFlags( const long flags );                 // Set all execution flags
        long GetFlags( const long mask ) const;     // Get execution flags within mask
        void SetFlags( const long flags, const long mask );
                                                                               // Set execution flags within mask

        // The available execution flags are

        static const long        NTF_NoPrePrune        = 1; //flag to suppress all search prepruning
        static const long        NTF_ForcePrePrune     = 2; //flag to force search prepruning
        static const long        NTF_NoFlip            = 4; //flag to suppress flips on insert
        static const long        NTF_ForceFlip         = 8; //flag to force flips on insert
        static const long        NTF_NoDefer           =16; //flag to prevent deferred insert
        static const long        NTF_AnnularKNN        =32; //flag to do KNN in annular pieces
        static const long        NTF_SphericalKNN      =64; //flag to do KNN as complete spheres

        template<typename InputContainer>
        CNearTree& operator=( const InputContainer& o );
                                                                  // put container's contents into a NearTree,
                                                                  // wiping out the current contents

        template<typename InputContainer>
        CNearTree& operator=( InputContainer& o );
                                                                  // put container's contents into a NearTree,
                                                                  // wiping out the current contents

        template<typename InputContainer>
        CNearTree& operator+=( const InputContainer& o );
                                                                  // add a container's contents to a NearTree

        template<typename InputContainer>
        CNearTree& operator+=( InputContainer& o );
                                                                  // add a container's contents to a NearTree

        template<typename InputContainer>
        CNearTree& operator-=( const InputContainer& o );
                                                                  // remove a container's contents from a NearTree
        template<typename InputContainer>
        CNearTree& operator-=( InputContainer& o );
                                                                  // remove a container's contents from a NearTree

        template<typename InputContainer>
        CNearTree& set_symmetric_difference( const InputContainer&, o );
                                                                  // remove the part of a container's
                                                                  // contents from a NearTree that is
                                                                  // already in the Neartree and add
                                                                  // in the contents of the container
                                                                  // that is not already in the Neartree
                                                                  // i.e. the exclusive or

        template<typename InputContainer>
        CNearTree& set_symmetric_difference( InputContainer&, o );
                                                                  // remove the part of a container's
                                                                  // contents from a NearTree that is
                                                                  // already in the Neartree and add
                                                                  // in the contents of the container
                                                                  // that is not already in the Neartree
                                                                  // i.e. the exclusive or

        void clear ( void );                                // removes all content from a tree

        void insert( const T& t );
           where t is an object of the type T

                all inserts are delayed until a search is performed or
                until an explicit call to CompleteDelayedInsertions
                is called or a search is called. The purpose is to distribute
                the objects a bit more  randomly. Excessively ordered objects
                leads to less than optimal trees.

                Starting with the 2.1 release, places objects in a queue for
                insertion later when  CompleteDelayInsert is called.  In
                earlier releases the default was immediate insertion.

                The following additional convenience insert template
                allow insertion of containers of objects

        template< typename InputContainer >
        void insert( ContainerType & o );      // e. g. ...

        void insert( const std::vector<T> & o );
        void insert( const std::list<T> & o );
        void insert( const std::set<T> & o );
        void insert( const CNearTree<T> & o );

        iterator NearestNeighbor ( const DistanceType & dRadius, const T& t ) const;
           returns an iterator to the nearest point to the probe point t or end() if there is none
        bool NearestNeighbor ( const DistanceType& dRadius,  T& tClosest,   const T& t ) const
           dRadius is the largest radius within which to search; make it
              very large if you want to include every point that was loaded.
           tClosest is returned as the object that was found closest to the probe
              point (if any were within radius dRadius of the probe)
           t is the probe point, used to search in the group of points insert'ed

           return value is true if some object was found within the search radius, false otherwise.
               If false is returned, tClosest is invalid (at best).

        iterator FarthestNeighbor ( T& const T& t ) const;
           returns an iterator to the nearest point to the probe point t or end() if there is none
        bool FarthestNeighbor ( T& tFarthest,   const T& t ) const;
           tFarthest is returned as the object that was found farthest from the probe
              point
           t is the probe point, used to search in the group of points Insert'ed
           return value is true if some object was found, false otherwise
              If false is returned, tFarthest is invalid (at best).

        iterator LeftNearestNeighbor ( const DistanceType & dRadius, const T& t ) const;
           returns an iterator to the nearest point to the probe point t or end() if there is none
        bool LeftNearestNeighbor ( const DistanceType& dRadius,  T& tClosest,   const T& t ) const;
           dRadius is the largest radius within which to search; make it
              very large if you want to include every point that was loaded.
           tClosest is returned as the object that was found closest to the probe
              point (if any were within radius dRadius of the probe)
           t is the probe point, used to search in the group of points insert'ed

           return value is true if some object was found within the search radius, false otherwise.
               If false is returned, tClosest is invalid (at best).

        iterator LeftFarthestNeighbor ( T& const T& t ) const;
           returns an iterator to the nearest point to the probe point t or end() if there is none
        bool LeftFarthestNeighbor ( T& tFarthest,   const T& t ) const;
           tFarthest is returned as the object that was found farthest from the probe
              point
           t is the probe point, used to search in the group of points Insert'ed
           return value is true if some object was found, false otherwise
              If false is returned, tFarthest is invalid (at best).

