This is a semi-official user manual for the convex hull package CH.
===================================================================

General
-------
The entire package consists of two parts, namely the SoS and the
floating point version.  Each version contains one program for every
dimension.  Currently, both versions are available for
dimensions 2 through 4.

The program names are ch followed by the dimension followed by an
optional 'f' for floating point, e.g.

  ch3   ... the 3D SoS version,
  ch4f  ... the 4D floating point version.


Synopsis
--------
  ch<D>[f] [options] InFile [OutFile]


Files
-----
InFile.sites  contains the input points, one point per line.  The
postfix ".sites" is appended by CH.  CH reads until EOF or the maximal
number of sites (currently 10000) are read. 
An input file for ch3 might look as follows.
        9105        3178        5319
        9094        3223         749
        9646        9315        2843
        6170        9511        9455
        1869        1672        1227
        2423        7103        7582
        8980         186        5500

For the SoS version the coordinates must be 1-word integers, the
floating point version accepts pascal REALs (C DOUBLEs).

OutFile, if specified, receives all trace information, diagnostics,
etc. produced by CH that would go to the screen by default, except for
the program logo.  However, every output related to the convex hull
goes to files InFile.* (see Options).


Options
-------
Options must be specified separately with a leading minus sign, e.g.
  ch4 -r -l -u MyData
The options currently available are:

    a   : Show results of calls to ChAbove (debugging only).
    c   : Check convex hull (debugging only).
    f   : Display information about the facets only.
    g   : Display all the information in the incidence structure relevant
          to the convex hull (a subset of i).
    i   : Display incidence structure after construction of hull (with
          text explaining the various parts).
    l   : Display only facets on lower part of the hull.
    r   : Display information about memory and time consumption.
    s   : Display sorted list of sites with original indices.
    t   : Trace execution.
    u   : Display only facets on upper part of the hull.

Options  a  and  c  are meant for debugging only.

Option  t  writes a dot for every site that is inserted into the
convex hull.

Options  f, g, i, l, u  write the respective output into different
files. The names of the files are displayed on the screen at the end
of execution.

Option  r  displays information about the size of the internal data
structure and the consumed resources.

Option  s  displays the list of sites (sorted with respect to
x4-coordinates) on the screen, together with their indices in the
original sequence.

Output format
-------------
Options  g  and  i  produce the incidence structure of the convex
hull, which is explained in 

   Herbert Edelsbrunner,
   "Algorithms in Combinatorial Geometry",
   Springer Verlag, 1987.
        
The amount of output generated by these options is significant.  For
most applications it is enough to know the facets of the convex hull.
For instance, in 3 dimensions the facets are the triangles on the
convex hull, in 4 dimensions the tetrahedra on the hull, etc.
Options  f, l, and  u   produce only facets.  Each facet is described
by the indices of its d vertices.  Again in 3 dimensions, an output

1 4 7

stands for the triangle defined by the first, third and 7th input
point.

--
Harald Rosenberger.
