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<html>
<head>
<title>
NearTree -- function library efficiently solving the Nearest Neighbor Problem
</title>
</head>
<body>
<font face="Arial,Helvetica,Times" size="3">
<table border=2>
<tr>
<td valign="center" width="88" align="center" height="35" bgcolor="cyan">
<font face="Arial,Helvetica,Times" size="2">
<a href="http://sf.net/projects/cvector" style="text-decoration:none">CVector</a>
</font>
</td>
<td valign="center"  width="88" align="center" height="35">
<a href="http://sourceforge.net/projects/neartree"><img src="http://sflogo.sourceforge.net/sflogo.php?group_id=237121&amp;type=10" width="80" height="15" alt="Get NearTree at SourceForge.net. Fast, secure and Free Open Source software downloads" /></a>
</td>
</tr>
</table>
<hr>
<center>
<h2 align=center>NearTree</h2>
Release 5.1.1<br />
<font size="-1">
24 April 2016<br />
&#169; Copyright 2001, 2008, 2009, 2010, 2011, 2014, 2016 Larry Andrews.<br />
All rights reserved <br />
based on<br />
Lawrence C. Andrews, Herbert J. Bernstein, &quot;<i>NearTree, a data structure <br />
    and a software toolkit for the nearest-neighbor problem</i>&quot;,<br />
    J. Appl. Crystallogr., Volume 49, Part 3 (June 2016),<br />
    doi: 10.1107/S1600576716004350, ISSN:1600-5767,<br />

<p>
Larry Andrews, &quot;<i><a href="Andrews_2001_TNEAR.pdf">A template for the nearest neighbor problem</a></i>&quot;,<br />
C/C++ Users Journal, Volume 19,  Issue 11  (November 2001), 40 - 49  (2001),<br />
ISSN:1075-2838,<br />
<a href="http://www.ddj.com/architect/184401449" style="text-decoration:none">www.ddj.com/architect/184401449</a>

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

<h4>YOU MAY REDISTRIBUTE NearTree UNDER THE TERMS OF THE <a href=lgpl.txt style="text-decoration:none">LGPL</a></h4>
<p>
</center>
<center>
<table border=1>
<tr>
<td><font face="Arial,Helvetica,Times" size="2">
<h4 align=center>LGPL NOTICES</h4>
<p>
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.
<p>
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.
<p>
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
</td>
</table>
</center>
<P>
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.
<font size="-1">
<p>Release 5.1.1 added a pdf of the 2001 Dr. Dobbs article, added with permission of
the editor.
<p>Release 5.1 augmented the Lloyd alogorithm code to allow for an arbitrary number
of cluster points.  The Makefile and README have been updated.
<p>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.
<p>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.
<p>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.
<p>Release 3.1 adjusted the randomization to be based on the depth rather
than the population and added an optional detailed height calculation.
<p>Release 3.0.2 added to randomization on insertion when the tree is not well balanced.
<p>Release 3.0.1 updated the diameter calculation and fixed some documentation errors. 
<p>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.
<p>Release 2.3.2 adds optional returns of vectors of ordinals of found objects
<p>Release 2.3.1 adds  Centroid method for Lloyd clustering.
<p>Release 2.3 added methods for clustering.
<p>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.
<p>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.
<p>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:
<ul>
<li>Convert to use of a self-contained portable random-number generator from Rob Harrison (2.1.1)
<li>Ensure wider use of const where appropriate (2.1.1)
<li>Correct typos and unclear wording in the README (2.1.2)
<li>Reorganize use of USE_LOCAL_HEADERS in CNearTreeTest.cpp (2.1.2)
<li>Change FAR macro to CNEARTREE_FAR (2.1.3)
<li>Add BelongsToPoints and SeparateByRadius (2.1.4)
<li>Fix dimensions for rhrand (2.1.5)
</ul>
<p>The 2.1 release was a minor update to the 2.0 release of 21 March 2009 to deal with the
following issues:
<ul>
<li>Make delayed insertion the default
<li>Complete the containerization of TNear.h
<li>Add code for K-nearest/farthest in TNear.h and in CNearTree.c
<li>Correct the InAnnulus search filter
</ul>
<P>Release 2.0 was a major update to the 1.0 release of 8 January 2009 to deal with the
following issues:
<ul>
<li>Replace use recursion with a stack, except in insertion logic
<li>Replace use of double with templated DistanceType (usually double)
<li>Provide constuctors to build NearTree from vectors, lists or sets
<li>Change &quot;Insert&quot; to &quot;insert&quot; for consistency with
other containers
<li>Add access function &quot;at&quot; or array type references [], and provide
contents of a neartree as a vector
<li>Add iterator support
<li>Provide delayed insertion logic
<li>Functions added for searches outside of a sphere or in an annular region
</ul>
</font>
<P>
Our thanks to Nicolas Brodu for suggesting the more general handling of the
distance type.
<p>
<b>Note:</b>  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. 
<hr>
<h4>Contents</h4>
<P>
<ul>
  <li><a href="#Installation">Installation</a>
  <li><a href="#Tnear.h">The C++ template: TNear.h</a>
  <li><a href="#CNearTree.c">The C NearTree API: CNearTree.c</a>
  <li><a href="#rhrand.h">A Portable pseudo-random number generator: rhrand.h</a>
</ul>
<hr>
<hr>
<h4><a name="Installation">Installation</a></h4>
<p>
The NearTree package is available at <a href="http://www.sourceforge.net/projects/neartree">www.sourceforge.net/projects/neartree</a>.
A source tarball is available at <a 
href="http://downloads.sourceforge.net/neartree/NearTree-5.1.1.tar.gz">downloads.sourceforge.net/neartree/NearTree-5.1.1.tar.gz</a>.
Later tarballs may be available.
<p>
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.
<P>
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
<p>
make
</p>
which should give the following information:
<p>
<pre><tt>
 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