        The "Left..." versions of NearestNeighbor and FarthestNeighbor are deprecated versions
        provided for compatibility with earlier releases of NearTree.  There are also "Short..."
        and "LeftShort..." versions of NearestNeighbor to support experimental prepruning logic.

        The following functions (BelongsToPoints, SeparateByRadius, FindInSphere, FindOutSphere,
        and FindInAnnulus) all return a container (ContainerType) that can be any standard library
        container (such as std::vector< T >) or CNearTree.

        If the input is a container of points t1:  The NearTree is examined. For each
        point input in the input container a new container of the same type is output
        in the vector of containers that will be returned. If N points are input, then N
        containers will be output. The points of the neartree will be examined. Copies
        of the neartree points are put into the output container (in the output vector)
        that corresponds to the input point that it is nearest to.  If a point in the
        NearTree is equidistant to more than one point in t1, then it is assigned to
        the first point in the container at that distance

        If the input is two points t1 and t2, then the corresponding Neartee point
        are place into containers group1 and group2, and, if group1_ordinals and
        group2_ordinals are provided the ordinals of into those vectors.
        The ordinals can be used as indices into the CNearTree itself.

        template<typename ContainerType>
        std::vector<ContainerType> BelongsToPoints ( const ContainerType& t1 ) const;

        template<typename ContainerType>
        void BelongsToPoints ( const T& t1, const T& t2,
            ContainerType& group1, ContainerType& group2 );
        template<typename ContainerType>
        void BelongsToPoints ( const T& t1, const T& t2,
            ContainerType& group1, ContainerType& group2,
        std::vector<size_t>& group1_ordinals, std::vector<size_t>& group2_ordinals);
        template<typename ContainerType>
        std::vector<ContainerType> BelongsToPoints ( const T& t1 );

        If the input is a container of points t1:  The NearTree is examined. For each
        point input in the input container a new container of the same type is output
        in the vector of containers that will be returned. If N points are input, then N
        containers will be output. The points of the neartree will be examined. Copies
        of the neartree points are put into the output container (in the output vector)
        that corresponds to the input point that it is nearest to.  If a point in the
        NearTree is equidistant to more than one point in t1, then it is assigned to
        the first point in the container at that distance

        If the input is two points t1 and t2, then the corresponding Neartee points
        are place into containers group1 and group2, and, if group1_ordinals and
        group2_ordinals are provided the ordinals of into those vectors.
        The ordinals can be used as indices into the CNearTree itself.

        template<typename ContainerTypeInside, typename ContainerTypeOutside>
        void SeparateByRadius ( const DistanceType radius, const T& probe,
            ContainerTypeInside& inside, ContainerTypeOutside& outside );
        template<typename ContainerTypeInside, typename ContainerTypeOutside>
        void SeparateByRadius ( const DistanceType radius, const T& probe,
            ContainerTypeInside& inside, ContainerTypeOutside& outside,
            std::vector<size_t>& inside_ordinals, std::vector<size_t>& outside_ordinals);
           return the points within radius of the probe in inside and the rest in outside
           if inside_ordinals and outside_ordinals are provided the ordinals of the
           found objects in the object store are put into those vectors.  The ordinals
           can be used as indices into the CNearTree itself.

        long FindInSphere ( const DistanceType& dRadius,
             ContainerType& tInside,   const T& t ) const;
        long FindInSphere ( const DistanceType& dRadius,
             ContainerType& tInside,
             std::vector<size_t>& tIndices, const T& t ) const;
        long FindInSphere ( const DistanceType& dRadius,
             CNearTree<  T >& tInside,  const T& t ) const;
        long LeftFindInSphere ( const DistanceType& dRadius,
             ContainerType& tInside,   const T& t ) const;
        long LeftFindInSphere ( const DistanceType& dRadius,
             ContainerType& tInside,
             std::vector<size_t>& tIndices, const T& t ) const;
        long LeftFindInSphere ( const DistanceType& dRadius,
             CNearTree<  T >& tInside,  const T& t ) const;
           dRadius is the radius within which to search; make it very large if you want to
               include every point that was loaded;
           tInside is returned as the NearTree or container of objects that were found within a radius dRadius
              of the probe point
           if the tIndices argument is given it will be returned as a vector
              of indices in the near tree of the objects returned.
           t is the probe point, used to search in the group of points Insert'ed

           return value is the count of the number of points found within the search radius
           the "Left..." versions are deprecated versions provided for compatibility with
           earlier NearTree releases.

