Volume approximation Files

This is a software to compute an approximation of the volume of a polytope 
given as an intersection of halfspaces.

To compile and use it, you need first to compile the CGAL library, or
download the precompiled library (this software has been tested with CGAL
4.1 and newer versions). You can follow these steps:


------------------------
1. Compile CGAL sources
------------------------

Follow the CGAL installation manual. It states that CGAL requires the Boost
libraries. In particular the header files and the threading library
binaries. Version 1.39 (or higher) are needed. Having GMP version 4.2 or
higher and MPFR version 2.2.1 or higher installed is recommended by CGAL. 
Once you have installed these libraries, execute:

$ cmake .
$ make


------------------
2. Compile sources
------------------

In folder examples execute:

$ cmake -DCGAL_DIR=_YOUR_CGAL_PATH_ .
$ make

where _YOUR_CGAL_PATH_ is the path where CGAL library was compiled. For
additional options, set by CMake flags, see the file README.FLAGS (it is
normally not needed to change default compilation options).


---------------------------
3. Use volume approximation
---------------------------

I. Input

To describe the polytope P={x: Ax<=b} where A is a matrix of dimension mxd 
and b a vector of dimension m, the corresponding .ine-file is given by:
----------------
file name
H-representation
begin
m d+1 numbertype
b A
end
----------------
where numbertype can be one of integer, float or rational. Note that the current 
implementation will convert any of the above numbertypes to the double C++ type. 

II. Run

./vol -h 

to display a help message about the program's options


./vol -f1 polytope_examples/cube10.ine

will approximate the volume of the 10-dim hypercube