</tt>
</pre>
<p>
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
<p>
export LIBTOOL=$HOME/bin/libtool
<p>
or in the Makefile
<p>
LIBTOOL = $(HOME)/bin/libtool
<p>
If you need to include local header files using #include &quot;...&quot; instead of #include &lt;...&gt;,
define the variable USE_LOCAL_HEADERS.  USE_LOCAL_HEADERS is the default for Visual
Studio under Microsoft Windows.
<p>
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.
<p>
If you define CNEARTREE_INSTRUMENTED, code will be enabled to track
node visits in searching the tree.
<p>
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.
<p>
 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
<p>
<pre><tt>
#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
</tt></pre>
<p>
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.
<p>
NOTE: A range of 10**15 is comparable to the diameter of the earth
vs. the separation of two bonded atoms.
<p>
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.
<p>
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.
<hr>
<hr>
<h4><a name="Tnear.h">The C++ template: TNear.h</a></h4>
<P>
This is a revised release of
<blockquote>
template &lt;typename T, typename DistanceType=double, int distMinValue=-1 &gt; class CNearTree;
</blockquote>
<P>
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 &quot;Left&quot;
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.
<p>
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.

<p>
CNearTree is the root class for the neartree. The actual data of the
tree is stored in NearTreeNode objects descending from a CNearTree.
<p>
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.
<p>
The type of the objects to be stored is the only <b>required</b> 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.
<p>
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.
<p>
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.
<p>

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.
<p>
<center>
<table>
<tr>
<td><font face="Arial,Helvetica,Times" size="3" colspan=2>
 DistanceType Norm( void );</font></td></tr>
 <tr><td>&nbsp;</td>
 <td><font face="Arial,Helvetica,Times" size="3">// a function &quot;Norm( void )&quot; of the templated class<br />
// to return DistanceType (usually will return a<br />
// &quot;length&quot; of type double)         
</font></td>
</tr>
<tr>
<td><font face="Arial,Helvetica,Times" size="3">
operator- ( );         </font></td><td><font face="Arial,Helvetica,Times" size="3">// geometrical (vector) difference of two objects
</font></td>
</tr>
<tr>
<td></td><td><font face="Arial,Helvetica,Times" size="3">//    a copy constructor would be nice
</font></td>
</tr>
<tr>
<td></td><td><font face="Arial,Helvetica,Times" size="3">//    a constructor would be nice
</font></td>
</tr>
<tr>
<td></td><td><font face="Arial,Helvetica,Times" size="3">//    a destructor would be nice
</font></td>
</tr>
</table>
</center>
<p>
The provided interface is:
<p>
<pre><tt>
    <b>#include &lt;TNear.h&gt;</b>
    
    // Constructors

    <b>CNearTree</b>( <b>void</b> );   // constructor
       // nstantiated by something like:      CNearTree &lt;T&gt; vTree;
       // for some type T
       
    <b>CNearTree</b>( <b>const ContainerType&lt;T&gt;</b> &amp; <i>o</i>);    // constructor from containers, e.g. ...

    <b>CNearTree</b>( <b>const std::vector&lt;T&gt;</b> &amp; <i>o</i> );     // constructor

    <b>CNearTree</b>( <b>const std::list&lt;T&gt;</b> &amp; <i>o</i> );       // constructor

    <b>CNearTree</b>( <b>const std::set&lt;T&gt;</b> &amp; <i>o</i> );        // constructor

    <b>CNearTree</b>( <b>const CNearTree&lt;T&gt;</b> &amp; <i>o</i> );       // constructor

    <b>CNearTree</b>( <b>const ContainerType&lt;T&gt;</b> &amp; <i>o1</i>, <b>const ContainerType&lt;T&gt;</b> &amp; <i>o2</i> );
                                                // 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. **


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

    // Destructor
    
    <b>~CNearTree</b>( <b>void</b> );  // destructor
    
    <b>void clear</b>( <b>void</b> );  // clear the NearTree
    
    // Flag Management
    
    <b>long GetFlags</b>( <b>void</b> ) <b>const</b>;                       // Get all execution flags
    <b>void SetFlags</b>( <b>const long</b> <i>flags</i> );                 // Set all execution flags
    <b>long GetFlags</b>( <b>const long</b> <i>mask</i> ) <b>const</b>;     // Get execution flags within mask
    <b>void SetFlags</b>( <b>const long</b> <i>flags</i>, <b>const long</b> <i>mask</i> );
                                                                           // Set execution flags within mask
                                                                           
    // The available execution flags are
    
    <b>static const long</b>        NTF_NoPrePrune        = 1; //flag to suppress all search prepruning
    <b>static const long</b>        NTF_ForcePrePrune     = 2; //flag to force search prepruning
    <b>static const long</b>        NTF_NoFlip            = 4; //flag to suppress flips on insert
    <b>static const long</b>        NTF_ForceFlip         = 8; //flag to force flips on insert
    <b>static const long</b>        NTF_NoDefer           =16; //flag to prevent deferred insert
    <b>static const long</b>        NTF_AnnularKNN        =32; //flag to do KNN in annular pieces
    <b>static const long</b>        NTF_SphericalKNN      =64; //flag to do KNN as complete spheres

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

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

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

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

    <b>template&lt;typename</b> <i>InputContainer</i>&gt;
    <b>CNearTree&amp; set_symmetric_difference</b>( <b>const InputContainer&amp;</b>, <i>o</i> );
                                                              // 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
                                                              
    <b>template&lt;typename</b> <i>InputContainer</i>&gt;
    <b>CNearTree&amp; set_symmetric_difference</b>( <b>InputContainer&amp;</b>, <i>o</i> );
                                                              // 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
    
    <b>void clear</b> ( void );                                // removes all content from a tree


    <b>void insert</b>( <b>const T&amp;</b> <i>t</i> );
       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


    <b>template&lt; typename</b> <i>InputContainer</i> &gt;
    <b>void insert</b>( <b>ContainerType</b> &amp; <i>o</i> );      // e. g. ...