        long FindOutSphere ( const DistanceType& dRadius,
             ContainerType& tOutside,   const T& t ) const;
        long FindOutSphere ( const DistanceType& dRadius,
             ContainerType& tOutside,
             std::vector<size_t>& tIndices, const T& t ) const;
        long FindOutSphere ( const DistanceType& dRadius,
             CNearTree<  T >& tOutside,   const T& t ) const;
        long LeftFindOutSphere ( const DistanceType& dRadius,
             ContainerType& tOutside,   const T& t ) const;
        long LeftFindOutSphere ( const DistanceType& dRadius,
             ContainerType& tOutside,
             std::vector<size_t>& tIndices, const T& t ) const;
        long LeftFindOutSphere ( const DistanceType& dRadius,
             CNearTree<  T >& tOutside,   const T& t ) const;
           dRadius is the radius outside of which to search
           tOutside is returned as the NearTree or container of objects that were found at
              or outside of radius dRadius of the probe point
           if the tIndices argument is given it will be returned as a vector
              of indices in the near tree of the objects returned.
           t is the probe point, used to search in the group of points Insert'ed

           return value is the count of the number of points found outside the search radius
           the "Left..." versions are deprecated versions provided for compatibility with
           earlier NearTree releases.

        long FindInAnnulus ( const DistanceType& dRadius1,
             const DistanceType& dRadius2,
             ContainerType& tInRing,   const T& t ) const;
        long FindInAnnulus ( const DistanceType& dRadius1,
             const DistanceType& dRadius2,
             ContainerType& tInRing,
             std::vector<size_t>& tIndices,  const T& t ) const;
        long FindInAnnulus ( const DistanceType& dRadius1,
             const DistanceType& dRadius2,
             CNearTree<  T >& tInRing,   const T& t ) const;
        long LeftFindInAnnulus ( const DistanceType& dRadius1,
             const DistanceType& dRadius2,
             ContainerType& tInRing,   const T& t ) const;
        long LeftFindInAnnulus ( const DistanceType& dRadius1,
             const DistanceType& dRadius2,
             ContainerType& tInRing,
             std::vector<size_t>& tIndices,  const T& t ) const;
        long LeftFindInAnnulus ( const DistanceType& dRadius1,
             const DistanceType& dRadius2,
             CNearTree<  T >& tInRing,   const T& t ) const;
           dRadius1 and  dRadius2 are the two radii between which to find data points
           tInRing is returned as the NearTree or container of objects that were found at
              or outside of a radius dRadius1 and at or inside of radius dRadius2 of the probe point
           if the tIndices argument is given it will be returned as a vector
              of indices in the near tree of the objects returned.
           t is the probe point, used to search in the group of points Insert'ed

           return value is the count of the number of points found within the annulus
           the "Left..." versions are deprecated versions provided for compatibility with
           earlier NearTree releases.

        long FindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
             ContainerType& tClosest, const T& t );
        long FindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
             ContainerType& tClosest,
             std::vector<size_t>& tIndices, const T& t );
        long FindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
             CNearTree<  T >& tClosest, const T& t );
        long LeftFindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
             ContainerType& tClosest, const T& t );
        long LeftFindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
             ContainerType& tClosest,
             std::vector<size_t>& tIndices, const T& t );
        long LeftFindK_NearestNeighbors ( const size_t k, const DistanceType& dRadius,
             CNearTree<  T >& tClosest, const T& t );
           k is the maximum number of nearest neighbors to return. Finds this many if possible
           dRadius within a sphere defined by dRadius, to search for the k-nearest-neighbors
           tClosest is returned as the ContainerType or NearTree of the objects found
           if the tIndices argument is given it will be returned as a vector
              of indices in the near tree of the objects returned.
           t is the probe point, used to search in the group of points insert'ed

           return value is the count of the number of points found within the sphere
           the "Left..." versions are deprecated versions provided for compatibility with
           earlier NearTree releases.

        long FindK_FarthestNeighbors ( const size_t k,
             ContainerType& tFarthest, const T& t );
        long FindK_FarthestNeighbors ( const size_t k,
             ContainerType& tFarthest,
             std::vector<size_t>& tIndices, const T& t );
        long FindK_FarthestNeighbors ( const size_t k,
              CNearTree<  T >& tFarthest, const T& t );
        long LeftFindK_FarthestNeighbors ( const size_t k,
             ContainerType& tFarthest, const T& t );
        long LeftFindK_FarthestNeighbors ( const size_t k,
             ContainerType& tFarthest,
             std::vector<size_t>& tIndices, const T& t );
        long LeftFindK_FarthestNeighbors ( const size_t k,
              CNearTree<  T >& tFarthest, const T& t );
           k is the maximum number of farthest neighbors to return. Finds this many if possible
           tFarthest is returned as the ContainerType or NearTree of the objects found
           if the tIndices argument is given it will be returned as a vector
              of indices in the near tree of the objects returned.
           t is the probe point, used to search in the group of points insert'ed

           return value is the count of the number of points found within the sphere
           the "Left..." versions are deprecated versions provided for compatibility with
           earlier NearTree releases.

