//#  eulerN -- program for statistical estimation of Euler characteristic of a 3-dimensional body
//#  given as a sufficiently dense "volumetric" point sampling
//#
//#  Copyright (c) 2005-2007 Bradford Jones, Konstantin Rybnikov, Karen Daniels, Daniel Klain
//#  Release 2: 1 June 2007 
//#
//#  This program is free software; you can redistribute it and/or modify it
//#  under the terms of the GNU General Public License as published by the
//#  Free Software Foundation; either version 2, or (at your option) any
//#  later version: http://www.gnu.org/licenses/gpl.txt.
//#
//#  This program 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 General Public License for more details.
//#-----------------------------------------------------------------------------
// This is release #2. 
// An error in main.cpp  caused it to reject correctly formatted input_script files (see readme.txt)
// This error was fixed.
//
// Other changes include:
//
// 1) Uniformization of names of .cpp and .h files: 
// all .cpp and  .h files containing the essential algorithms start from capital letters; 
// main.cpp and math_vector.cpp were left unchanged
//
// 2) More transparent syntax for the configuration files. See readme.txt .
//
// 3) Certain unnecessary files have been removed.
//
// Remaining problems:
// The program seems to ignore points in the first slice in the direction d, where d is any 3D vector.
// For example, if you use as input a set of point with the same third coordinate, the program will return zero.
// This does not affect the computation when there are many splices of when the "first slice" contains very few // points, but is certainly undesirable. After all Euler characteristic is invariant under homotopic equivalence!
// This error has to do with inaccurate coding of the start of the 3D integration. It will be fixed in the next // release.
// 