    <b>void insert</b>( <b>const std::vector&lt;T&gt;</b> &amp; <i>o</i> );
    <b>void insert</b>( <b>const std::list&lt;T&gt;</b> &amp; <i>o</i> );
    <b>void insert</b>( <b>const std::set&lt;T&gt;</b> &amp; <i>o</i> );
    <b>void insert</b>( <b>const CNearTree&lt;T&gt;</b> &amp; <i>o</i> );

    

    <b>iterator NearestNeighbor</b> ( <b>const DistanceType &amp;</b> <i>dRadius</i>, <b>const T&amp;</b> <i>t</i> ) <b>const</b>;
       returns an iterator to the nearest point to the probe point <i>t</i> or end() if there is none
    <b>bool NearestNeighbor</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,  <b>T&amp;</b> <i>tClosest</i>,   <b>const T&amp;</b> <i>t</i> ) <b>const</b>
       <i>dRadius</i> is the largest radius within which to search; make it
          very large if you want to include every point that was loaded.
       <i>tClosest</i> is returned as the object that was found closest to the probe
          point (if any were within radius dRadius of the probe)
       <i>t</i> 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).


    <b>iterator FarthestNeighbor</b> ( <b>T&amp;</b> <b>const T&amp;</b> <i>t</i> ) <b>const</b>;
       returns an iterator to the nearest point to the probe point <i>t</i> or end() if there is none
    <b>bool FarthestNeighbor</b> ( <b>T&amp;</b> <i>tFarthest</i>,   <b>const T&amp;</b> <i>t</i> ) <b>const</b>;
       <i>tFarthest</i> is returned as the object that was found farthest from the probe
          point
       <i>t</i> 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).

    <b>iterator LeftNearestNeighbor</b> ( <b>const DistanceType &amp;</b> <i>dRadius</i>, <b>const T&amp;</b> <i>t</i> ) <b>const</b>;
       returns an iterator to the nearest point to the probe point <i>t</i> or end() if there is none
    <b>bool LeftNearestNeighbor</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,  <b>T&amp;</b> <i>tClosest</i>,   <b>const T&amp;</b> <i>t</i> ) <b>const</b>;
       <i>dRadius</i> is the largest radius within which to search; make it
          very large if you want to include every point that was loaded.
       <i>tClosest</i> is returned as the object that was found closest to the probe
          point (if any were within radius dRadius of the probe)
       <i>t</i> 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).


    <b>iterator LeftFarthestNeighbor</b> ( <b>T&amp;</b> <b>const T&amp;</b> <i>t</i> ) <b>const</b>;
       returns an iterator to the nearest point to the probe point <i>t</i> or end() if there is none
    <b>bool LeftFarthestNeighbor</b> ( <b>T&amp;</b> <i>tFarthest</i>,   <b>const T&amp;</b> <i>t</i> ) <b>const</b>;
       <i>tFarthest</i> is returned as the object that was found farthest from the probe
          point
       <i>t</i> 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&lt; T &gt;) 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.


     
    <b>template&lt;typename</b> <i>ContainerType</i>&gt;
    <b>std::vector&lt;ContainerType&gt; BelongsToPoints</b> ( <b>const ContainerType&amp;</b> <i>t1</i> ) <b>const</b>;

    <b>template&lt;typename</b> <i>ContainerType</i>&gt;
    <b>void BelongsToPoints</b> ( <b>const T&amp;</b> <i>t1</i>, <b>const T&amp;</b> <i>t2</i>, 
        <b>ContainerType&amp;</b> <i>group1</i>, <b>ContainerType&amp;</b> <i>group2</i> );
    <b>template&lt;typename</b> <i>ContainerType</i>&gt;
    <b>void BelongsToPoints</b> ( <b>const T&amp;</b> <i>t1</i>, <b>const T&amp;</b> <i>t2</i>, 
        <b>ContainerType&amp;</b> <i>group1</i>, <b>ContainerType&amp;</b> <i>group2</i>,
    <b>std::vector&lt;size_t&gt;&amp;</b> <i>group1_ordinals</i>, <b>std::vector&lt;size_t&gt;&amp;</b> <i>group2_ordinals</i>);
    <b>template&lt;typename</b> <i>ContainerType</i>&gt;
    <b>std::vector&lt;ContainerType&gt; BelongsToPoints</b> ( <b>const T&amp;</b> <i>t1</i> );
    
    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.
    
    
    <b>template&lt;typename</b> <i>ContainerTypeInside</i>, <b>typename</b> <i>ContainerTypeOutside</i>&gt;
    <b>void SeparateByRadius</b> ( <b>const DistanceType</b> <i>radius</i>, <b>const T&amp;</b> <i>probe</i>, 
        <b>ContainerTypeInside&amp;</b> <i>inside</i>, <b>ContainerTypeOutside&amp;</b> <i>outside</i> );
    <b>template&lt;typename</b> <i>ContainerTypeInside</i>, <b>typename</b> <i>ContainerTypeOutside</i>&gt;
    <b>void SeparateByRadius</b> ( <b>const DistanceType</b> <i>radius</i>, <b>const T&amp;</b> <i>probe</i>, 
        <b>ContainerTypeInside&amp;</b> <i>inside</i>, <b>ContainerTypeOutside&amp;</b> <i>outside</i>,
        <b>std::vector&lt;size_t&gt;&amp;</b> <i>inside_ordinals</i>, <b>std::vector&lt;size_t&gt;&amp;</b> <i>outside_ordinals</i>);
       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.


    <b>long FindInSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,  
         <b>ContainerType&amp;</b> <i>tInside</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long FindInSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,  
         <b>ContainerType&amp;</b> <i>tInside</i>,   
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t ) <b>const</b>;
    <b>long FindInSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tInside</i>,  <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindInSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,  
         <b>ContainerType&amp;</b> <i>tInside</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindInSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,  
         <b>ContainerType&amp;</b> <i>tInside</i>,   
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindInSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tInside</i>,  <b>const T&amp;</b> t ) <b>const</b>;
       <i>dRadius</i> is the radius within which to search; make it very large if you want to
           include every point that was loaded;
       <i>tInside</i> is returned as the NearTree or container of objects that were found within a radius dRadius
          of the probe point
       if the <i>tIndices</i> argument is given it will be returned as a vector
          of indices in the near tree of the objects returned.
       <i>t</i> 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.