    Access Functions:

         T at ( const size_t n ) const;
            returns the n'th item of the internal data store.  This is not
            guaranteed to be in the order of insertion.

         T operator[] ( const size_t n );
            returns the n'th item of the internal data store.  This is not
            guaranteed to be in the order of insertion.

         template<typename ContainerType>
         operator ContainerType ( void ) const ;
            returns all of the inserted objects in the tree in a container of type ContainerType.
            ContainerType can be std::vector<T>, etc, or other containers, including CNearTree<T>.
            The returned vector contents are not guaranteed to be returned in the order loaded.

         iterator begin ( void ) const;
            returns an iterator to the beginning of the internal data store

         iterator end ( void ) const;
            returns an iterator to the end of the data store (one beyond the last item)

         iterator back ( void ) const;
            returns an iterator to the last data item of the internal data store

    Information and special operation functions:

         void ImmediateInsert( const T&aamp; t );
            insert places objects in a queue for insertion later when CompleteDelayInsert
            is called or a search is called. ImmediateInsert inserts the data immediately
            into the tree (with the potential of a less balanced tree). ImmediateInsert is not
            intended for the ordinary user.

         void CompleteDelayedInsert ( void );
            completes insertion for all delayed objects. sqrt(n) of them are inserted by
            random choice.  The rest are inserted in linear order as originally queued.
            CompleteDelayedInsert is invoked at the beginning of all searches, so the
            average user will never need to call it.

         size_t GetDeferredSize ( void );
            returns the number of delayed objects that have not yet completed insertion. This is
            mainly for information about details of the tree.

         size_t GetTotalSize ( void );
            returns the number of objects that have been insert'ed plus those DelayInsert'ed

         size_t size ( void );
            identical to GetTotalSize

         size_t GetDepth ( void );
            returns the maximum tree layers from the root.  This is mainly for information about
            details of the tree.

         double GetDimEstimate ( void );  // returns an estimate of the Hausdorff dimension
         double GetDimEstimate ( const double DimEstimateEsd );
                                                        // returns an estimate of the Hausdorff dimension
                                                        // to within the given esd
         double GetDimEstimateEsd ( void );
                                                        // returns an estimate of the esd

         double GetDiamEstimate ( void );  // returns an estimate of the diameter

         DistanceType GetMeanSpacing ( void );   // returns an estimate object spacing
         DistanceType GetVarSpacing ( void );   // returns an estimate object spacing variance

         size_t GetNodeVisits ( void );   // returns the number of node visits if
                                                       // CNEARTREE_INSTRUMENTED as defined, 0 otherwise
         void SetNodeVisits,/b> ( const size_t visits);
                                                       // set the number of node visits

         T Centroid ( void );
            returns the centroid of a neartree.

         bool empty ( void );
            returns true if the tree is empty, otherwise false

    Iterators:

         Random access iterators are provided for accessing the data in a CNearTree. The most important
         expected use is to retrieve the objects returned from one of the sphere search functions that
         can return a CNearTree. However, they can be used with any CNearTree.

         They should function in a fashion essentially the same as STL iterators. There is no assurance
         that data will be returned in the order it was loaded, just that it is accessible.  This is the
         list of iterators. The same set is available for const_iterator.

         iterator ( void ) { }; // constructor
         explicit iterator ( const const_iterator& s );
         iterator& operator=   ( const iterator& s );
         iterator& operator=   ( const const_iterator& s );
         iterator  operator++  ( const int n );
         iterator  operator--  ( const int n );
         iterator& operator++  ( void );
         iterator& operator--  ( void );
         iterator  operator+   ( const long n ) const;
         iterator  operator-   ( const long n ) const;
         iterator& operator+=  ( const long n );
         iterator& operator-=  ( const long n );
         T         operator*   ( void )        const;

         bool      operator==  ( const iterator& t ) const;
         bool      operator!=  ( const iterator& t ) const;
         bool      operator==  ( const const_iterator& t ) const;
         bool      operator!=  ( const const_iterator& t ) const;
         bool      operator>  ( const iterator& t ) const;
         bool      operator>  ( const const_iterator& t ) const;
         bool      operator<  ( const iterator& t ) const;
         bool      operator<  ( const const_iterator& t ) const;

         const T * const operator->  ( void )   const;
         long get_position ( void ) const;
         const CNearTree< T, DistanceType, distMinValue > * get_parent ( void  );

So a complete program is:

     #include "TNear.h"
     #include <cstdio>
     void main()
     {
       CNearTree< double > dT;
       double dNear;
       dT.Insert( 1.5 );
       if ( dT.NearestNeighbor( 10000.0,   dNear,  2.0 )) printf( "%f\n",double(dNear-2.0) );
     }

and it should print 0.5 (that's how for 2.0 is from 1.5). For more examples of the use of TNear.h, see main.cpp and CNearTreeTest.cpp.

#### The C NearTree API: CNearTree.c

#### Synopsis

> #include <CNearTree.h>

> double CNearTreeDistsq ( CNearTreeHandle treehandle, void * coord1, void * coord2 );

> double CNearTreeDist ( CNearTreeHandle treehandle, void * coord1, void * coord2 );

> int CNearTreeSetNorm ( const CNearTreeHandle treehandle, int treenorm );

> int CNearTreeNodeCreate ( const CNearTreeHandle treehandle, CNearTreeNodeHandle * treenodehandle )

> int CNearTreeCreate ( CNearTreeHandle * treehandle, size_t treedim, int treetype );

> int CNearTreeFree ( const CNearTreeHandle treehandle );

> int CNearTreeClear ( CNearTreeHandle * treehandle );

> int CNearTreeNodeFree ( CNearTreeNodeHandle * treenodehandle );

> int CNearTreeInsert( const CNearTreeHandle treehandle, const void * coord, const void * obj );

> int CNearTreeImmediateInsert ( const CNearTreeHandle treehandle, const void * coord, const void * obj );

> int CNearTreeDelayedInsert ( const CNearTreeHandle treehandle, const void * coord, const void * obj ); /* ***DEPRECATED*** */

> int CNearTreeNodeInsert ( const CNearTreeHandle treehandle, CNearTreeNodeHandle treenodehandle, size_t index; size_t * depth );

> int CNearTreeNodeInsert_Flip ( const CNearTreeHandle treehandle, CNearTreeNodeHandle treenodehandle, size_t index; size_t * depth );

> int CNearTreeNodeReInsert_Flip ( const CNearTreeHandle treehandle, const CNearTreeNodeHandle treenodehandle, const CNearTreeNodeHandle pntn, size_t * depth );

> int CNearTreeCompleteDelayedInsert ( const CNearTreeHandle treehandle ) int CNearTreeZeroIfEmpty ( const CNearTreeHandle treehandle );

> int CNearTreeGetSize ( const CNearTreeHandle treehandle, size_t * size );

> int CNearTreeGetTotalSize ( const CNearTreeHandle treehandle, size_t * size ); /* ***DEPRECATED*** */

> size_t CNearTreeSize ( const CNearTreeHandle treehandle);

> int CNearTreeGetDeferredSize ( const CNearTreeHandle treehandle, size_t * size );

> int CNearTreeGetDelayedSize ( const CNearTreeHandle treehandle, size_t * size ); /* ***DEPRECATED*** */

> int CNearTreeGetDepth ( const CNearTreeHandle treehandle, size_t * depth )

> int CNearTreeGetFlags ( const CNearTreeHandle treehandle, long * flags, const long mask )

> int CNearTreeSetFlags ( const CNearTreeHandle treehandle, const long flags, const long mask )

> int CNearTreeGetMeanSpacing ( const CNearTreeHandle treehandle, double * spacing );

> int CNearTreeGetVarSpacing ( const CNearTreeHandle treehandle, double * varspacing );

> int CNearTreeCount ( const CNearTreeHandle treehandle, size_t * count );

> int CNearTreeNodeCount ( const CNearTreeNodeHandle treenodehandle, size_t * count );

> #ifdef CNEARTREE_INSTRUMENTED

> int CNearTreeGetNodeVisits ( const CNearTreeHandle treehandle, size_t * visits);

> int CNearTreeSetNodeVisits ( const CNearTreeHandle treehandle, const size_t visits );

> #endif

> int CNearTreeGetDiamEstimate ( const CNearTreeHandle treehandle, double * diamest );

> int CNearTreeGetDimEstimateEsd ( const CNearTreeHandle treehandle, double * dimestesd );

> int CNearTreeGetDimEstimate ( const CNearTreeHandle treehandle, double * dimest, const double DimEstimateEsd );

> int CNearTreeNearestNeighbor ( const CNearTreeHandle treehandle, const double dRadius, void * * coordClosest, void * * objClosest, const void * coord );

> int CNearLeftTreeNearestNeighbor ( const CNearTreeHandle treehandle, const double dRadius, void * * coordClosest, void * * objClosest, const void * coord ); /* ***DEPRECATED*** */

> int CNearTreeFarthestNeighbor ( const CNearTreeHandle treehandle, void * * coordFarthest, void * * objFarthest, const void * coord );

> int CNearTreeFindInSphere ( const CNearTreeHandle treehandle, const double dRadius, CVectorHandle coordInside, CVectorHandle objInside, const void * coord, int resetcount );

> int CNearTreeFindTreeInSphere ( const CNearTreeHandle treehandle, const double dRadius, CNearTreeHandle foundInside, const void * coord, int resetcount )

> int CNearTreeFindOutSphere ( const CNearTreeHandle treehandle, const double dRadius, CVectorHandle coordOutside, CVectorHandle objOutside, const void * coord, int resetcount );

> int CNearTreeFindTreeOutSphere ( const CNearTreeHandle treehandle, const double dRadius, CNearTreeHandle foundOutside, const void * coord, int resetcount )