    <b>long FindOutSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tOutside</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long FindOutSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tOutside</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t ) <b>const</b>;
    <b>long FindOutSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tOutside</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindOutSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tOutside</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindOutSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tOutside</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindOutSphere</b> ( <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tOutside</i>,   <b>const T&amp;</b> t ) <b>const</b>;
       <i>dRadius</i> is the radius outside of which to search
       <i>tOutside</i> is returned as the NearTree or container of objects that were found at
          or outside of radius dRadius of the probe point
       if the <i>tIndices</i> argument is given it will be returned as a vector
          of indices in the near tree of the objects returned.
       <i>t</i> 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.
    
    <b>long FindInAnnulus</b> ( <b>const DistanceType&amp;</b> <i>dRadius1</i>,
         <b>const DistanceType&amp;</b> <i>dRadius2</i>, 
         <b>ContainerType&amp;</b> <i>tInRing</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long FindInAnnulus</b> ( <b>const DistanceType&amp;</b> <i>dRadius1</i>,
         <b>const DistanceType&amp;</b> <i>dRadius2</i>, 
         <b>ContainerType&amp;</b> <i>tInRing</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices,  <b>const T&amp;</b> t ) <b>const</b>;
    <b>long FindInAnnulus</b> ( <b>const DistanceType&amp;</b> <i>dRadius1</i>, 
         <b>const DistanceType&amp;</b> <i>dRadius2</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tInRing</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindInAnnulus</b> ( <b>const DistanceType&amp;</b> <i>dRadius1</i>,
         <b>const DistanceType&amp;</b> <i>dRadius2</i>, 
         <b>ContainerType&amp;</b> <i>tInRing</i>,   <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindInAnnulus</b> ( <b>const DistanceType&amp;</b> <i>dRadius1</i>,
         <b>const DistanceType&amp;</b> <i>dRadius2</i>, 
         <b>ContainerType&amp;</b> <i>tInRing</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices,  <b>const T&amp;</b> t ) <b>const</b>;
    <b>long LeftFindInAnnulus</b> ( <b>const DistanceType&amp;</b> <i>dRadius1</i>, 
         <b>const DistanceType&amp;</b> <i>dRadius2</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tInRing</i>,   <b>const T&amp;</b> t ) <b>const</b>;
       <i>dRadius1</i> and  <i>dRadius2</i> are the two radii between which to find data points
       <i>tInRing</i> 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 <i>tIndices</i> argument is given it will be returned as a vector
          of indices in the near tree of the objects returned.
       <i>t</i> 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.
    
    <b>long FindK_NearestNeighbors</b> ( <b>const size_t</b> <i>k</i>, <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tClosest</i>, <b>const T&amp;</b> t );
    <b>long FindK_NearestNeighbors</b> ( <b>const size_t</b> <i>k</i>, <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tClosest</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t );
    <b>long FindK_NearestNeighbors</b> ( <b>const size_t</b> <i>k</i>, <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tClosest</i>, <b>const T&amp;</b> t );
    <b>long LeftFindK_NearestNeighbors</b> ( <b>const size_t</b> <i>k</i>, <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tClosest</i>, <b>const T&amp;</b> t );
    <b>long LeftFindK_NearestNeighbors</b> ( <b>const size_t</b> <i>k</i>, <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>ContainerType&amp;</b> <i>tClosest</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t );
    <b>long LeftFindK_NearestNeighbors</b> ( <b>const size_t</b> <i>k</i>, <b>const DistanceType&amp;</b> <i>dRadius</i>,
         <b>CNearTree&lt;  T &gt;&amp;</b> <i>tClosest</i>, <b>const T&amp;</b> t );
       <i>k</i> is the maximum number of nearest neighbors to return. Finds this many if possible
       <i>dRadius</i> within a sphere defined by dRadius, to search for the k-nearest-neighbors
       <i>tClosest</i> is returned as the ContainerType or NearTree of the objects found
       if the <i>tIndices</i> argument is given it will be returned as a vector
          of indices in the near tree of the objects returned.
       <i>t</i> 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.


    <b>long FindK_FarthestNeighbors</b> ( <b>const size_t</b> <i>k</i>,
         <b>ContainerType&amp;</b> <i>tFarthest</i>, <b>const T&amp;</b> t );
    <b>long FindK_FarthestNeighbors</b> ( <b>const size_t</b> <i>k</i>,
         <b>ContainerType&amp;</b> <i>tFarthest</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t );
    <b>long FindK_FarthestNeighbors</b> ( <b>const size_t</b> <i>k</i>, 
          <b>CNearTree&lt;  T &gt;&amp;</b> <i>tFarthest</i>, <b>const T&amp;</b> t );
    <b>long LeftFindK_FarthestNeighbors</b> ( <b>const size_t</b> <i>k</i>,
         <b>ContainerType&amp;</b> <i>tFarthest</i>, <b>const T&amp;</b> t );
    <b>long LeftFindK_FarthestNeighbors</b> ( <b>const size_t</b> <i>k</i>,
         <b>ContainerType&amp;</b> <i>tFarthest</i>,
         <b>std::vector&lt;size_t&gt;&amp;</b> tIndices, <b>const T&amp;</b> t );
    <b>long LeftFindK_FarthestNeighbors</b> ( <b>const size_t</b> <i>k</i>, 
          <b>CNearTree&lt;  T &gt;&amp;</b> <i>tFarthest</i>, <b>const T&amp;</b> t );
       <i>k</i> is the maximum number of farthest neighbors to return. Finds this many if possible
       <i>tFarthest</i> is returned as the ContainerType or NearTree of the objects found
       if the <i>tIndices</i> argument is given it will be returned as a vector
          of indices in the near tree of the objects returned.
       <i>t</i> 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.