> int CNearTreeFindInAnnulus ( const CNearTreeHandle treehandle, const double dRadiusInner, const double dRadiusOuter, CVectorHandle coordInRing, CVectorHandle objInRing, const void * coord, int resetcount );

> int CNearTreeFindTreeInAnnulus ( const CNearTreeHandle treehandle, const double dRadiusInner, const double dRadiusOuter, CNearTreeHandle foundInRing, const void * coord, int resetcount )

> int CNearTreeFindKNearest ( const CNearTreeHandle treehandle, const size_t k, const double dRadius, CVectorHandle coordClosest, CVectorHandle objClosest, const void * coord, int resetcount );

> int CNearTreeFindKTreeNearest ( const CNearTreeHandle treehandle, const size_t k, const double dRadius, CNearTreeHandle foundClosest, const void * coord, int resetcount )

> int CNearTreeFindKFarthest ( const CNearTreeHandle treehandle, const size_t k, const double dRadius, CVectorHandle coordFarthest, CVectorHandle objFarthest, const void * coord, int resetcount );

> int CNearTreeFindKTreeFarthest ( const CNearTreeHandle treehandle, const size_t k, const double dRadius, CNearTreeHandle foundFarthest, const void * coord, int resetcount )

> int CNearTreeNearest ( const CNearTreeHandle treehandle, double * dRadius, void * * coordClosest, void * * objClosest, const void * coord );

> int CNearTreeLeftNearest ( const CNearTreeHandle treehandle, double * dRadius, void * * coordClosest, void * * objClosest, const void * coord ); /* ***DEPRECATED*** */

> int CNearTreeFindFarthest ( const CNearTreeHandle treehandle, double * dRadius, void * * coordFarthest, void * * objFarthest, const void * coord );

> int CNearTreeObjects ( const CNearTreeHandle treehandle, CVectorHandle * vectorhandle );

> void * CNearTreeObjectAt ( const CNearTreeHandle treehandle, size_t index );

> int CNearTreeCoords ( const CNearTreeHandle treehandle, CVectorHandle * vectorhandle );

> void * CNearTreeCoordAt ( const CNearTreeHandle treehandle, size_t index );

The NearTree API works with coordinate vectors in an arbitrary number of dimensions. Each neartree is accessed by a pointer of type CNearTreeHandle which points to a struct of type CNearTree, which points to a tree of nodes of type CNearTreeNode:

        typedef struct _CNearTreeNode {
            size_t           m_indexLeft;    /* index of left coords in m_CoordStore
                                                and of left object in m_ObjectStore     */
            size_t           m_indexRight;   /* index of right coords in m_CoordStore
                                                and of right object in m_ObjectStore     */
            double           m_dMaxLeft;     /* longest distance from the left object
                                                to anything below it in the tree            */
            double           m_dMaxRight;    /* longest distance from the right object
                                                to anything below it in the tree            */
            struct _CNearTreeNode * m_pLeftBranch;
                                             /* tree descending from the left object        */
            struct _CNearTreeNode * m_pRightBranch;
                                             /* tree descending from the right object       */
            long              m_iflags;      /* flags
            size_t            m_iTreeSize;   /* size of this node tree  */
    #ifdef CNEARTREE_INSTRUMENTED
            size_t            m_Height;      /* height of this node     */
    #endif

    */
        } CNearTreeNode;

        typedef CNearTreeNode * CNearTreeNodeHandle;

        typedef struct {
            CNearTreeNodeHandle m_ptTree;     /* pointer to the actual tree                  */
            size_t           m_szdimension;   /* dimension of the coordinates                */
            size_t           m_szsize;        /* size of this tree                           */
            size_t           m_szdepth;       /* depth of this tree                          */
            int              m_iflags;        /* flags                                       */
            CVectorHandle    m_ObjectStore;   /* all inserted objects                        */
            CVectorHandle    m_CoordStore;    /* all inserted coordinates                    */
            CVectorHandle    m_DelayedIndices;/* objects queued for insertion                */
            CRHrand          m_rhr;           /* random number generator                     */
            double           m_DiamEstimate;  /* estimated diameter */
            double           m_SumSpacings;   /* sum of spacings at time of insertion */
            double           m_SumSpacingsSq; /* sum of spacings squared at time of insertion */
            double           m_DimEstimate;   /* estimated dimension */
            double           m_DimEstimateEsd;/* estimated dimension estimated standard deviation */
    #ifdef CNEARTREE_INSTRUMENTED
            size_t           m_NodeVisits;    /* number of node visits */
    #endif

        } CNearTree;

        typedef CNearTree     FAR * CNearTreeHandle;

        /*  Execution Control Flags */

    #define CNTF_NOPREPRUNE    0x10000L     /*flag to suppress all search prepruning */
    #define CNTF_FORCEPREPRUNE 0x20000L     /*flag to force search prepruning       */
    #define CNTF_NOFLIP        0x40000L     /*flag to suppress flips on insert      */
    #define CNTF_FORCEFLIP     0x80000L     /*flag to force flips on insert         */
    #define CNTF_NODEFER      0x100000L     /*flag to prevent deferred insert       */
    #define CNTF_SKNN         0x200000L     /*flag to use spherical KNN             */

The internal operation of the API depends on the function CNearTreeDist that returns the distance (L1, L2 or L-infinity) between two coordinate vectors as a double according to the parameters of the given tree. Note that the tree may store the coordinates as integers or as doubles, but the distance is always computed as a double. If this function is replaced by a user function, it is important that the replacement obey the triangle inequality.

A neartree is created by CNearTreeCreate and freed by CNearTreeFree. treedim is the dimension of the coordinate vectors and treetype is one of the three predefined constants CNEARTREE_TYPE_DOUBLE for double or CNEARTREE_TYPE_INTEGER for integer or CNEARTREE_TYPE_STRING, optionally ORed with CNEARTREE_NORM_L1, CNEARTREE_NORM_L2 or CNEARTREE_NORM_LINF for L1, L2 or L-infinity norms, CNEARTREE_NORM_SPHERE or CNEARTREE_NORM_HSPHERE for a spherical or hemispherical norm (L1-norm combination of radial and spherical/hemispherical triangle distances), or CNEARTREE_NORM_HAMMING for the string-Hamming distance norm (add one for each differing character position).

Starting with release 2.1, all insertions are delayed by default, unless the insertions is done by a call to CNearTreeImmediateInsert. The insertions that have been queued are completed by a call to CNearTreeCompleteDelayedInsert or by any search. The insertions are actually done in a randomized order, either for an initial block of sqrt(#queue) by default. or for the entire queue if the flag CNEARTREE_DEFER_ALL is ored with treetype.

Starting with release 3 (formerly called release 2.4) optionally, you may also define CNEARTREE_FORCEFLIP to maximize tree reorganization on insertion, CNEARTREE_NOFLIP to suppress tree reorganization on insertion, CNEARTREE_NODEFER to make all insertions immediate, CNEARTREE_FORCEPREPUNE to do searches first with a tighter estimate on the search radius, and CNEARTREE_NOPREPRUNE to suppress that behavior. The defaults are to do tree reorganization on insertion, to defer insertions, but not to preprune the search radius. If you define CNEARTREE_INSTRUMENTED, code will be enabled to track node visits in searching the tree.

The flags CNEARTREE_DEFER_ALL and CNEARTREE_FLIP used in prior releases are deprecated, but are still defined. They have no effect.

When first created, a neartree has no right or left node and with the dMax-below set to negative values so that any match found will be stored since it will greater than the negative value. The tree is then populated by calls to CNearTreeInsert, with each call providing a coordinate vector coord and an optional object pointer obj. The API copies the coordinate vector, but does not copy the object. Later, when a search is requested or an explicit call to CNearTreeCompleteDelayedInsert is made, the tree is populated in the order left, right and then the nearer child, working from a randomized selection from the items queued for insertion.

Optionally, the actual insertions may done immediately by calling CNearTreeImmediateInsert instead of CNearTreeInsert. For upwards compatibility of the library for existing code, the deprecated CNearTreeDelayedInsert is provided as an deprecated alternate call to CNearTreeInsert.

The neartree is searched for the nearest or farthest coordinate vector in the neartree to a given probe coordinate vector coord by CNearTreeNearestNeighbor and CNearTreeFarthestNeighbor, respectively. Starting with release 3, the search is balanced, following the left or right branch first depending on which child node is closest. The former left-first behavior is deprecated, but still available in CNearLeftTreeNearestNeighbor. The given radius confines the search to a sphere around the probe. If more than a single extremal coordinate point is needed, CNearTreeFindInSphere can be used to obtain a CVector result vector of all the coordinate vectors that satisfy the constraint of being within a specified radius, or CNearTreeFindOutSphere can be used to obtain a CVector result vector of all the coordinates that satisfy the constraint of being outside a specified radius. CNearTreeFindIn Annulus can be used to obtain a CVector result vector of all the coordinates that satisfy the constraint of being between two specified radii from the probe. CNearTreeFindKNearest can be used to obtain a CVector result vector of the k coordinates closest to the probe point such that all results are within the specified radius of the probe point, or CNearTreeFindKFarthest to obtain a CVector result vector of the k coordinates farthest from the probe point such that all results are at or outside the specified radius of the probe point. The vectors themselves are not copied into the result vector. If the parameter resetcount is true (non zero) the result vector is cleared before the search. A CVector result vector of the matching object pointers is returned if objs is not NULL. Aternatively the forms CNearTreeFindTreeInSphere, CNearTreeFindTreeOutSphere, CNearTreeFindTreeInAnnulus, CNearTreeFindKTreeNearest, CNearTreeFindKTreeFarthest can be used to obtain CNearTrees rather than CVectors of results. The functions CNearTreeNearest and CNearTreeFindFarthest implement CNearTreeNearestNeighbor and CNearTreeFarthestNeighbor, respectively, adjusting the radius of the search while the search is in progress and are not normally used by users.