   
<hr>

Access Functions:

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

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

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

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

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

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

<hr>

Information and special operation functions:

     <b>void ImmediateInsert</b>( <b>const</b> <b>T</b>&aamp; <i>t</i> );
        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.

     <b>void CompleteDelayedInsert</b> ( <b>void</b> );
        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.

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

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

     <b>size_t size</b> ( <b>void</b> );
        identical to GetTotalSize

     <b>size_t GetDepth</b> ( <b>void</b> );
        returns the maximum tree layers from the root.  This is mainly for information about 
        details of the tree.
        
     <b>double GetDimEstimate</b> ( <b>void</b> );  // returns an estimate of the Hausdorff dimension
     <b>double GetDimEstimate</b> ( <b>const double</b> <i>DimEstimateEsd</i> );
                                                    // returns an estimate of the Hausdorff dimension
                                                    // to within the given esd
     <b>double GetDimEstimateEsd</b> ( <b>void</b> );
                                                    // returns an estimate of the esd

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

     <b>DistanceType GetMeanSpacing</b> ( <b>void</b> );   // returns an estimate object spacing
     <b>DistanceType GetVarSpacing</b> ( <b>void</b> );   // returns an estimate object spacing variance
     
     <b>size_t GetNodeVisits</b> ( <b>void</b> );   // returns the number of node visits if
                                                   // CNEARTREE_INSTRUMENTED as defined, 0 otherwise
     <b>void SetNodeVisits,/b> ( <b>const size_t</b> <i>visits</b>);
                                                   // set the number of node visits
     

        
     <b>T Centroid</b> ( <b>void</b> );
        returns the centroid of a neartree.

     <b>bool empty</b> ( <b>void</b> );
        returns true if the tree is empty, otherwise false
        
        
<hr>

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.

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

     <b>bool      operator== </b> ( <b>const iterator&amp;</b> <i>t</i> ) <b>const</b>;
     <b>bool      operator!= </b> ( <b>const iterator&amp;</b> <i>t</i> ) <b>const</b>;
     <b>bool      operator== </b> ( <b>const const_iterator&amp;</b> </i>t</i> ) <b>const</b>;
     <b>bool      operator!= </b> ( <b>const const_iterator&amp;</b> </i>t</i> ) <b>const</b>;
     <b>bool      operator&gt; </b> ( <b>const iterator&amp;</b> </i>t</i> ) <b>const</b>;
     <b>bool      operator&gt; </b> ( <b>const const_iterator&amp;</b> </i>t</i> ) <b>const</b>;
     <b>bool      operator&lt; </b> ( <b>const iterator&amp;</b> </i>t</i> ) <b>const</b>;
     <b>bool      operator&lt; </b> ( <b>const const_iterator&amp;</b> </i>t</i> ) <b>const</b>;


     <b>const T * const operator-> </b> ( <b>void</b> )   <b>const</b>;
     <b>long get_position</b> ( <b>void</b> ) <b>const</b>;
     <b>const CNearTree&lt; T, DistanceType, distMinValue &gt; * get_parent</b> ( <b>void</b>  );
         

<hr>
  </tt>
</pre>
<p>
So a complete program is:
<p>
<pre>
<tt>
 #include "TNear.h"
 #include &lt;cstdio&gt;
 void main()
 {
   CNearTree&lt; double &gt; dT;
   double dNear;
   dT.Insert( 1.5 );
   if ( dT.NearestNeighbor( 10000.0,   dNear,  2.0 )) printf( "%f\n",double(dNear-2.0) );
 }
</tt>
</pre>
   
 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 <a href="main.cpp">main.cpp</a> and <a href="CNearTreeTest.cpp">CNearTreeTest.cpp</a>.

<hr>
<hr>
<h4><a name="CNearTree.c">The C NearTree API: CNearTree.c</a></h4>
<h4>Synopsis</h4>
<P>
<blockquote>
<font size="-1">
<b>#include &lt;CNearTree.h&gt;</b>
<P>
<p>   
     <b>double</b> <b>CNearTreeDistsq</b> ( <b>CNearTreeHandle</b> <i>treehandle</i>, <b>void *</b> <i>coord1</i>,
                           <b>void *</b> <i>coord2</i> );
<p>   
     <b>double</b> <b>CNearTreeDist</b> ( <b>CNearTreeHandle</b> <i>treehandle</i>, <b>void *</b> <i>coord1</i>,
                           <b>void *</b> <i>coord2</i> );
<p>
     <b>int</b> <b>CNearTreeSetNorm</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>int</b> <i>treenorm</i> );
                                                 
<p>
     <b>int</b> <b>CNearTreeNodeCreate</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,  
                               <b>CNearTreeNodeHandle *</b> <i>treenodehandle</i> )     

<p> 
     <b>int</b> <b>CNearTreeCreate</b> ( <b>CNearTreeHandle *</b> <i>treehandle</i>, 
                        <b>size_t</b> <i>treedim</i>, 
                        <b>int</b> <i>treetype</i> );
<p>    
    <b>int</b> <b>CNearTreeFree</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i> );
 
<p>    
    <b>int</b> <b>CNearTreeClear</b> ( <b>CNearTreeHandle *</b> <i>treehandle</i> );
 
<p>
    <b>int</b> <b>CNearTreeNodeFree</b> ( <b>CNearTreeNodeHandle *</b> <i>treenodehandle</i> );    