The size of the tree as a count of objects can be obtained using the function NearTreeGetSize or the macro NearTreeSize. The size of the tree as a count of nodes and the depth of the tree can be obtained using the functions CNearTreeCount and CNearTreeGetDepth. Estimates of the Hausdorff dimension, the esd of that estimate, the diameter, the spacing and the variance of the spacing can be obtained with CNearTreeGetDimEstimate, CNearTreeGetDimEstimateEsd, CNearTreeGetDiamEstimate, CNearTreeGetMeanSpacing and CNearTreeGetVarSpacing.

#### Returns

If CNearTreeDist fails, it returns -1. Except for CNearTreeDist, all the functions in the API return 0 ( CNEARTREE_SUCCESS ) for success. If dynamic memory allocation fails, CNEARTREE_MALLOC_FAILED is returned. If a call is made with an improper argument, CNEARTREE_BAD_ARGUMENT is returned. If a search fails to find anything, CNEARTREE_NOT_FOUND is returned. If there is a failure in an attempt to free a CNearTree, CNEARTREE_FREE_FAILED is returned. If any of the internal call to CVector fail, CNEARTREE_CVECTOR_FAILED is returned. For convenience in debugging, the formerly negative values of these returns are now positive.

#### Examples

To create a neartree for 3-dimensional vectors of doubles:

    #include <CNearTree.h>
    CNearTreeHandle treehandle;
    int bReturn;

     ...

     bReturn = !CNearTreeCreate(&treehandle,3,CNEARTREE_TYPE_DOUBLE);

To insert a copy of a 3-dimensional vector of doubles into this tree, with no associated object:

        double v[3];

     ...

        v[0] = 1.; v[1] = 2.; v[2] = 3.;
        bReturn = !CNearTreeInsert(treehandle,&v[0],NULL);

To search for the nearest neighbor to a probe vector vSearch in a radius of 3., returning a pointer to the resulting vector in vBest:

        double * vBest;
        void * vvBest;
        double vSearch[3];
        double   dRad = =3.;

      ...

        if ( !CNearTreeNearestNeighbor(treehandle,dRad,&vvBest,NULL,vSearch))
            {   vBest = (double *)vvBest; }

Note the use of a separate void * vvBest instead of a cast of &vBest to avoid compiler type punning warnings.

For more examples of the use of CNearTree.c, see main.c and CNearTreeTest.c in the release kit.

#### A Portable pseudo-random number generator: rhrand.h

rhrand.h is a portable pseudo-random number generator based one by Rob Harrison, derived from "one in J.M.Hammersley and D.C. Handscomb, 'Monte Carlo Methods,' Methuen & Co., London and Wiley & Sons, New York, 1964, p47". See also, D. E. Knuth "The Art of Computer Programming", Volume 2, "Seminumerical Alogorithms, Third Edition, Addison-Wesley, Reading MA, 1997.

rhrand.h is a header file in which a C++ class, RHrand, is defined, and a C struct typedef CRHrand is defined.

The C++ interface is

        static const int RHRAND_MAX = 32767;  /* the integer range accessible as RHrand::RHRAND_MAX */

        RHrand(void)                          /* the default constructor */

        RHrand( const int iseed )             /* a constructor to start with the given seed */

        ~RHrand( void)                        /* a destructor */

        void srandom( const int iseed)        /* reset the generator based on the given seed */

        double urand( void )                  /* return a random double uniformly distributed in [0,1) */

        int random ( void )                   /* return a random integer uniformly distributed in [0, RHRAND_MAX-1] */

In C++ code, typical use is

    #include <rhhand.h>
        RHrand rhr;

    ...

        x = rhr.urand();

The C interface is suppressed in RHRAND_NOCCODE is defined. Otherwise the C interface is based on defining a struct of type CRHRrand and calling macros that refer to a handle of type RCRHrandHandle.

        typedef struct CRHrand_ {           /* the struct used in random number generattion */
            double buffer[55];
            int indx;
            int jndx;
            int kndx;
            double dTemp;
        } CRHrand;

        typedef CRHrand * CRHrandHandle;     /* the type to be used in maro calls */

        #define CRHRAND_MAX 32767            /* the integer range */

        #define CRHrandSrandom(randhandle,iseed) ...
                                             /* a macro to call to initialize CHRrandHandle randhandle
                                                using see int iseed */

        #define CRHrandUrand(randhandle) ... /* a macro to return a random double uniformly distributed in [0,1) */

        #define CRHrandRandom(randhandle) ((int)(CRHrandUrand(randhandle)*(double)CRHRAND_MAX))
                                             /* a macro to return a random integer uniformly distributed in
                                                [0, CRHRAND_MAX-1] */

Typical use is

    #include <rhhand.h>
        CRHrand rhr;

    ...

        CRHrandSrandom(&rhr, 0 );

    ...

        x = CRHrandUrand(&rhr);

Updated 25 April 2016