<p>
 
    <b>int</b> <b>CNearTreeInsert</b>( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                        <b>const</b> <b>void *</b> <i>coord</i>, 
                        <b>const</b> <b>void *</b> <i>obj</i> );
<p>
    <b>int</b> <b>CNearTreeImmediateInsert</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                        <b>const</b> <b>void *</b> <i>coord</i>, 
                        <b>const</b> <b>void *</b> <i>obj</i> );
<p>
    <b>int</b> <b>CNearTreeDelayedInsert</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                        <b>const</b> <b>void *</b> <i>coord</i>, 
                        <b>const</b> <b>void *</b> <i>obj</i> ); /* ***DEPRECATED*** */
<p>
   <b>int</b> <b>CNearTreeNodeInsert</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                        <b>CNearTreeNodeHandle</b> <i>treenodehandle</i>, 
                        <b>size_t</b> <i>index</i>;
                        <b>size_t *</b> <i>depth</i> );
<p>
   <b>int</b> <b>CNearTreeNodeInsert_Flip</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                        <b>CNearTreeNodeHandle</b> <i>treenodehandle</i>, 
                        <b>size_t</b> <i>index</i>;
                        <b>size_t *</b> <i>depth</i> );
<p>
   <b>int CNearTreeNodeReInsert_Flip</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>,
                                   <b>const CNearTreeNodeHandle</b> <i>treenodehandle</i>,
                                   <b>const CNearTreeNodeHandle</b> <i>pntn</i>,
                                   <b>size_t *</b> <i>depth</i> );

<p>
    <b>int</b> <b>CNearTreeCompleteDelayedInsert</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i> )

    
    <b>int</b> <b>CNearTreeZeroIfEmpty</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i> );
<p>
 
    <b>int</b> <b>CNearTreeGetSize</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>size_t *</b> <i>size</i> );
<p>
 
    <b>int</b> <b>CNearTreeGetTotalSize</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>size_t *</b> <i>size</i> ); /* ***DEPRECATED*** */

    
<p>
 
    <b>size_t</b> <b>CNearTreeSize</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>);
    
<p>
    <b>int</b> <b>CNearTreeGetDeferredSize</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>size_t *</b> <i>size</i> );
<p>
    <b>int</b> <b>CNearTreeGetDelayedSize</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>size_t *</b> <i>size</i> ); /* ***DEPRECATED*** */

<p>
    <b>int</b> <b>CNearTreeGetDepth</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>size_t *</b> <i>depth</i> )
    
<p>
    <b>int</b> <b>CNearTreeGetFlags</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>long  *</b> <i>flags</i>, <b>const long</b> <i>mask</i> )
     
<p>
    <b>int</b> <b>CNearTreeSetFlags</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>const long</b> <i>flags</i>, <b>const long</b> <i>mask</i> )

<p>
    <b>int</b> <b>CNearTreeGetMeanSpacing</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>, 
                                 <b>double *</b> <i>spacing</i>  );
<p>
    <b>int</b> <b>CNearTreeGetVarSpacing</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>, 
                                <b>double *</b> <i>varspacing</i>  );
<p>
    <b>int</b> <b>CNearTreeCount</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>, 
                       <b>size_t  *</b> <i>count</i> );
<p>
    <b>int</b> <b>CNearTreeNodeCount</b> ( <b>const CNearTreeNodeHandle</b> <i>treenodehandle</i>, 
                        <b>size_t  *</b> <i>count</i> );
<p>
 
#ifdef CNEARTREE_INSTRUMENTED
<p>
    <b>int</b> <b>CNearTreeGetNodeVisits</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>,
                                <b>size_t *</b> <i>visits</i>);
<p>
    <b>int</b> <b>CNearTreeSetNodeVisits</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>,
                                <b>const size_t</b> <i>visits</i> );
<p>
#endif    
<p>

    <b>int</b> <b>CNearTreeGetDiamEstimate</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>,
                                  <b>double *</b> <i>diamest</i> );
<p>     
    <b>int</b> <b>CNearTreeGetDimEstimateEsd</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>,
                                  <b>double *</b> <i>dimestesd</i> );
<p>
    <b>int CNearTreeGetDimEstimate</b> ( <b>const CNearTreeHandle</b> <i>treehandle</i>,
                                 <b>double *</b> <i>dimest</i>,
                                 <b>const double</b> <i>DimEstimateEsd</i> );
<p>     
    <b>int</b> <b>CNearTreeNearestNeighbor</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, 
                                  <b>const</b> <b>double</b> dRadius,  
                                  <b>void * *</b> <i>coordClosest</i>,
                                  <b>void * *</b>  <i>objClosest</i>, 
                                  <b>const</b> <b>void *</b> <i>coord</i> );
<p>     
    <b>int</b> <b>CNearLeftTreeNearestNeighbor</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, 
                                  <b>const</b> <b>double</b> dRadius,  
                                  <b>void * *</b> <i>coordClosest</i>,
                                  <b>void * *</b>  <i>objClosest</i>, 
                                  <b>const</b> <b>void *</b> <i>coord</i> );  /* ***DEPRECATED*** */
<p>     
    <b>int</b> <b>CNearTreeFarthestNeighbor</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, 
                                   <b>void *</b> * <i>coordFarthest</i>,
                                   <b>void *</b> * <i>objFarthest</i>,   
                                   <b>const</b> <b>void *</b> <i>coord</i> );
<p>          
    <b>int</b> <b>CNearTreeFindInSphere</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CVectorHandle</b> <i>coordInside</i>,
                               <b>CVectorHandle</b> <i>objInside</i>,
                               <b>const</b> <b>void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> );
<p>                               
    <b>int</b> <b>CNearTreeFindTreeInSphere</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CNearTreeHandle</b> <i>foundInside</i>,
                               <b>const void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> )
<p>          
    <b>int</b> <b>CNearTreeFindOutSphere</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CVectorHandle</b> <i>coordOutside</i>,
                               <b>CVectorHandle</b> <i>objOutside</i>,
                               <b>const</b> <b>void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> );
<p>                               
    <b>int</b> <b>CNearTreeFindTreeOutSphere</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CNearTreeHandle</b> <i>foundOutside</i>,
                               <b>const void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> )
<p>          
    <b>int</b> <b>CNearTreeFindInAnnulus</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>double</b> <i>dRadiusInner</i>,
                               <b>const</b> <b>double</b> <i>dRadiusOuter</i>,
                               <b>CVectorHandle</b> <i>coordInRing</i>,
                               <b>CVectorHandle</b> <i>objInRing</i>,
                               <b>const</b> <b>void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> );
<p>                               
    <b>int</b> <b>CNearTreeFindTreeInAnnulus</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>double</b> <i>dRadiusInner</i>,
                               <b>const</b> <b>double</b> <i>dRadiusOuter</i>,
                               <b>CNearTreeHandle</b> <i>foundInRing</i>,
                               <b>const void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> )
<p>          
    <b>int</b> <b>CNearTreeFindKNearest</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>size_t</b> <i>k</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CVectorHandle</b> <i>coordClosest</i>,
                               <b>CVectorHandle</b> <i>objClosest</i>,
                               <b>const</b> <b>void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> );
<p>                               
    <b>int</b> <b>CNearTreeFindKTreeNearest</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>size_t</b> <i>k</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CNearTreeHandle</b> <i>foundClosest</i>,
                               <b>const void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> )
<p>          
    <b>int</b> <b>CNearTreeFindKFarthest</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>size_t</b> <i>k</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CVectorHandle</b> <i>coordFarthest</i>,
                               <b>CVectorHandle</b> <i>objFarthest</i>,
                               <b>const</b> <b>void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> );
<p>                               
    <b>int</b> <b>CNearTreeFindKTreeFarthest</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>const</b> <b>size_t</b> <i>k</i>,
                               <b>const</b> <b>double</b> <i>dRadius</i>,
                               <b>CNearTreeHandle</b> <i>foundFarthest</i>,
                               <b>const void *</b> <i>coord</i>,
                               <b>int</b> <i>resetcount</i> )
<p> 
    <b>int</b> <b>CNearTreeNearest</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, 
                          <b>double</b> * dRadius,  
                          <b>void *</b> * <i>coordClosest</i>,
                          <b>void *</b> * <i>objClosest</i>,
                          <b>const</b> <b>void *</b> <i>coord</i> );
<p> 
    <b>int</b> <b>CNearTreeLeftNearest</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, 
                          <b>double</b> * dRadius,  
                          <b>void *</b> * <i>coordClosest</i>,
                          <b>void *</b> * <i>objClosest</i>,
                          <b>const</b> <b>void *</b> <i>coord</i> );  /* ***DEPRECATED*** */
<p>     
    <b>int</b> <b>CNearTreeFindFarthest</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>,
                               <b>double</b> * dRadius,  
                               <b>void *</b> * <i>coordFarthest</i>,
                               <b>void *</b> * <i>objFarthest</i>,
                               <b>const</b> <b>void *</b> <i>coord</i> );
<p>
    <b>int</b> <b>CNearTreeObjects</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>CVectorHandle *</b> <i>vectorhandle</i> );
<p>
    <b>void *</b> <b>CNearTreeObjectAt</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>size_t</b> <i>index</i> );
<p>
    <b>int</b> <b>CNearTreeCoords</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, <b>CVectorHandle *</b> <i>vectorhandle</i> );
<p>
    <b>void *</b> <b>CNearTreeCoordAt</b> ( <b>const</b> <b>CNearTreeHandle</b> <i>treehandle</i>, 
                                <b>size_t</b> <i>index</i> );
</font>
</blockquote>
<p>    

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


</pre></tt>
</p>
The internal operation of the API depends on the function <b>CNearTreeDist</b> 
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.
<P>
A neartree is created by  <b>CNearTreeCreate</b> and freed by <b>CNearTreeFree</b>.
<i>treedim</i> is the dimension of the coordinate vectors and <i>treetype</i>
is one of the three predefined constants <b>CNEARTREE_TYPE_DOUBLE</b> for double
or <b>CNEARTREE_TYPE_INTEGER</b> for integer or <b>CNEARTREE_TYPE_STRING</b>, 
optionally ORed with <b>CNEARTREE_NORM_L1</b>, <b>CNEARTREE_NORM_L2</b> or CNEARTREE_NORM_LINF</b> 
for L1, L2 or L-infinity norms, <b>CNEARTREE_NORM_SPHERE</b> or <b>CNEARTREE_NORM_HSPHERE</b> for
a spherical or hemispherical norm (L1-norm combination of radial and spherical/hemispherical 
triangle distances), or <b>CNEARTREE_NORM_HAMMING</b> for the string-Hamming distance norm
(add one for each differing character position).

<p>
Starting with release 2.1, all insertions are delayed by default, unless the insertions is
done by a call to <b>CNearTreeImmediateInsert</b>.   The insertions that have been queued
are completed by a call to <b>CNearTreeCompleteDelayedInsert</b> 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 <b>CNEARTREE_DEFER_ALL</b> is ored with
<i>treetype</i>. 

<p>Starting with release 3 (formerly called release 2.4) optionally, you may also define 
<b>CNEARTREE_FORCEFLIP</b> to maximize tree reorganization on insertion, 
<b>CNEARTREE_NOFLIP</b> to suppress tree reorganization on insertion, <b>CNEARTREE_NODEFER</b> 
to make all insertions immediate, <b>CNEARTREE_FORCEPREPUNE</b> to do searches first with a 
tighter estimate on the search radius, and <b>CNEARTREE_NOPREPRUNE</b> 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. 
<p>
The flags <b>CNEARTREE_DEFER_ALL</b> and <b>CNEARTREE_FLIP</b> used in prior releases
are deprecated, but are still defined.  They have no effect.
<p>
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
<b>CNearTreeInsert</b>, with each call providing a coordinate vector <i>coord</i>
and an optional object pointer <i>obj</i>.  The API copies the coordinate vector,
but does not copy the object.  Later, when a search is requested or an explicit call
to <b>CNearTreeCompleteDelayedInsert</b> 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.
<p>
Optionally, the actual insertions may done immediately by calling <b>CNearTreeImmediateInsert</b>
instead of <b>CNearTreeInsert</b>.  For upwards compatibility of the library for existing
code, the deprecated <b>CNearTreeDelayedInsert</b> is provided as an deprecated alternate
call to <b>CNearTreeInsert</b>. 
<p>
The neartree is searched for the nearest or farthest coordinate vector in the neartree to a given
probe coordinate vector <i>coord</i> by <b>CNearTreeNearestNeighbor</b> and 
<b>CNearTreeFarthestNeighbor</b>, 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
<b>CNearLeftTreeNearestNeighbor</b>.  The given radius confines the search
to a sphere around the probe.  If more than a single extremal coordinate point is
needed, <b>CNearTreeFindInSphere</b> 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 <b>CNearTreeFindOutSphere</b> can be used to obtain a CVector result vector
of all the coordinates that satisfy the constraint of being outside a specified radius.
<b>CNearTreeFindIn Annulus</b> 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.
<b>CNearTreeFindKNearest</b> can be used to obtain a CVector result vector of the <i>k</i>
coordinates closest to the probe point such that all results are within the specified
radius of the probe point, or <b>CNearTreeFindKFarthest</b> to obtain a CVector result vector 
of the <i>k</i> 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 <i>resetcount</i> is true (non
zero) the result vector is cleared before the search.   A CVector result vector
of the matching object pointers is returned if <i>objs</i> is not NULL. 
Aternatively the forms <b>CNearTreeFindTreeInSphere</b>, <b>CNearTreeFindTreeOutSphere</b>,
<b>CNearTreeFindTreeInAnnulus</b>, <b>CNearTreeFindKTreeNearest</b>, <b>CNearTreeFindKTreeFarthest</b>
can be used to obtain CNearTrees rather than CVectors of results.  The functions
<b>CNearTreeNearest</b> and <b>CNearTreeFindFarthest</b> implement <b>CNearTreeNearestNeighbor</b> and 
<b>CNearTreeFarthestNeighbor</b>, respectively, adjusting the radius of the search while
the search is in progress and are not normally used by users.
<p>
<p>The size of the tree as a count of objects can be obtained using the function
<b>NearTreeGetSize</b> or the macro <b>NearTreeSize</b>.  The size of the tree
as a count of nodes and the depth of the tree can be obtained using the functions
<b>CNearTreeCount</b> and <b>CNearTreeGetDepth</b>.  Estimates of the Hausdorff
dimension, the esd of that estimate, the diameter, the spacing and the variance
of the spacing can be obtained with <b>CNearTreeGetDimEstimate</b>, 
<b>CNearTreeGetDimEstimateEsd</b>,
<b>CNearTreeGetDiamEstimate</b>, <b>CNearTreeGetMeanSpacing</b> and 
<b>CNearTreeGetVarSpacing</b>.
<P>
<h4>Returns</h4>
If <b>CNearTreeDist</b> fails, it returns -1.  Except for <b>CNearTreeDist</b>, all the functions 
in the API return 0 ( <b>CNEARTREE_SUCCESS</b> ) for
success.    If dynamic memory allocation fails, <b>CNEARTREE_MALLOC_FAILED</b> is returned.
If a call is made with an improper argument, <b>CNEARTREE_BAD_ARGUMENT</b> is returned.
If a search fails to find anything, <b>CNEARTREE_NOT_FOUND</b> is returned.  If there is
a failure in an attempt to free a CNearTree, <b>CNEARTREE_FREE_FAILED</b> is returned.  If
any of the internal call to CVector fail, <b>CNEARTREE_CVECTOR_FAILED</b> is returned.  For
convenience in debugging, the formerly negative values of these returns are now positive.
<p>
<h4>Examples</h4>
<P>
To create a neartree for 3-dimensional vectors of doubles:
<P>
<pre>
<tt> 
#include &lt;CNearTree.h&gt;
CNearTreeHandle treehandle;
int bReturn;
 
 ...
 
 bReturn = !CNearTreeCreate(&treehandle,3,CNEARTREE_TYPE_DOUBLE);
</tt>
</pre>
<p>
 
To insert a copy of a 3-dimensional vector of doubles into this tree,
with no associated object:
<P>
<pre>
<tt> 
    double v[3];
 
 ...
     
    v[0] = 1.; v[1] = 2.; v[2] = 3.;
    bReturn = !CNearTreeInsert(treehandle,&amp;v[0],NULL);
</tt>
</pre>
<p>
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:
<P>
<pre>
<tt> 
    double * vBest;
    void * vvBest;
    double vSearch[3];
    double   dRad = =3.;
    
  ...
  
    if ( !CNearTreeNearestNeighbor(treehandle,dRad,&amp;vvBest,NULL,vSearch))
        {   vBest = (double *)vvBest; }
</tt>
</pre>
<p>
Note the use of a separate void * vvBest instead of a cast of &amp;vBest to avoid compiler 
type punning warnings.
<P>
For more examples of the use of CNearTree.c, see <a href="main.c">main.c</a> and <a href="CNearTreeTest.c">CNearTreeTest.c</a>
in the release kit.
<hr>
<hr>
<h4><a name="rhrand.h">A Portable pseudo-random number generator: rhrand.h</a></h4>
<p>
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 &amp; Co., London and Wiley &amp; 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.
<p>
rhrand.h is a header file in which a C++ class, RHrand, is defined, and a
C struct typedef CRHrand is defined.
<p>
The C++ interface is
<p>
<pre><tt>
    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] */

</tt></pre>
<p>
In C++ code, typical use is

<pre><tt>
#include &lt;rhhand.h&gt;
    RHrand rhr;

...

    x = rhr.urand();
</pre></tt>


<p>
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.
<p>
<pre><tt>
    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] */
</tt></pre>
<p>
Typical use is 

<pre><tt>
#include &lt;rhhand.h&gt;
    CRHrand rhr;

...

    CRHrandSrandom(&amp;rhr, 0 ); 

...

    x = CRHrandUrand(&amp;rhr);
</pre></tt>


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